diff --git a/README.md b/README.md
index 8d2a0aeb..49c8c698 100644
--- a/README.md
+++ b/README.md
@@ -5,7 +5,7 @@
 
 <h1 align="center" style="border-bottom: none;">🚀 Literature Survey</h1>
 
-Welcome to Team VPE's Literature Survey Template Repository! 📚✨ This repository provides you with a quick setup to create your very own automated literature survey website using Semantic Scholar's [Recommendation API](https://api.semanticscholar.org/api-docs/recommendations).
+Welcome to Team VPE's Literature Survey Template Repository! 📚✨ This repository provides you with a quick setup to create your very own automated literature survey website using Semantic Scholar's [Recommendation API](https://api.semanticscholar.org/api-docs/recommendations), and provides an option to import the recommended articles to your [Zotero](https://www.zotero.org/) account.
 
 ### Types of Recommendations
 Semantic Scholar provides 2 types of recommendations:
@@ -66,6 +66,16 @@ Head over to the localhost link that pops up in your terminal.
 
 12. (Optional) Edit custom.css if you'd like to change the styling of web pages.
 
+### Zotero Plugin
+If you'd like to read the recommended articles in your Zotero Account:
+1. Create an account with Zotero
+2. Under the `Settings` tab in your GitHub repo, click on `Secrets and variables`, and select `Actions`
+3. Set the following `Repository secrets`:
+    - `ZOTERO_API_KEY` as Zotero API key (you can get it [here](https://www.zotero.org/settings/keys/new))
+    - `LIBRARY_ID` as your group ID (this can be found by opening the group's page: https://www.zotero.org/groups/groupname , and hovering over the group settings link. The ID is the integer after /groups/)
+    - `TEST_COLLECTION_KEY` as your collection's key (enter `https://api.zotero.org/groups/<LIBRARY_ID>/collections?key=<ZOTERO_API_KEY>` in your browser to view all the collections in your group; choose the key of the collection in which you'd like the recommended articles to be sotred)
+4. The changes take effect only when the code is re-run. This can happen either the next time the code is scheduled for a run (Mondays) or under the `Actions` tab, select `mkdocs-deploy` from the left panel, and click on `Run workflow`.
+
 ### Bugs? Feature Requests?
 If you encounter any bugs or have brilliant ideas for new features, please head over to the [Issues](https://github.com/VirtualPatientEngine/literatureSurvey/issues) and let us know.
 
diff --git a/app/code/literature_fetch_recommendation_api.py b/app/code/literature_fetch_recommendation_api.py
index d9b028a0..0073e5b1 100755
--- a/app/code/literature_fetch_recommendation_api.py
+++ b/app/code/literature_fetch_recommendation_api.py
@@ -179,7 +179,7 @@ def create_template(template,
         if len(topic_obj.paper_ids['positive']) == 0:
             print (f'No positive articles for {topic_obj.topic}. Skipping...')
         else:
-            search_response_json = utils.add_recommendations(topic_obj, limit=300)
+            search_response_json = utils.add_recommendations(topic_obj, limit=200)
             for paper_data in search_response_json['recommendedPapers']:
                 paper_id = paper_data['paperId']
                 # skip the ones with publication date is null
@@ -208,6 +208,8 @@ def create_template(template,
             for article_id, article_obj in topic_obj.paper_ids[article_type].items():
                 utils.update_h_index(article_obj, author_details)
         print (f'Fetched the details of the authors (n={len(author_details)}) for {topic}.')
+        # Add the recommended articles to Zotero
+        utils.add_recommended_articles_to_zotero(topic, topic_obj.paper_ids)
         # Create the markdown text
         markdown_text = create_template(
                                         ("../../templates", "topic.txt"),
diff --git a/app/code/utils.py b/app/code/utils.py
index 2c13da1e..13415124 100755
--- a/app/code/utils.py
+++ b/app/code/utils.py
@@ -4,17 +4,57 @@
 script to define utility functions
 '''
 
+import os
 import sys
 import re
 import matplotlib.pyplot as plt
 import pandas as pd
 import yaml
 import requests
+from pyzotero import zotero
 
 FIELDS = 'paperId,url,authors,journal,title,'
 FIELDS += 'publicationTypes,publicationDate,citationCount,'
 FIELDS += 'publicationVenue,externalIds,abstract'
 
+LIBRARY_TYPE = 'group'
+LIBRARY_ID = os.environ.get('LIBRARY_ID')
+ZOTERO_API_KEY = os.environ.get('ZOTERO_API_KEY')
+TEST_COLLECTION_KEY = os.environ.get('TEST_COLLECTION_KEY')
+
+def add_recommended_articles_to_zotero(topic_name, paper_ids):
+    """
+    Add the recommended articles to zotero
+    """
+    if LIBRARY_ID is None or ZOTERO_API_KEY is None or TEST_COLLECTION_KEY is None:
+        print ('Zotero credentials not found.')
+    else:
+        print ('Adding recommended articles to Zotero.')
+        # Create a zotero object
+        zot = zotero.Zotero(LIBRARY_ID, LIBRARY_TYPE, ZOTERO_API_KEY)
+        new_items = []
+        for _, paper_obj in paper_ids['recommended'].items():
+            # create a template for the paper
+            template = zot.item_template('journalArticle')
+            template['title'] = paper_obj.info.title
+            template['creators'] = []
+            for author in paper_obj.authors:
+                template['creators'].append({'creatorType': 'author',
+                                            'name': author.author_name})
+            template['publicationTitle'] = paper_obj.info.journal
+            template['date'] = paper_obj.info.publication_date
+            template['abstractNote'] = paper_obj.info.abstract
+            template['url'] = paper_obj.info.url
+            # assign topic names as tags
+            template['tags'] = [{'tag': topic_name}]
+            # assign the paper to the collection
+            template['collections'] = [TEST_COLLECTION_KEY]
+            new_items.append(template)
+        # add all the items to zotero, only 50 items at a time
+        for i in range(0, len(new_items), 50):
+            zot.check_items(new_items[i:i+50])
+            zot.create_items(new_items[i:i+50])
+
 def add_negative_articles(topic_obj, dic):
     """
     Add the negative articles to the topic object
@@ -25,15 +65,19 @@ def add_negative_articles(topic_obj, dic):
         # Skip the current topic
         if topic == topic_obj.topic:
             continue
-        # Add the articles from the other topics
-        # as negative articles to the current topic
+        # Add the negative articles to the topic object
         for paper_id in dic[topic].paper_ids['positive']:
-            # Skip if the article is already in the negative articles
+            # Skip if the paper id is already in the negative articles
             if paper_id in topic_obj.paper_ids['negative']:
                 continue
-            # Skip if the article is already in the positive articles
+            # Skip if the paper id is already in the positive articles
+            # i.e. do not add the same paper id to both positive and negative articles
             if paper_id in topic_obj.paper_ids['positive']:
                 continue
+            # Skip if the paper id if it is marked to be not used for recommendation
+            paper_obj = dic[topic].paper_ids['positive'][paper_id]
+            if paper_obj.use_for_recommendation is False:
+                continue
             topic_obj.paper_ids['negative'][paper_id]=dic[topic].paper_ids['positive'][paper_id]
     print (f'Added {len(topic_obj.paper_ids["negative"])} negative articles for {topic_obj.topic}.')
 
@@ -175,18 +219,14 @@ def add_recommendations(topic_obj,
     params = {'fields': fields, 'limit': limit}
     # Select positive articles that have use_for_recommendation set to True
     positive_paper_ids = []
-    count = 0
+    # count = 0
     for paper_id, paper_obj in topic_obj.paper_ids['positive'].items():
         if paper_obj.use_for_recommendation is False:
             continue
         positive_paper_ids.append(paper_id)
-        count += 1
-        if count == 10:
-            break
     json = {
-            # 'positivePaperIds': list(topic_obj.paper_ids['positive'].keys())[:10],
             'positivePaperIds': positive_paper_ids,
-            'negativePaperIds': list(topic_obj.paper_ids['negative'].keys())[:10],
+            'negativePaperIds': list(topic_obj.paper_ids['negative'].keys()),
             }
     status_code = 0
     while status_code not in [200, 400, 404]:
diff --git a/docs/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378.md b/docs/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378.md
deleted file mode 100644
index 2373fca1..00000000
--- a/docs/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378.md
+++ /dev/null
@@ -1,249 +0,0 @@
----
-hide:
- - navigation
----
-<!DOCTYPE html>
-#
-<html lang="en">
-<head>
-  <meta charset="utf-8">
-</head>
-
-<body>
-  <p>
-  <i class="footer">This page was last updated on 2024-08-08 13:17:20 UTC</i>
-  </p>
-  
-  <div class="note info" onclick="startIntro()">
-    <p>
-      <button type="button" class="buttons">
-        <div style="display: flex; align-items: center;">
-        Click here for a quick intro of the page! <i class="material-icons">help</i>
-        </div>
-      </button>
-    </p>
-  </div>
-
-  <p>
-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Mechanistic dynamical models allow us to study the behavior of complex biological systems. They can provide an objective and quantitative understanding that would be difficult to achieve through other means. However, the systematic development of these models is a non-trivial exercise and an open problem in computational biology. Currently, many research efforts are focused on model discovery, i.e. automating the development of interpretable models from data. One of the main frameworks is sparse regression, where the sparse identification of nonlinear dynamics (SINDy) algorithm and its variants have enjoyed great success. SINDy-PI is an extension which allows the discovery of rational nonlinear terms, thus enabling the identification of kinetic functions common in biochemical networks, such as Michaelis-Menten. SINDy-PI also pays special attention to the recovery of parsimonious models (Occam’s razor). Here we focus on biological models composed of sets of deterministic nonlinear ordinary differential equations. We present a methodology that, combined with SINDy-PI, allows the automatic discovery of structurally identifiable and observable models which are also mechanistically interpretable. The lack of structural identifiability and observability makes it impossible to uniquely infer parameter and state variables, which can compromise the usefulness of a model by distorting its mechanistic significance and hampering its ability to produce biological insights. We illustrate the performance of our method with six case studies. We find that, despite enforcing sparsity, SINDy-PI sometimes yields models that are unidentifiable. In these cases we show how our method transforms their equations in order to obtain a structurally identifiable and observable model which is also interpretable. Author summary Dynamical models provide a quantitative understanding of complex biological systems. Since their development is far from trivial, in recent years many research efforts focus on obtaining these models automatically from data. One of the most effective approaches is based on implicit sparse regression. This technique is able to infer biochemical networks with kinetic functions containing rational nonlinear terms. However, as we show here, one limitation is that it may yield models that are unidentifiable. These features may lead to inaccurate mechanistic interpretations and wrong biological insights. To overcome this limitation, we propose an integrated methodology that applies additional procedures in order to ensure that the discovered models are structurally identifiable, observable, and interpretable. We demonstrate our method with six challenging case studies of increasing model complexity.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9a935f921441c1d39252f9097a4b7db51e06ede4" target='_blank'>Distilling identifiable and interpretable dynamic models from biological data</a></td>
-          <td>
-            Gemma Massonis, A. F. Villaverde, J. Banga
-          </td>
-          <td>2023-03-15</td>
-          <td>PLOS Computational Biology</td>
-          <td>3</td>
-          <td>54</td>
-        </tr>
-    
-        <tr id="High-throughput data acquisition in synthetic biology leads to an abundance of data that need to be processed and aggregated into useful biological models. Building dynamical models based on this wealth of data is of paramount importance to understand and optimize designs of synthetic biology constructs. However, building models manually for each data set is inconvenient and might become infeasible for highly complex synthetic systems. In this paper, we present state-of-the-art system identification techniques and combine them with chemical reaction network theory (CRNT) to generate dynamic models automatically. On the system identification side, Sparse Bayesian Learning offers methods to learn from data the sparsest set of dictionary functions necessary to capture the dynamics of the system into ODE models; on the CRNT side, building on such sparse ODE models, all possible network structures within a given parameter uncertainty region can be computed. Additionally, the system identification process can be complemented with constraints on the parameters to, for example, enforce stability or non-negativity-thus offering relevant physical constraints over the possible network structures. In this way, the wealth of data can be translated into biologically relevant network structures, which then steers the data acquisition, thereby providing a vital step for closed-loop system identification.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4fc5648a33fd287d34439fb1d94e6a3550dced02" target='_blank'>Characterization of Biologically Relevant Network Structures form Time-series Data</a></td>
-          <td>
-            Z. Tuza, G. Stan
-          </td>
-          <td>2018-09-24</td>
-          <td>2018 IEEE Conference on Decision and Control (CDC)</td>
-          <td>3</td>
-          <td>34</td>
-        </tr>
-    
-        <tr id="Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with ODE model descriptions containing polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated parameters. To solve the network reconstruction problem, we cast it as a compressive sensing (CS) problem and use sparse Bayesian learning (SBL) algorithms as a computationally efficient and robust way to obtain its solution.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fe99d10da6e29a5300354f92dab476490ec6f3ef" target='_blank'>Reconstruction of arbitrary biochemical reaction networks: A compressive sensing approach</a></td>
-          <td>
-            W. Pan, Ye Yuan, G. Stan
-          </td>
-          <td>2012-05-08</td>
-          <td>2012 IEEE 51st IEEE Conference on Decision and Control (CDC)</td>
-          <td>33</td>
-          <td>34</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c7d8c73a530880d1f4ea37dc48dd6a25e338239a" target='_blank'>Inferring sparse networks for noisy transient processes</a></td>
-          <td>
-            H. M. Tran, S. Bukkapatnam
-          </td>
-          <td>2016-02-26</td>
-          <td>Scientific Reports</td>
-          <td>6</td>
-          <td>34</td>
-        </tr>
-    
-        <tr id="It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the capacity to generate extremely large datasets. We seek to develop generalized identifiability conditions for informing the design of automated experiments to discover predictive nonlinear biological models. For linear systems, identifiability is characterized by persistence of excitation conditions. For nonlinear systems, no such persistence of excitation conditions exist. We use the input-Koopman operator method to model nonlinear systems and derive identifiability conditions for open-loop systems initialized from a single initial condition. We show that nonlinear identifiability is intrinsically tied to the rank of a given dataset’s power spectral density, transformed through the lifted Koopman observable space. We illustrate these identifiability conditions with a simulated synthetic gene circuit model, the repressilator. We illustrate how rank degeneracy in datasets results in overfitted nonlinear models of the repressilator, resulting in poor predictive accuracy. Our findings provide novel experimental design criteria for discovery of globally predictive nonlinear models of biological phenomena.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d1a0eb601192ddc63263a7a8fb974af0db52db2c" target='_blank'>Koopman Operators for Generalized Persistence of Excitation Conditions for Nonlinear Systems</a></td>
-          <td>
-            N. Boddupalli, A. Hasnain, S. Nandanoori, Enoch Yeung
-          </td>
-          <td>2019-06-25</td>
-          <td>2019 IEEE 58th Conference on Decision and Control (CDC)</td>
-          <td>5</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8" target='_blank'>Learning sparse nonlinear dynamics via mixed-integer optimization</a></td>
-          <td>
-            D. Bertsimas, Wes Gurnee
-          </td>
-          <td>2022-06-01</td>
-          <td>Nonlinear Dynamics</td>
-          <td>27</td>
-          <td>90</td>
-        </tr>
-    
-        <tr id="Systems biology is a new discipline built upon the premise that an understanding of how cells and organisms carry out their functions cannot be gained by looking at cellular components in isolation. Instead, consideration of the interplay between the parts of systems is indispensable for analyzing, modeling, and predicting systems' behavior. Studying biological processes under this premise, systems biology combines experimental techniques and computational methods in order to construct predictive models. Both in building and utilizing models of biological systems, inverse problems arise at several occasions, for example, (i) when experimental time series and steady state data are used to construct biochemical reaction networks, (ii) when model parameters are identified that capture underlying mechanisms or (iii) when desired qualitative behavior such as bistability or limit cycle oscillations is engineered by proper choices of parameter combinations. In this paper we review principles of the modeling process in systems biology and illustrate the ill-posedness and regularization of parameter identification problems in that context. Furthermore, we discuss the methodology of qualitative inverse problems and demonstrate how sparsity enforcing regularization allows the determination of key reaction mechanisms underlying the qualitative behavior.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fee3f9a238cbcb13dd1cd858e1734538018aa1aa" target='_blank'>Inverse problems in systems biology</a></td>
-          <td>
-            H. Engl, Christoph Flamm, P. Kügler, James Lu, S. Müller, P. Schuster
-          </td>
-          <td>2009-12-01</td>
-          <td>Inverse Problems</td>
-          <td>136</td>
-          <td>48</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1626b462b65d4084a24fb31c4e4ca3fc212a307a" target='_blank'>Set-base dynamical parameter estimation and model invalidation for biochemical reaction networks</a></td>
-          <td>
-            Philipp Rumschinski, S. Borchers, S. Bosio, R. Weismantel, R. Findeisen
-          </td>
-          <td>2010-05-25</td>
-          <td>BMC Systems Biology</td>
-          <td>67</td>
-          <td>47</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
-
-</body>
-
-<script>
-var dataTableOptions = {
-        initComplete: function () {
-        this.api()
-            .columns()
-            .every(function () {
-                let column = this;
- 
-                // Create select element
-                let select = document.createElement('select');
-                select.add(new Option(''));
-                column.footer().replaceChildren(select);
- 
-                // Apply listener for user change in value
-                select.addEventListener('change', function () {
-                    column
-                        .search(select.value, {exact: true})
-                        .draw();
-                });
-
-                // keep the width of the select element same as the column
-                select.style.width = '100%';
- 
-                // Add list of options
-                column
-                    .data()
-                    .unique()
-                    .sort()
-                    .each(function (d, j) {
-                        select.add(new Option(d));
-                    });
-            });
-    },
-    scrollX: false,
-    scrollCollapse: true,
-    paging: true,
-    fixedColumns: true,
-    columnDefs: [
-        {"className": "dt-center", "targets": "_all"},
-        // set width for both columns 0 and 1 as 25%
-        { width: '5%', targets: 0 },
-        { width: '25%', targets: 1 },
-        { width: '20%', targets: 2 },
-        { width: '10%', targets: 3 },
-        { width: '20%', targets: 4 }
-
-      ],
-    pageLength: 10,
-    layout: {
-        topStart: {
-            buttons: ['copy', 'csv', 'excel', 'pdf', 'print']
-        }
-    }
-  }
-  new DataTable('#table1', dataTableOptions);
-  
-  var table = $('#table1').DataTable();
-  $('#table1 tbody').on('click', 'td:first-child', function () {
-    var tr = $(this).closest('tr');
-    var row = table.row( tr );
-
-    var rowId = tr.attr('id');
-    // alert(rowId);
-
-    if (row.child.isShown()) {
-      // This row is already open - close it.
-      row.child.hide();
-      tr.removeClass('shown');
-      tr.find('td:first-child').html('<i class="material-icons">visibility_off</i>');
-    } else {
-      // Open row.
-      // row.child('foo').show();
-      var content = '<div class="child-row-content"><strong>Abstract:</strong> ' + rowId + '</div>';
-      row.child(content).show();
-      tr.addClass('shown');
-      tr.find('td:first-child').html('<i class="material-icons">visibility</i>');
-    }
-  });
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-<style>
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-    text-align: justify;
-    text-justify: inter-word;
-    word-wrap: break-word; /* Ensure long words are broken */
-    white-space: normal; /* Ensure text wraps to the next line */
-    max-width: 100%; /* Ensure content does not exceed the table width */
-    padding: 10px; /* Optional: add some padding for better readability */
-    /* font size */
-    font-size: small;
-  }
-</style>
-</html>
\ No newline at end of file
diff --git a/docs/recommendations/0acd117521ef5aafb09fed02ab415523b330b058.md b/docs/recommendations/0acd117521ef5aafb09fed02ab415523b330b058.md
deleted file mode 100644
index 51c0d3d7..00000000
--- a/docs/recommendations/0acd117521ef5aafb09fed02ab415523b330b058.md
+++ /dev/null
@@ -1,249 +0,0 @@
----
-hide:
- - navigation
----
-<!DOCTYPE html>
-#
-<html lang="en">
-<head>
-  <meta charset="utf-8">
-</head>
-
-<body>
-  <p>
-  <i class="footer">This page was last updated on 2024-08-08 13:17:27 UTC</i>
-  </p>
-  
-  <div class="note info" onclick="startIntro()">
-    <p>
-      <button type="button" class="buttons">
-        <div style="display: flex; align-items: center;">
-        Click here for a quick intro of the page! <i class="material-icons">help</i>
-        </div>
-      </button>
-    </p>
-  </div>
-
-  <p>
-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Data-driven discovery of partial differential equations</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="This study presents a general framework, namely, Sparse Spatiotemporal System Discovery (S3d), for discovering dynamical models given by Partial Differential Equations (PDEs) from spatiotemporal data. S3d is built on the recent development of sparse Bayesian learning, which enforces sparsity in the estimated PDEs. This approach enables a balance between model complexity and fitting error with theoretical guarantees. The proposed framework integrates Bayesian inference and a sparse priori distribution with the sparse regression method. It also introduces a principled iterative re-weighted algorithm to select dominant features in PDEs and solve for the sparse coefficients. We have demonstrated the discovery of the complex Ginzburg-Landau equation from a traveling-wave convection experiment, as well as several other PDEs, including the important cases of Navier-Stokes and sine-Gordon equations, from simulated data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a28eb9166ed38ff571770f8d6cb1558b0089e507" target='_blank'>Machine discovery of partial differential equations from spatiotemporal data: A sparse Bayesian learning framework.</a></td>
-          <td>
-            Ye Yuan, Xiuting Li, Liang Li, Frank J. Jiang, Xiuchuan Tang, Fumin Zhang, Jorge Gonçalves, H.U. Voss, Han Ding, Jürgen Kurths
-          </td>
-          <td>2023-11-01</td>
-          <td>Chaos</td>
-          <td>2</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which physical terms are necessary and which can be removed (because they are physically negligible in the sense that they do not affect the dynamics too much) from a pool of candidate functions. The method is built on the recent development of Sparse Bayesian Learning; which enforces the sparsity in the to-be-identified PDEs, and therefore can balance the model complexity and fitting error with theoretical guarantees. Without leveraging prior knowledge or assumptions in the discovery process, we use an automated approach to discover ten types of PDEs, including the famous Navier-Stokes and sine-Gordon equations, from simulation data alone. Moreover, we demonstrate our data-driven discovery process with the Complex Ginzburg-Landau Equation (CGLE) using data measured from a traveling-wave convection experiment. Our machine discovery approach presents solutions that has the potential to inspire, support and assist physicists for the establishment of physical laws from measured spatiotemporal data, especially in notorious fields that are often too complex to allow a straightforward establishment of physical law, such as biophysics, fluid dynamics, neuroscience or nonlinear optics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/85835648e0d92d2b6115a66525b1f5d54af4f83e" target='_blank'>Machine Discovery of Partial Differential Equations from Spatiotemporal Data</a></td>
-          <td>
-            Ye Yuan, Junlin Li, Liang Li, Frank Jiang, Xiuchuan Tang, Fumin Zhang, Sheng Liu, J. Gonçalves, H. Voss, Xiuting Li, J. Kurths, Han Ding
-          </td>
-          <td>2019-09-15</td>
-          <td>ArXiv</td>
-          <td>9</td>
-          <td>106</td>
-        </tr>
-    
-        <tr id="Significance Understanding dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled technology, including aircraft, combustion engines, satellites, and electrical power. This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. There are many critical data-driven problems, such as understanding cognition from neural recordings, inferring climate patterns, determining stability of financial markets, predicting and suppressing the spread of disease, and controlling turbulence for greener transportation and energy. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an important role in these efforts. Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5d150cec2775f9bc863760448f14104cc8f42368" target='_blank'>Discovering governing equations from data by sparse identification of nonlinear dynamical systems</a></td>
-          <td>
-            S. Brunton, J. Proctor, J. Kutz
-          </td>
-          <td>2015-09-11</td>
-          <td>Proceedings of the National Academy of Sciences</td>
-          <td>3168</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1f18c5206491626d36c2271aaf491dbc945f6247" target='_blank'>Automatically discovering ordinary differential equations from data with sparse regression</a></td>
-          <td>
-            Kevin Egan, Weizhen Li, Rui Carvalho
-          </td>
-          <td>2024-01-09</td>
-          <td>Communications Physics</td>
-          <td>7</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e596988b1df3a0bc78bf72c0bfdb21c85eaab6c9" target='_blank'>Physics-informed learning of governing equations from scarce data</a></td>
-          <td>
-            Zhao Chen, Yang Liu, Hao Sun
-          </td>
-          <td>2020-05-05</td>
-          <td>Nature Communications</td>
-          <td>234</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model discovery algorithms based on sparse regression can actually recover the underlying physical processes. In this work, we show the design matrices used to infer the equations by sparse regression can violate the irrepresentability condition (IRC) of the Lasso, even when derived from analytical PDE solutions (i.e. without additional noise). Sparse regression techniques which can recover the true underlying model under violated IRC conditions are therefore required, leading to the introduction of the randomised adaptive Lasso. We show once the latter is integrated within the deep learning model discovery framework DeepMod, a wide variety of nonlinear and chaotic canonical PDEs can be recovered: (1) up to $\mathcal{O}(2)$ higher noise-to-sample ratios than state-of-the-art algorithms, (2) with a single set of hyperparameters, which paves the road towards truly automated model discovery.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/45633bde87d3fecdb0ef577036f2465e70c51f24" target='_blank'>Sparsistent Model Discovery</a></td>
-          <td>
-            Georges Tod, G. Both, R. Kusters
-          </td>
-          <td>2021-06-22</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/29fd552660768b191c36d16894faee7db5f18949" target='_blank'>Supplementary material from "Learning partial differential equations via data discovery and sparse optimization"</a></td>
-          <td>
-            Hayden Schaeffer
-          </td>
-          <td>2017-01-16</td>
-          <td></td>
-          <td>0</td>
-          <td>15</td>
-        </tr>
-    
-        <tr id="We propose a regression method based upon group sparsity that is capable of discovering parametrized governing dynamical equations of motion of a given system by time series measurements. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. This gives a promising new technique for disambiguating governing equations from simple parametric dependencies in physical, biological and engineering systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a8bbfc159dd6951e50e366daa7359626873aec45" target='_blank'>Data-Driven discovery of governing physical laws and their parametric dependencies in engineering, physics and biology</a></td>
-          <td>
-            J. Kutz, Samuel H. Rudy, A. Alla, S. Brunton
-          </td>
-          <td>2017-12-01</td>
-          <td>2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)</td>
-          <td>12</td>
-          <td>63</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Deep learning models for global coordinate transformations that linearise PDEs</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Significance Governing equations are essential to the study of physical systems, providing models that can generalize to predict previously unseen behaviors. There are many systems of interest across disciplines where large quantities of data have been collected, but the underlying governing equations remain unknown. This work introduces an approach to discover governing models from data. The proposed method addresses a key limitation of prior approaches by simultaneously discovering coordinates that admit a parsimonious dynamical model. Developing parsimonious and interpretable governing models has the potential to transform our understanding of complex systems, including in neuroscience, biology, and climate science. The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam’s razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. This method places the discovery of coordinates and models on an equal footing.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3c9961153493370500020c81527b3548c96f81e0" target='_blank'>Data-driven discovery of coordinates and governing equations</a></td>
-          <td>
-            Kathleen P. Champion, Bethany Lusch, J. Kutz, S. Brunton
-          </td>
-          <td>2019-03-29</td>
-          <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>589</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Machine learning models have emerged as powerful tools in physics and engineering. In this work, we use an autoencoder with latent space penalization to discover approximate finite-dimensional manifolds of two canonical partial differential equations. We test this method on the Kuramoto-Sivashinsky (K-S), Korteweg-de Vries (KdV), and damped KdV equations. We show that the resulting optimal latent space of the K-S equation is consistent with the dimension of the inertial manifold. We then uncover a nonlinear basis representing the manifold of the latent space for the K-S equation. The results for the KdV equation show that it is more difficult to recover a reduced latent space, which is consistent with the truly infinite-dimensional dynamics of the KdV equation. In the case of the damped KdV equation, we find that the number of active dimensions decreases with increasing damping coefficient.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9d96b33045db6f4c60e5b333c46c25d14efab89d" target='_blank'>Learning a reduced basis of dynamical systems using an autoencoder.</a></td>
-          <td>
-            David Sondak, P. Protopapas
-          </td>
-          <td>2020-11-14</td>
-          <td>Physical review. E</td>
-          <td>2</td>
-          <td>33</td>
-        </tr>
-    
-        <tr id="We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. We develop approaches for learning nonlinear state space models of the dynamics for general manifold latent spaces using training strategies related to Variational Autoencoders (VAEs). Our methods are referred to as Geometric Dynamic (GD) Variational Autoencoders (GD-VAEs). We learn encoders and decoders for the system states and evolution based on deep neural network architectures that include general Multilayer Perceptrons (MLPs), Convolutional Neural Networks (CNNs), and Transpose CNNs (T-CNNs). Motivated by problems arising in parameterized PDEs and physics, we investigate the performance of our methods on tasks for learning low dimensional representations of the nonlinear Burgers equations, constrained mechanical systems, and spatial fields of reaction-diffusion systems. GD-VAEs provide methods for obtaining representations for use in diverse learning tasks involving dynamics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5bf6a5ba35370f1f4da0b66a633cabb82ae02906" target='_blank'>GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions</a></td>
-          <td>
-            Ryan Lopez, P. Atzberger
-          </td>
-          <td>2022-06-10</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical models of the physical world. In the current era of abundance of data and advanced machine learning capabilities, the natural question arises: How can we automatically uncover the underlying laws of physics from high-dimensional data generated from experiments? In this work, we put forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time. Specifically, we approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks. The first network acts as a prior on the unknown solution and essentially enables us to avoid numerical differentiations which are inherently ill-conditioned and unstable. The second network represents the nonlinear dynamics and helps us distill the mechanisms that govern the evolution of a given spatiotemporal data-set. We test the effectiveness of our approach for several benchmark problems spanning a number of scientific domains and demonstrate how the proposed framework can help us accurately learn the underlying dynamics and forecast future states of the system. In particular, we study the Burgers', Korteweg-de Vries (KdV), Kuramoto-Sivashinsky, nonlinear Schr\"{o}dinger, and Navier-Stokes equations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ebcc0e71ef6a77d05e7ab064435bc2da87c55e91" target='_blank'>Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations</a></td>
-          <td>
-            M. Raissi
-          </td>
-          <td>2018-01-20</td>
-          <td>J. Mach. Learn. Res.</td>
-          <td>658</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification task, it allows for the modification of the weights via a continuous group of symmetry. This is a significant shift from traditional models where the architecture and weights are essentially fixed. We wish to promote the (internal) symmetry as a new desirable property for a neural network, and to draw attention to the PDE perspective in analyzing and interpreting ConvNets in the broader Deep Learning community.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9cdb5a3028a57129e017bbbac4f29c871da38fe1" target='_blank'>A Novel Convolutional Neural Network Architecture with a Continuous Symmetry</a></td>
-          <td>
-            Y. Liu, Han-Juan Shao, Bing Bai
-          </td>
-          <td>2023-08-03</td>
-          <td>ArXiv, DBLP</td>
-          <td>1</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="In this article we address the question whether it is possible to learn the differential equations describing the physical properties of a dynamical system, subject to non-conservative forces, from observations of its realspace trajectory(ies) only. We introduce a network that incorporates a difference approximation for the second order derivative in terms of residual connections between convolutional blocks, whose shared weights represent the coefficients of a second order ordinary differential equation. We further combine this solver-like architecture with a convolutional network, capable of learning the relation between trajectories of coupled oscillators and therefore allows us to make a stable forecast even if the system is only partially observed. We optimize this map together with the solver network, while sharing their weights, to form a powerful framework capable of learning the complex physical properties of a dissipative dynamical system.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/67daa96e83d87d4c7fa06ea7ba72a73612276560" target='_blank'>Learning second order coupled differential equations that are subject to non-conservative forces</a></td>
-          <td>
-            R. Müller, J. L. Janssen, J. Camacaro, C. Bessega
-          </td>
-          <td>2020-10-17</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eed8e9f62f9efc009a937a18ab5f336801dc659f" target='_blank'>Phase space learning with neural networks</a></td>
-          <td>
-            Jaime Lopez Garcia, Ángel Rivero Jiménez
-          </td>
-          <td>2020-06-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e6fe1bae9fb6aa3f3dc91df642bbe933811728f9" target='_blank'>A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data</a></td>
-          <td>
-            Elham Kiyani, K. Shukla, G. Karniadakis, M. Karttunen
-          </td>
-          <td>2023-05-18</td>
-          <td>ArXiv</td>
-          <td>10</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems, enabling the analysis and prediction of complex temporal behaviors. However, how to improve the model's stability and physical interpretability remains a challenge. This paper introduces new conservation relations in Neural ODEs using Lie symmetries in both the hidden state dynamics and the back propagation dynamics. These conservation laws are then incorporated into the loss function as additional regularization terms, potentially enhancing the physical interpretability and generalizability of the model. To illustrate this method, the paper derives Lie symmetries and conservation laws in a simple Neural ODE designed to monitor charged particles in a sinusoidal electric field. New loss functions are constructed from these conservation relations, demonstrating the applicability symmetry-regularized Neural ODE in typical modeling tasks, such as data-driven discovery of dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9827f402bc2fc9561f674b5bdfc992fb7dd32e2e" target='_blank'>Symmetry-regularized neural ordinary differential equations</a></td>
-          <td>
-            Wenbo Hao
-          </td>
-          <td>2023-11-28</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders (VAEs) for learning from observations nonlinear state space models. We develop ways to incorporate geometric and topological priors through general manifold latent space representations. We investigate the performance of our methods for learning low dimensional representations for the nonlinear Burgers equation and constrained mechanical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ef0917e87a88ca324c81eaa51062e1bdaf632085" target='_blank'>Variational Autoencoders for Learning Nonlinear Dynamics of PDEs and Reductions</a></td>
-          <td>
-            Ryan Lopez, P. Atzberger
-          </td>
-          <td>2020-12-07</td>
-          <td>ArXiv</td>
-          <td>14</td>
-          <td>24</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b.md b/docs/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b.md
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Sparse Graph Learning from Spatiotemporal Time Series</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ccea298edb788edf821aef58f0952c3e8debc25a" target='_blank'>Graph Deep Learning for Time Series Forecasting</a></td>
-          <td>
-            Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi
-          </td>
-          <td>2023-10-24</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="Graph neural networks (GNNs) have been widely applied in multi-variate time-series forecasting (MTSF) tasks because of their capability in capturing the correlations among different time-series. These graph-based learning approaches improve the forecasting performance by discovering and understanding the underlying graph structures, which represent the data correlation. When the explicit prior graph structures are not available, most existing works cannot guarantee the sparsity of the generated graphs that make the overall model computational expensive and less interpretable. In this work, we propose a decoupled training method, which includes a graph generating module and a GNNs forecasting module. First, we use Graphical Lasso (or GraphLASSO) to directly exploit the sparsity pattern from data to build graph structures in both static and time-varying cases. Second, we fit these graph structures and the input data into a Graph Convolutional Recurrent Network (GCRN) to train a forecasting model. The experimental results on three real-world datasets show that our novel approach has competitive performance against existing state-of-the-art forecasting algorithms while providing sparse, meaningful and explainable graph structures and reducing training time by approximately 40%. Our PyTorch implementation is publicly available at https://github.com/HySonLab/GraphLASSO">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ae010c11b07b251f5f1a1d51c439678961c92c8a" target='_blank'>Sparsity exploitation via discovering graphical models in multi-variate time-series forecasting</a></td>
-          <td>
-            Ngoc-Dung Do, T. Hy, D. Nguyen
-          </td>
-          <td>2023-06-29</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="Time series forecasting lies at the core of important real-world applications in many fields of science and engineering. The abundance of large time series datasets that consist of complex patterns and long-term dependencies has led to the development of various neural network architectures. Graph neural network approaches, which jointly learn a graph structure based on the correlation of raw values of multivariate time series while forecasting, have recently seen great success. However, such solutions are often costly to train and difficult to scale. In this paper, we propose TimeGNN, a method that learns dynamic temporal graph representations that can capture the evolution of inter-series patterns along with the correlations of multiple series. TimeGNN achieves inference times 4 to 80 times faster than other state-of-the-art graph-based methods while achieving comparable forecasting performance">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d9916caa8da69496ecc8e0b1c229c73a60d6f861" target='_blank'>TimeGNN: Temporal Dynamic Graph Learning for Time Series Forecasting</a></td>
-          <td>
-            Nancy R. Xu, Chrysoula Kosma, M. Vazirgiannis
-          </td>
-          <td>2023-07-27</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>54</td>
-        </tr>
-    
-        <tr id="Accurate forecasting of multivariate time series is an extensively studied subject in finance, transportation, and computer science. Fully mining the correlation and causation between the variables in a multivariate time series exhibits noticeable results in improving the performance of a time series model. Recently, some models have explored the dependencies between variables through end-to-end graph structure learning without the need for predefined graphs. However, current models do not incorporate the trade-off between efficiency and flexibility and lack the guidance of domain knowledge in the design of graph structure learning algorithms. This paper alleviates the above issues by proposing Balanced Graph Structure Learning for Forecasting (BGSLF), a novel deep learning model that joins graph structure learning and forecasting. Technically, BGSLF leverages the spatial information into convolutional operations and extracts temporal dynamics using the diffusion convolutional recurrent network. The proposed framework balance the trade-off between efficiency and flexibility by introducing Multi-Graph Generation Network (MGN) and Graph Selection Module. In addition, a method named Smooth Sparse Unit (SSU) is designed to sparse the learned graph structures, which conforms to the sparse spatial correlations in the real world. Extensive experiments on four real-world datasets demonstrate that our model achieves state-of-the-art performances with minor trainable parameters. Code will be made publicly available.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cf803de5a63ec6893960af15756a8e4766c99e0d" target='_blank'>Balanced Graph Structure Learning for Multivariate Time Series Forecasting</a></td>
-          <td>
-            Weijun Chen, Yanze Wang, Chengshuo Du, Zhenglong Jia, Feng Liu, Ran Chen
-          </td>
-          <td>2022-01-24</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>10</td>
-        </tr>
-    
-        <tr id="We study a recent class of models which uses graph neural networks (GNNs) to improve forecasting in multivariate time series. The core assumption behind these models is that there is a latent graph between the time series (nodes) that governs the evolution of the multivariate time series. By parameterizing a graph in a differentiable way, the models aim to improve forecasting quality. We compare four recent models of this class on the forecasting task. Further, we perform ablations to study their behavior under changing conditions, e.g., when disabling the graph-learning modules and providing the ground-truth relations instead. Based on our findings, we propose novel ways of combining the existing architectures.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0b85207ac9a9271850fe8c44f5e8c84d00ff3409" target='_blank'>A Study of Joint Graph Inference and Forecasting</a></td>
-          <td>
-            Daniel Zügner, François-Xavier Aubet, Victor Garcia Satorras, Tim Januschowski, Stephan Günnemann, Jan Gasthaus
-          </td>
-          <td>2021-09-10</td>
-          <td>ArXiv</td>
-          <td>12</td>
-          <td>45</td>
-        </tr>
-    
-        <tr id="Multivariate time-series forecasting is a critical task for many applications, and graph time-series network is widely studied due to its capability to capture the spatial-temporal correlation simultaneously. However, most existing works focus more on learning with the explicit prior graph structure, while ignoring potential information from the implicit graph structure, yielding incomplete structure modeling. Some recent works attempts to learn the intrinsic or implicit graph structure directly, while lacking a way to combine explicit prior structure with implicit structure together. In this paper, we propose Regularized Graph Structure Learning (RGSL) model to incorporate both explicit prior structure and implicit structure together, and learn the forecasting deep networks along with the graph structure. RGSL consists of two innovative modules. First, we derive an implicit dense similarity matrix through node embedding, and learn the sparse graph structure using the Regularized Graph Generation (RGG) based on the Gumbel Softmax trick. Second, we propose a Laplacian Matrix Mixed-up Module (LM3) to fuse the explicit graph and implicit graph together. We conduct experiments on three real-word datasets. Results show that the proposed RGSL model outperforms existing graph forecasting algorithms with a notable margin, while learning meaningful graph structure simultaneously. Our code and models are made publicly available at https://github.com/alipay/RGSL.git.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a092b7e51c21d41528ba49a339efaaf81d72ca7b" target='_blank'>Regularized Graph Structure Learning with Semantic Knowledge for Multi-variates Time-Series Forecasting</a></td>
-          <td>
-            Hongyuan Yu, Ting Li, Weichen Yu, Jianguo Li, Yan Huang, Liang Wang, A. Liu
-          </td>
-          <td>2022-07-01</td>
-          <td>ArXiv, DBLP</td>
-          <td>37</td>
-          <td>33</td>
-        </tr>
-    
-        <tr id="Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the performance of a time series model. When using deep neural networks as forecasting models, we hypothesize that exploiting the pairwise information among multiple (multivariate) time series also improves their forecast. If an explicit graph structure is known, graph neural networks (GNNs) have been demonstrated as powerful tools to exploit the structure. In this work, we propose learning the structure simultaneously with the GNN if the graph is unknown. We cast the problem as learning a probabilistic graph model through optimizing the mean performance over the graph distribution. The distribution is parameterized by a neural network so that discrete graphs can be sampled differentiably through reparameterization. Empirical evaluations show that our method is simpler, more efficient, and better performing than a recently proposed bilevel learning approach for graph structure learning, as well as a broad array of forecasting models, either deep or non-deep learning based, and graph or non-graph based.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/401930b2dc738a5a67d136bc9a2d04461c5bf93a" target='_blank'>Discrete Graph Structure Learning for Forecasting Multiple Time Series</a></td>
-          <td>
-            Chao Shang, Jie Chen, J. Bi
-          </td>
-          <td>2021-01-18</td>
-          <td>ArXiv</td>
-          <td>174</td>
-          <td>36</td>
-        </tr>
-    
-        <tr id="Multi-variate time series forecasting is an important problem with a wide range of applications. Recent works model the relations between time-series as graphs and have shown that propagating information over the relation graph can improve time series forecasting. However, in many cases, relational information is not available or is noisy and reliable. Moreover, most works ignore the underlying uncertainty of time-series both for structure learning and deriving the forecasts resulting in the structure not capturing the uncertainty resulting in forecast distributions with poor uncertainty estimates. We tackle this challenge and introduce STOIC, that leverages stochastic correlations between time-series to learn underlying structure between time-series and to provide well-calibrated and accurate forecasts. Over a wide-range of benchmark datasets STOIC provides around 16% more accurate and 14% better-calibrated forecasts. STOIC also shows better adaptation to noise in data during inference and captures important and useful relational information in various benchmarks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7d4b412399f89c9cd66cffc4ab811b74172dcc63" target='_blank'>Learning Graph Structures and Uncertainty for Accurate and Calibrated Time-series Forecasting</a></td>
-          <td>
-            Harshavardhan Kamarthi, Lingkai Kong, Alexander Rodríguez, Chao Zhang, B. A. Prakash
-          </td>
-          <td>2024-07-02</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>9</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
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-    Recommendations for the article <i>From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
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-  </thead>
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-    
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-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e09301c9f56ba547e0a203efaeb9295594e5b840" target='_blank'>Deep Probabilistic Koopman: Long-term time-series forecasting under periodic uncertainties</a></td>
-          <td>
-            Alex Troy Mallen, Henning Lange, J. Kutz
-          </td>
-          <td>2021-06-10</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>31</td>
-        </tr>
-    
-        <tr id="Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the Temporally-Consistent Koopman Autoencoder (tcKAE), designed to generate accurate long-term predictions even with constrained and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE's superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasmas, fluid flows, and sea surface temperature data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bb0e700722b318f57b605b0cb12d99e1c70318ef" target='_blank'>Temporally-Consistent Koopman Autoencoders for Forecasting Dynamical Systems</a></td>
-          <td>
-            I. Nayak, Debdipta Goswami, Mrinal Kumar, Fernando L. Teixeira
-          </td>
-          <td>2024-03-19</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>8</td>
-        </tr>
-    
-        <tr id="Machine learning has countless applications in time series analysis: controlling smart grids, detecting mechanical failures, and analyzing stock prices. Fourier mode decomposition (FMD) is the most common method of analysis because it decomposes time series into finite waveform components, or modes, but its principal shortcoming is that FMD assumes every mode has a constant amplitude, an assumption that rarely holds in real-world data. In contrast, Koopman mode decomposition (KMD) can detect modes with exponentially-increasing or - decreasing amplitudes, although it has mostly been applied to diagnosing data errors, not to prediction. What has kept KMD from being applied to prediction is partly a shortcoming in a mathematical formulation. This paper seeks to remedy that shortcoming: it provides a mathematically-precise formulation of KMD as a practical tool. This formulation, in turn, allows us to develop a novel practical method for prediction of future data. We further demonstrate our method's effectiveness using both synthetic data and real plasma flow data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d38f5f062ba848e0b48918719b454626d1a8f0b7" target='_blank'>Predictive Nonlinear Modeling by Koopman Mode Decomposition</a></td>
-          <td>
-            Akira Kusaba, Kilho Shin, D. Shepard, T. Kuboyama
-          </td>
-          <td>2020-11-01</td>
-          <td>2020 International Conference on Data Mining Workshops (ICDMW)</td>
-          <td>0</td>
-          <td>13</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a7e49ad93693c3a21d3bedc135f409eb8055c17e" target='_blank'>Koopman Operator Framework for Time Series Modeling and Analysis</a></td>
-          <td>
-            A. Surana
-          </td>
-          <td>2018-01-09</td>
-          <td>Journal of Nonlinear Science</td>
-          <td>35</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a7e49ad93693c3a21d3bedc135f409eb8055c17e" target='_blank'>Koopman Operator Framework for Time Series Modeling and Analysis</a></td>
-          <td>
-            A. Surana
-          </td>
-          <td>2018-01-09</td>
-          <td>Journal of Nonlinear Science</td>
-          <td>35</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data are small. The proposed model is based on the Koopman operator theory, where the decay rate and frequency information is used by restricting the eigenvalues of the Koopman operator that describe linear evolution in a Koopman space. We use neural networks to find an appropriate Koopman space, which are trained by minimizing multi-step forecasting and backcasting errors using irregularly sampled time-series data. Experiments on various time-series datasets demonstrate that the proposed method achieves higher forecasting performance given a single short training sequence than the existing methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/90813609def379739274d4db8337b155ac43e48e" target='_blank'>Modeling Nonlinear Dynamics in Continuous Time with Inductive Biases on Decay Rates and/or Frequencies</a></td>
-          <td>
-            Tomoharu Iwata, Y. Kawahara
-          </td>
-          <td>2022-12-26</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>30</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1ca50905705b56d8e6fef689520be72e75951bd7" target='_blank'>High-dimensional time series prediction using kernel-based Koopman mode regression</a></td>
-          <td>
-            Jia-Chen Hua, Farzad Noorian, Duncan J. M. Moss, P. Leong, G. Gunaratne
-          </td>
-          <td>2017-09-15</td>
-          <td>Nonlinear Dynamics</td>
-          <td>25</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="Recurrent neural networks are widely used on time series data, yet such models often ignore the underlying physical structures in such sequences. A new class of physics-based methods related to Koopman theory has been introduced, offering an alternative for processing nonlinear dynamical systems. In this work, we propose a novel Consistent Koopman Autoencoder model which, unlike the majority of existing work, leverages the forward and backward dynamics. Key to our approach is a new analysis which explores the interplay between consistent dynamics and their associated Koopman operators. Our network is directly related to the derived analysis, and its computational requirements are comparable to other baselines. We evaluate our method on a wide range of high-dimensional and short-term dependent problems, and it achieves accurate estimates for significant prediction horizons, while also being robust to noise.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0872dfacadb282200f909e167e34dd9a7d9f27cd" target='_blank'>Forecasting Sequential Data using Consistent Koopman Autoencoders</a></td>
-          <td>
-            Omri Azencot, N. Benjamin Erichson, Vanessa Lin, Michael W. Mahoney
-          </td>
-          <td>2020-03-04</td>
-          <td>ArXiv</td>
-          <td>109</td>
-          <td>64</td>
-        </tr>
-    
-        <tr id="Electricity load forecasting is crucial for effectively managing and optimizing power grids. Over the past few decades, various statistical and deep learning approaches have been used to develop load forecasting models. This paper presents an interpretable machine learning approach that identifies load dynamics using data-driven methods within an operator-theoretic framework. We represent the load data using the Koopman operator, which is inherent to the underlying dynamics. By computing the corresponding eigenfunctions, we decompose the load dynamics into coherent spatiotemporal patterns that are the most robust features of the dynamics. Each pattern evolves independently according to its single frequency, making its predictability based on linear dynamics. We emphasize that the load dynamics are constructed based on coherent spatiotemporal patterns that are intrinsic to the dynamics and are capable of encoding rich dynamical features at multiple time scales. These features are related to complex interactions over interconnected power grids and different exogenous effects. To implement the Koopman operator approach more efficiently, we cluster the load data using a modern kernel-based clustering approach and identify power stations with similar load patterns, particularly those with synchronized dynamics. We evaluate our approach using a large-scale dataset from a renewable electric power system within the continental European electricity system and show that the Koopman-based approach outperforms a deep learning (LSTM) architecture in terms of accuracy and computational efficiency. The code for this paper has been deposited in a GitHub repository, which can be accessed at the following address github.com/Shakeri-Lab/Power-Grids.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/01f2acb6064e53144d500ff9b5a337330691a33b" target='_blank'>Characterizing the load profile in power grids by Koopman mode decomposition of interconnected dynamics</a></td>
-          <td>
-            A. Tavasoli, Behnaz Moradijamei, Heman Shakeri
-          </td>
-          <td>2023-04-16</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="Koopman spectral analysis has attracted attention for understanding nonlinear dynamical systems by which we can analyze nonlinear dynamics with a linear regime by lifting observations using a nonlinear function. For analysis, we need to find an appropriate lift function. Although several methods have been proposed for estimating a lift function based on neural networks, the existing methods train neural networks without spectral analysis. In this paper, we propose neural dynamic mode decomposition, in which neural networks are trained such that the forecast error is minimized when the dynamics is modeled based on spectral decomposition in the lifted space. With our proposed method, the forecast error is backpropagated through the neural networks and the spectral decomposition, enabling end-to-end learning of Koopman spectral analysis. When information is available on the frequencies or the growth rates of the dynamics, the proposed method can exploit it as regularizers for training. We also propose an extension of our approach when observations are influenced by exogenous control time-series. Our experiments demonstrate the effectiveness of our proposed method in terms of eigenvalue estimation and forecast performance.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/729f577cdcfebf5f5bbc4e38eeec21e462147f99" target='_blank'>Neural Dynamic Mode Decomposition for End-to-End Modeling of Nonlinear Dynamics</a></td>
-          <td>
-            Tomoharu Iwata, Y. Kawahara
-          </td>
-          <td>2020-12-11</td>
-          <td>ArXiv</td>
-          <td>9</td>
-          <td>30</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <i class="footer">This page was last updated on 2024-08-08 13:16:44 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Large Language Models Are Zero-Shot Time Series Forecasters</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4fb78450650894091b0a55b5504a8b0a6f3dec37" target='_blank'>Chronos: Learning the Language of Time Series</a></td>
-          <td>
-            Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, Yuyang Wang
-          </td>
-          <td>2024-03-12</td>
-          <td>ArXiv</td>
-          <td>23</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To further exploit the general-purpose token transition and multi-step generation ability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which independently projects time series segments into the embedding space and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability of the LLM size. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By adopting textual timestamps as position embeddings, AutoTimes integrates multimodality for multivariate scenarios. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over 5 times training/inference speedup compared to advanced LLM-based forecasters.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d488445bb2bf6719bc48a4d39bd906116274abda" target='_blank'>AutoTimes: Autoregressive Time Series Forecasters via Large Language Models</a></td>
-          <td>
-            Yong Liu, Guo Qin, Xiangdong Huang, Jianmin Wang, Mingsheng Long
-          </td>
-          <td>2024-02-04</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="Large language models (LLMs) are being applied to time series tasks, particularly time series forecasting. However, are language models actually useful for time series? After a series of ablation studies on three recent and popular LLM-based time series forecasting methods, we find that removing the LLM component or replacing it with a basic attention layer does not degrade the forecasting results -- in most cases the results even improved. We also find that despite their significant computational cost, pretrained LLMs do no better than models trained from scratch, do not represent the sequential dependencies in time series, and do not assist in few-shot settings. Additionally, we explore time series encoders and reveal that patching and attention structures perform similarly to state-of-the-art LLM-based forecasters.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/df0d604b8e8e3b2947d9865d735f204c08635012" target='_blank'>Are Language Models Actually Useful for Time Series Forecasting?</a></td>
-          <td>
-            Mingtian Tan, Mike A. Merrill, Vinayak Gupta, Tim Althoff, Tom Hartvigsen
-          </td>
-          <td>2024-06-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world data-scarce scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progress has been achieved with the emergence of large language models, exhibiting unprecedented abilities such as few-shot generalization, scalability, and task generality, which are however absent in small deep models. To change the status quo of training scenario-specific small models from scratch, this paper aims at the early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), which is generative pre-trained by next token prediction and adapted to various downstream tasks with promising capabilities as an LTSM. Code and datasets are available at: https://github.com/thuml/Large-Time-Series-Model.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/73f58b90697f957832f5090946894480849dea3a" target='_blank'>Timer: Generative Pre-trained Transformers Are Large Time Series Models</a></td>
-          <td>
-            Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
-          </td>
-          <td>2024-02-04</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="In this paper, we introduce TimeGPT, the first foundation model for time series, capable of generating accurate predictions for diverse datasets not seen during training. We evaluate our pre-trained model against established statistical, machine learning, and deep learning methods, demonstrating that TimeGPT zero-shot inference excels in performance, efficiency, and simplicity. Our study provides compelling evidence that insights from other domains of artificial intelligence can be effectively applied to time series analysis. We conclude that large-scale time series models offer an exciting opportunity to democratize access to precise predictions and reduce uncertainty by leveraging the capabilities of contemporary advancements in deep learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/32b15b02bd2640346678a773079c5d42190bbac9" target='_blank'>TimeGPT-1</a></td>
-          <td>
-            Azul Garza, Cristian Challu, Max Mergenthaler-Canseco
-          </td>
-          <td>2023-10-05</td>
-          <td>ArXiv</td>
-          <td>39</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Predicting future values in multivariate time series is vital across various domains. This work explores the use of large language models (LLMs) for this task. However, LLMs typically handle one-dimensional data. We introduce MultiCast, a zero-shot LLM-based approach for multivariate time series forecasting. It allows LLMs to receive multivariate time series as input, through three novel token multiplexing solutions that effectively reduce dimensionality while preserving key repetitive patterns. Additionally, a quantization scheme helps LLMs to better learn these patterns, while significantly reducing token use for practical applications. We showcase the performance of our approach in terms of RMSE and execution time against state-of-the-art approaches on three real-world datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/695663f05473270744f228e9beeb7578ceee7c68" target='_blank'>MultiCast: Zero-Shot Multivariate Time Series Forecasting Using LLMs</a></td>
-          <td>
-            Georgios Chatzigeorgakidis, Konstantinos Lentzos, Dimitrios Skoutas
-          </td>
-          <td>2024-05-13</td>
-          <td>2024 IEEE 40th International Conference on Data Engineering Workshops (ICDEW)</td>
-          <td>0</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that Time-LLM is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277" target='_blank'>Time-LLM: Time Series Forecasting by Reprogramming Large Language Models</a></td>
-          <td>
-            Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y. Zhang, X. Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, Qingsong Wen
-          </td>
-          <td>2023-10-03</td>
-          <td>ArXiv</td>
-          <td>111</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="Time-series forecasting (TSF) finds broad applications in real-world scenarios. Prompting off-the-shelf Large Language Models (LLMs) demonstrates strong zero-shot TSF capabilities while preserving computational efficiency. However, existing prompting methods oversimplify TSF as language next-token predictions, overlooking its dynamic nature and lack of integration with state-of-the-art prompt strategies such as Chain-of-Thought. Thus, we propose LSTPrompt, a novel approach for prompting LLMs in zero-shot TSF tasks. LSTPrompt decomposes TSF into short-term and long-term forecasting sub-tasks, tailoring prompts to each. LSTPrompt guides LLMs to regularly reassess forecasting mechanisms to enhance adaptability. Extensive evaluations demonstrate consistently better performance of LSTPrompt than existing prompting methods, and competitive results compared to foundation TSF models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bbf272d92b76cc5f1e6f793dcfeb5edd4abed7ef" target='_blank'>LSTPrompt: Large Language Models as Zero-Shot Time Series Forecasters by Long-Short-Term Prompting</a></td>
-          <td>
-            Haoxin Liu, Zhiyuan Zhao, Jindong Wang, Harshavardhan Kamarthi, B. A. Prakash
-          </td>
-          <td>2024-02-25</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="This paper presents a novel study on harnessing Large Language Models' (LLMs) outstanding knowledge and reasoning abilities for explainable financial time series forecasting. The application of machine learning models to financial time series comes with several challenges, including the difficulty in cross-sequence reasoning and inference, the hurdle of incorporating multi-modal signals from historical news, financial knowledge graphs, etc., and the issue of interpreting and explaining the model results. In this paper, we focus on NASDAQ-100 stocks, making use of publicly accessible historical stock price data, company metadata, and historical economic/financial news. We conduct experiments to illustrate the potential of LLMs in offering a unified solution to the aforementioned challenges. Our experiments include trying zero-shot/few-shot inference with GPT-4 and instruction-based fine-tuning with a public LLM model Open LLaMA. We demonstrate our approach outperforms a few baselines, including the widely applied classic ARMA-GARCH model and a gradient-boosting tree model. Through the performance comparison results and a few examples, we find LLMs can make a well-thought decision by reasoning over information from both textual news and price time series and extracting insights, leveraging cross-sequence information, and utilizing the inherent knowledge embedded within the LLM. Additionally, we show that a publicly available LLM such as Open-LLaMA, after fine-tuning, can comprehend the instruction to generate explainable forecasts and achieve reasonable performance, albeit relatively inferior in comparison to GPT-4.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/681253389d2cc27103753749f4c7556699d55471" target='_blank'>Temporal Data Meets LLM - Explainable Financial Time Series Forecasting</a></td>
-          <td>
-            Xinli Yu, Zheng Chen, Yuan Ling, Shujing Dong, Zongying Liu, Yanbin Lu
-          </td>
-          <td>2023-06-19</td>
-          <td>ArXiv</td>
-          <td>34</td>
-          <td>8</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277.md b/docs/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277.md
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Time-LLM: Time Series Forecasting by Reprogramming Large Language Models</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Unlike natural language processing and computer vision, the development of Foundation Models (FMs) for time series forecasting is blocked due to data scarcity. While recent efforts are focused on building such FMs by unlocking the potential of language models (LMs) for time series analysis, dedicated parameters for various downstream forecasting tasks need training, which hinders the common knowledge sharing across domains. Moreover, data owners may hesitate to share the access to local data due to privacy concerns and copyright protection, which makes it impossible to simply construct a FM on cross-domain training instances. To address these issues, we propose Time-FFM, a Federated Foundation Model for Time series forecasting by leveraging pretrained LMs. Specifically, we begin by transforming time series into the modality of text tokens. To bootstrap LMs for time series reasoning, we propose a prompt adaption module to determine domain-customized prompts dynamically instead of artificially. Given the data heterogeneity across domains, we design a personalized federated training strategy by learning global encoders and local prediction heads. Our comprehensive experiments indicate that Time-FFM outperforms state-of-the-arts and promises effective few-shot and zero-shot forecaster.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68a65925ac6d270ca27a4fe99e58cf2ed0795821" target='_blank'>Time-FFM: Towards LM-Empowered Federated Foundation Model for Time Series Forecasting</a></td>
-          <td>
-            Qingxiang Liu, Xu Liu, Chenghao Liu, Qingsong Wen, Yuxuan Liang
-          </td>
-          <td>2024-05-23</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="Time-series forecasting (TSF) finds broad applications in real-world scenarios. Prompting off-the-shelf Large Language Models (LLMs) demonstrates strong zero-shot TSF capabilities while preserving computational efficiency. However, existing prompting methods oversimplify TSF as language next-token predictions, overlooking its dynamic nature and lack of integration with state-of-the-art prompt strategies such as Chain-of-Thought. Thus, we propose LSTPrompt, a novel approach for prompting LLMs in zero-shot TSF tasks. LSTPrompt decomposes TSF into short-term and long-term forecasting sub-tasks, tailoring prompts to each. LSTPrompt guides LLMs to regularly reassess forecasting mechanisms to enhance adaptability. Extensive evaluations demonstrate consistently better performance of LSTPrompt than existing prompting methods, and competitive results compared to foundation TSF models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bbf272d92b76cc5f1e6f793dcfeb5edd4abed7ef" target='_blank'>LSTPrompt: Large Language Models as Zero-Shot Time Series Forecasters by Long-Short-Term Prompting</a></td>
-          <td>
-            Haoxin Liu, Zhiyuan Zhao, Jindong Wang, Harshavardhan Kamarthi, B. A. Prakash
-          </td>
-          <td>2024-02-25</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="This paper presents a new perspective on time series forecasting. In existing time series forecasting methods, the models take a sequence of numerical values as input and yield numerical values as output. The existing SOTA models are largely based on the Transformer architecture, modified with multiple encoding mechanisms to incorporate the context and semantics around the historical data. Inspired by the successes of pre-trained language foundation models, we pose a question about whether these models can also be adapted to solve time-series forecasting. Thus, we propose a new forecasting paradigm: prompt-based time series forecasting (PromptCast). In this novel task, the numerical input and output are transformed into prompts and the forecasting task is framed in a sentence-to-sentence manner, making it possible to directly apply language models for forecasting purposes. To support and facilitate the research of this task, we also present a large-scale dataset (PISA) that includes three real-world forecasting scenarios. We evaluate different SOTA numerical-based forecasting methods and language generation models. The benchmark results with various forecasting settings demonstrate the proposed PromptCast with language generation models is a promising research direction. Additionally, in comparison to conventional numerical-based forecasting, PromptCast shows a much better generalization ability under the zero-shot setting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/863171ed35ca0035074f73bb202b153cc346f2f3" target='_blank'>PromptCast: A New Prompt-Based Learning Paradigm for Time Series Forecasting</a></td>
-          <td>
-            Hao Xue, Flora D.Salim
-          </td>
-          <td>2022-09-20</td>
-          <td>IEEE Transactions on Knowledge and Data Engineering</td>
-          <td>56</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="Inspired by Large Language Models (LLMs), Time Series Forecasting (TSF), a long-standing task in time series analysis, is undergoing a transition towards Large Time Series Models (LTSMs), aiming to train universal transformer-based models for TSF. However, training LTSMs on heterogeneous time series data poses unique challenges, including diverse frequencies, dimensions, and patterns across datasets. Recent endeavors have studied and evaluated various design choices aimed at enhancing LTSM training and generalization capabilities, spanning pre-processing techniques, model configurations, and dataset configurations. In this work, we comprehensively analyze these design choices and aim to identify the best practices for training LTSM. Moreover, we propose \emph{time series prompt}, a novel statistical prompting strategy tailored to time series data. Furthermore, based on the observations in our analysis, we introduce \texttt{LTSM-bundle}, which bundles the best design choices we have identified. Empirical results demonstrate that \texttt{LTSM-bundle} achieves superior zero-shot and few-shot performances compared to state-of-the-art LSTMs and traditional TSF methods on benchmark datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/631c05be8806b43fac7aaf4d041de59562ac17f9" target='_blank'>Understanding Different Design Choices in Training Large Time Series Models</a></td>
-          <td>
-            Yu-Neng Chuang, Songchen Li, Jiayi Yuan, Guanchu Wang, Kwei-Herng Lai, Leisheng Yu, Sirui Ding, Chia-yuan Chang, Qiaoyu Tan, D. Zha, Xia Hu
-          </td>
-          <td>2024-06-20</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>22</td>
-        </tr>
-    
-        <tr id="Time series data are ubiquitous across various domains, making time series analysis critically important. Traditional time series models are task-specific, featuring singular functionality and limited generalization capacity. Recently, large language foundation models have unveiled their remarkable capabilities for cross-task transferability, zero-shot/few-shot learning, and decision-making explainability. This success has sparked interest in the exploration of foundation models to solve multiple time series challenges simultaneously. There are two main research lines, namely pre-training foundation models from scratch for time series and adapting large language foundation models for time series. They both contribute to the development of a unified model that is highly generalizable, versatile, and comprehensible for time series analysis. This survey offers a 3E analytical framework for comprehensive examination of related research. Specifically, we examine existing works from three dimensions, namely Effectiveness, Efficiency and Explainability. In each dimension, we focus on discussing how related works devise tailored solution by considering unique challenges in the realm of time series. Furthermore, we provide a domain taxonomy to help followers keep up with the domain-specific advancements. In addition, we introduce extensive resources to facilitate the field's development, including datasets, open-source, time series libraries. A GitHub repository is also maintained for resource updates (https://github.com/start2020/Awesome-TimeSeries-LLM-FM).">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/522828823ff726598675971036fff01b57320578" target='_blank'>A Survey of Time Series Foundation Models: Generalizing Time Series Representation with Large Language Model</a></td>
-          <td>
-            Jiexia Ye, Weiqi Zhang, Ke Yi, Yongzi Yu, Ziyue Li, Jia Li, F. Tsung
-          </td>
-          <td>2024-05-03</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>47</td>
-        </tr>
-    
-        <tr id="Recent Transformer-based large language models (LLMs) demonstrate in-context learning ability to perform various functions based solely on the provided context, without updating model parameters. To fully utilize the in-context capabilities in time series forecasting (TSF) problems, unlike previous Transformer-based or LLM-based time series forecasting methods, we reformulate"time series forecasting tasks"as input tokens by constructing a series of (lookback, future) pairs within the tokens. This method aligns more closely with the inherent in-context mechanisms, and is more parameter-efficient without the need of using pre-trained LLM parameters. Furthermore, it addresses issues such as overfitting in existing Transformer-based TSF models, consistently achieving better performance across full-data, few-shot, and zero-shot settings compared to previous architectures.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3777e8d6cda553cbd9e3bbd6484e613386f3a59e" target='_blank'>In-context Time Series Predictor</a></td>
-          <td>
-            Jiecheng Lu, Yan Sun, Shihao Yang
-          </td>
-          <td>2024-05-23</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Multivariate time-series forecasting is vital in various domains, e.g., economic planning and weather prediction. Deep train-from-scratch models have exhibited effective performance yet require large amounts of data, which limits real-world applicability. Recently, researchers have leveraged the representation learning transferability of pre-trained Large Language Models (LLMs) to handle limited non-linguistic datasets effectively. However, incorporating LLMs with time-series data presents challenges of limited adaptation due to different compositions between time-series and linguistic data, and the inability to process multi-scale temporal information. To tackle these challenges, we propose LLM4TS, a framework for time-series forecasting with pre-trained LLMs. LLM4TS consists of a two-stage fine-tuning strategy: the \textit{time-series alignment} stage to align LLMs with the nuances of time-series data, and the \textit{forecasting fine-tuning} stage for downstream time-series forecasting tasks. Furthermore, our framework features a novel two-level aggregation method that integrates multi-scale temporal data within pre-trained LLMs, enhancing their ability to interpret time-specific information. In experiments across 7 time-series forecasting datasets, LLM4TS is superior to existing state-of-the-art methods compared with trained-from-scratch models in full-shot scenarios, and also achieves an average improvement of 6.84% in MSE in few-shot scenarios. In addition, evaluations compared with different self-supervised learning approaches highlight LLM4TS's effectiveness with representation learning in forecasting tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/663dc434fabc1cf1d3e85fff3f7ddcd313035d18" target='_blank'>LLM4TS: Aligning Pre-Trained LLMs as Data-Efficient Time-Series Forecasters</a></td>
-          <td>
-            Ching Chang, Wenjie Peng, Tien-Fu Chen
-          </td>
-          <td>2023-08-16</td>
-          <td>ArXiv</td>
-          <td>15</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Large language models (LLMs) are being applied to time series tasks, particularly time series forecasting. However, are language models actually useful for time series? After a series of ablation studies on three recent and popular LLM-based time series forecasting methods, we find that removing the LLM component or replacing it with a basic attention layer does not degrade the forecasting results -- in most cases the results even improved. We also find that despite their significant computational cost, pretrained LLMs do no better than models trained from scratch, do not represent the sequential dependencies in time series, and do not assist in few-shot settings. Additionally, we explore time series encoders and reveal that patching and attention structures perform similarly to state-of-the-art LLM-based forecasters.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/df0d604b8e8e3b2947d9865d735f204c08635012" target='_blank'>Are Language Models Actually Useful for Time Series Forecasting?</a></td>
-          <td>
-            Mingtian Tan, Mike A. Merrill, Vinayak Gupta, Tim Althoff, Tom Hartvigsen
-          </td>
-          <td>2024-06-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Motivated by recent advances in large language models for Natural Language Processing (NLP), we design a time-series foundation model for forecasting whose out-of-the-box zero-shot performance on a variety of public datasets comes close to the accuracy of state-of-the-art supervised forecasting models for each individual dataset. Our model is based on pretraining a patched-decoder style attention model on a large time-series corpus, and can work well across different forecasting history lengths, prediction lengths and temporal granularities.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f45f85fa1beaa795c24c4ff86f1f2deece72252f" target='_blank'>A decoder-only foundation model for time-series forecasting</a></td>
-          <td>
-            Abhimanyu Das, Weihao Kong, Rajat Sen, Yichen Zhou
-          </td>
-          <td>2023-10-14</td>
-          <td>ArXiv</td>
-          <td>45</td>
-          <td>14</td>
-        </tr>
-    
-        <tr id="Foundation models of time series have not been fully developed due to the limited availability of time series corpora and the underexploration of scalable pre-training. Based on the similar sequential formulation of time series and natural language, increasing research demonstrates the feasibility of leveraging large language models (LLM) for time series. Nevertheless, the inherent autoregressive property and decoder-only architecture of LLMs have not been fully considered, resulting in insufficient utilization of LLM abilities. To further exploit the general-purpose token transition and multi-step generation ability of large language models, we propose AutoTimes to repurpose LLMs as autoregressive time series forecasters, which independently projects time series segments into the embedding space and autoregressively generates future predictions with arbitrary lengths. Compatible with any decoder-only LLMs, the consequent forecaster exhibits the flexibility of the lookback length and scalability of the LLM size. Further, we formulate time series as prompts, extending the context for prediction beyond the lookback window, termed in-context forecasting. By adopting textual timestamps as position embeddings, AutoTimes integrates multimodality for multivariate scenarios. Empirically, AutoTimes achieves state-of-the-art with 0.1% trainable parameters and over 5 times training/inference speedup compared to advanced LLM-based forecasters.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d488445bb2bf6719bc48a4d39bd906116274abda" target='_blank'>AutoTimes: Autoregressive Time Series Forecasters via Large Language Models</a></td>
-          <td>
-            Yong Liu, Guo Qin, Xiangdong Huang, Jianmin Wang, Mingsheng Long
-          </td>
-          <td>2024-02-04</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>65</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Graph-Mamba: Towards Long-Range Graph Sequence Modeling with Selective State Spaces</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We propose a heterogeneous graph mamba network (HGMN) as the first exploration in leveraging the selective state space models (SSSMs) for heterogeneous graph learning. Compared with the literature, our HGMN overcomes two major challenges: (i) capturing long-range dependencies among heterogeneous nodes and (ii) adapting SSSMs to heterogeneous graph data. Our key contribution is a general graph architecture that can solve heterogeneous nodes in real-world scenarios, followed an efficient flow. Methodologically, we introduce a two-level efficient tokenization approach that first captures long-range dependencies within identical node types, and subsequently across all node types. Empirically, we conduct comparisons between our framework and 19 state-of-the-art methods on the heterogeneous benchmarks. The extensive comparisons demonstrate that our framework outperforms other methods in both the accuracy and efficiency dimensions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/55fce293c79bbb9bdec86d25c8a3896f426a0549" target='_blank'>HeteGraph-Mamba: Heterogeneous Graph Learning via Selective State Space Model</a></td>
-          <td>
-            Zhenyu Pan, Yoonsung Jeong, Xiaoda Liu, Han Liu
-          </td>
-          <td>2024-05-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Graph Neural Networks (GNNs) have shown promising potential in graph representation learning. The majority of GNNs define a local message-passing mechanism, propagating information over the graph by stacking multiple layers. These methods, however, are known to suffer from two major limitations: over-squashing and poor capturing of long-range dependencies. Recently, Graph Transformers (GTs) emerged as a powerful alternative to Message-Passing Neural Networks (MPNNs). GTs, however, have quadratic computational cost, lack inductive biases on graph structures, and rely on complex Positional/Structural Encodings (SE/PE). In this paper, we show that while Transformers, complex message-passing, and SE/PE are sufficient for good performance in practice, neither is necessary. Motivated by the recent success of State Space Models (SSMs), such as Mamba, we present Graph Mamba Networks (GMNs), a general framework for a new class of GNNs based on selective SSMs. We discuss and categorize the new challenges when adapting SSMs to graph-structured data, and present four required and one optional steps to design GMNs, where we choose (1) Neighborhood Tokenization, (2) Token Ordering, (3) Architecture of Bidirectional Selective SSM Encoder, (4) Local Encoding, and dispensable (5) PE and SE. We further provide theoretical justification for the power of GMNs. Experiments demonstrate that despite much less computational cost, GMNs attain an outstanding performance in long-range, small-scale, large-scale, and heterophilic benchmark datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2dda6da7375bf5e8bcf60f87b17ba10757f3bc57" target='_blank'>Graph Mamba: Towards Learning on Graphs with State Space Models</a></td>
-          <td>
-            Ali Behrouz, Farnoosh Hashemi
-          </td>
-          <td>2024-02-13</td>
-          <td>ArXiv</td>
-          <td>30</td>
-          <td>8</td>
-        </tr>
-    
-        <tr id="Message-passing graph neural networks (GNNs), while excelling at capturing local relationships, often struggle with long-range dependencies on graphs. Conversely, graph transformers (GTs) enable information exchange between all nodes but oversimplify the graph structure by treating them as a set of fixed-length vectors. This work proposes a novel architecture, NeuralWalker, that overcomes the limitations of both methods by combining random walks with message passing. NeuralWalker achieves this by treating random walks as sequences, allowing for the application of recent advances in sequence models in order to capture long-range dependencies within these walks. Based on this concept, we propose a framework that offers (1) more expressive graph representations through random walk sequences, (2) the ability to utilize any sequence model for capturing long-range dependencies, and (3) the flexibility by integrating various GNN and GT architectures. Our experimental evaluations demonstrate that NeuralWalker achieves significant performance improvements on 19 graph and node benchmark datasets, notably outperforming existing methods by up to 13% on the PascalVoc-SP and COCO-SP datasets. Code is available at https://github.com/BorgwardtLab/NeuralWalker.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0702ac9db3ea20810ffdb9f35bde85cdfaf27a3d" target='_blank'>Learning Long Range Dependencies on Graphs via Random Walks</a></td>
-          <td>
-            Dexiong Chen, Till Hendrik Schulz, Karsten Borgwardt
-          </td>
-          <td>2024-06-05</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>8</td>
-        </tr>
-    
-        <tr id="Machine learning on graphs has recently found extensive applications across domains. However, the commonly used Message Passing Neural Networks (MPNNs) suffer from limited expressive power and struggle to capture long-range dependencies. Graph transformers offer a strong alternative due to their global attention mechanism, but they come with great computational overheads, especially for large graphs. In recent years, State Space Models (SSMs) have emerged as a compelling approach to replace full attention in transformers to model sequential data. It blends the strengths of RNNs and CNNs, offering a) efficient computation, b) the ability to capture long-range dependencies, and c) good generalization across sequences of various lengths. However, extending SSMs to graph-structured data presents unique challenges due to the lack of canonical node ordering in graphs. In this work, we propose Graph State Space Convolution (GSSC) as a principled extension of SSMs to graph-structured data. By leveraging global permutation-equivariant set aggregation and factorizable graph kernels that rely on relative node distances as the convolution kernels, GSSC preserves all three advantages of SSMs. We demonstrate the provably stronger expressiveness of GSSC than MPNNs in counting graph substructures and show its effectiveness across 10 real-world, widely used benchmark datasets, where GSSC achieves best results on 7 out of 10 datasets with all significant improvements compared to the state-of-the-art baselines and second-best results on the other 3 datasets. Our findings highlight the potential of GSSC as a powerful and scalable model for graph machine learning. Our code is available at https://github.com/Graph-COM/GSSC.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/93a9b7940e902f989e27f94061d3b699a2fc4d13" target='_blank'>What Can We Learn from State Space Models for Machine Learning on Graphs?</a></td>
-          <td>
-            Yinan Huang, Siqi Miao, Pan Li
-          </td>
-          <td>2024-06-09</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Graph representation learning (GRL) is fundamental in multi-graph applications like molecular property prediction. Graph neural networks (GNNs) have emerged as a popular method for GRL. However, existing GRL methods primarily focus on designing GNN models with enhanced expressiveness while overlooking the memory efficiency of algorithms during training. The memory inefficiency problem is caused by a contextual constraint imposed on node representations, which requires each node to be context-dependent on its input graph. In this paper, we propose a novel method, called context sketching (COS), for memory-efficient graph representation learning in multi-graph scenarios. We first formally define the contextual constraint based on the enclosed $\infty-$hop subgraphs of nodes. Subsequently, we propose to relax the original contextual constraint by requiring each node to be context-dependent on its enclosed $k-$hop subgraph $(k \ll \infty)$ which is a contextual sketch of the enclosed $\infty$-hop subgraph. Lastly, we prove that COS constructs an optimal solution to a memory-related objective associated with graph coarsening. Experiments on four widely used benchmark datasets demonstrate that COS can reduce the memory footprint of baselines by a large margin with almost no accuracy loss.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/54288b7e9ce29a338f2b11981c6b84f4f0cb9a50" target='_blank'>Context Sketching for Memory-efficient Graph Representation Learning</a></td>
-          <td>
-            Kai-Lang Yao, Wusuo Li
-          </td>
-          <td>2023-12-01</td>
-          <td>2023 IEEE International Conference on Data Mining (ICDM)</td>
-          <td>0</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="Graph Neural Networks (GNNs) have shown impressive performance in graph representation learning, but they face challenges in capturing long-range dependencies due to their limited expressive power. To address this, Graph Transformers (GTs) were introduced, utilizing self-attention mechanism to effectively model pairwise node relationships. Despite their advantages, GTs suffer from quadratic complexity w.r.t. the number of nodes in the graph, hindering their applicability to large graphs. In this work, we present Graph-Enhanced Contextual Operator (GECO), a scalable and effective alternative to GTs that leverages neighborhood propagation and global convolutions to effectively capture local and global dependencies in quasilinear time. Our study on synthetic datasets reveals that GECO reaches 169x speedup on a graph with 2M nodes w.r.t. optimized attention. Further evaluations on diverse range of benchmarks showcase that GECO scales to large graphs where traditional GTs often face memory and time limitations. Notably, GECO consistently achieves comparable or superior quality compared to baselines, improving the SOTA up to 4.5%, and offering a scalable and effective solution for large-scale graph learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/48052c9ebe066b9fcd653897dabf18582ec7e7fb" target='_blank'>A Scalable and Effective Alternative to Graph Transformers</a></td>
-          <td>
-            Kaan Sancak, Zhigang Hua, Jin Fang, Yan Xie, Andrey Malevich, Bo Long, M. F. Balin, Ümit V. Çatalyürek
-          </td>
-          <td>2024-06-17</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="The Transformer architecture has achieved remarkable success in a number of domains including natural language processing and computer vision. However, when it comes to graph-structured data, transformers have not achieved competitive performance, especially on large graphs. In this paper, we identify the main deficiencies of current graph transformers:(1) Existing node sampling strategies in Graph Transformers are agnostic to the graph characteristics and the training process. (2) Most sampling strategies only focus on local neighbors and neglect the long-range dependencies in the graph. We conduct experimental investigations on synthetic datasets to show that existing sampling strategies are sub-optimal. To tackle the aforementioned problems, we formulate the optimization strategies of node sampling in Graph Transformer as an adversary bandit problem, where the rewards are related to the attention weights and can vary in the training procedure. Meanwhile, we propose a hierarchical attention scheme with graph coarsening to capture the long-range interactions while reducing computational complexity. Finally, we conduct extensive experiments on real-world datasets to demonstrate the superiority of our method over existing graph transformers and popular GNNs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5152b9391762aefc532f85a801093bd38a6688c6" target='_blank'>Hierarchical Graph Transformer with Adaptive Node Sampling</a></td>
-          <td>
-            Zaixin Zhang, Qi Liu, Qingyong Hu, Cheekong Lee
-          </td>
-          <td>2022-10-08</td>
-          <td>ArXiv</td>
-          <td>57</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="Transformer-based models have recently shown success in representation learning on graph-structured data beyond natural language processing and computer vision. However, the success is limited to small-scale graphs due to the drawbacks of full dot-product attention on graphs such as the quadratic complexity with respect to the number of nodes and message aggregation from enormous irrelevant nodes. To address these issues, we propose Deformable Graph Transformer (DGT) that performs sparse attention via dynamically sampled relevant nodes for efficiently handling large-scale graphs with a linear complexity in the number of nodes. Specifically, our framework first constructs multiple node sequences with various criteria to consider both structural and semantic proximity. Then, combining with our learnable Katz Positional Encodings, the sparse attention is applied to the node sequences for learning node representations with a significantly reduced computational cost. Extensive experiments demonstrate that our DGT achieves state-of-the-art performance on 7 graph benchmark datasets with 2.5 - 449 times less computational cost compared to transformer-based graph models with full attention.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1fb264b21eaf9046387ffddd7a8bf5262674682c" target='_blank'>Deformable Graph Transformer</a></td>
-          <td>
-            Jinyoung Park, Seongjun Yun, Hyeon-ju Park, Jaewoo Kang, Jisu Jeong, KyungHyun Kim, Jung-Woo Ha, Hyunwoo J. Kim
-          </td>
-          <td>2022-06-29</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>27</td>
-        </tr>
-    
-  </tbody>
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-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/2232751169e57a14723bfffb4ab26aa0e0e3839a.md b/docs/recommendations/2232751169e57a14723bfffb4ab26aa0e0e3839a.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:06:26 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Rediscovering orbital mechanics with machine learning</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true force vector when trained on n-body gravitational and spring-like simulations. We use symbolic regression to fit explicit algebraic equations to our trained model's message function and recover the symbolic form of Newton's law of gravitation without prior knowledge. We also show that our model generalizes better at inference time to systems with more bodies than had been experienced during training. Our approach is extensible, in principle, to any unknown interaction law learned by a graph network, and offers a valuable technique for interpreting and inferring explicit causal theories about the world from implicit knowledge captured by deep learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a6aad9ccdcb7674a3b7ab710f0a80d205834f847" target='_blank'>Learning Symbolic Physics with Graph Networks</a></td>
-          <td>
-            M. Cranmer, Rui Xu, P. Battaglia, S. Ho
-          </td>
-          <td>2019-09-12</td>
-          <td>ArXiv</td>
-          <td>77</td>
-          <td>68</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e87f78aebc1966defb271e39d09f5f0939c79e05" target='_blank'>Celestial Machine Learning - From Data to Mars and Beyond with AI Feynman</a></td>
-          <td>
-            Zi-Yu Khoo, A. Yang, J. Low, S. Bressan
-          </td>
-          <td>2023-12-15</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>32</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f97840db878f0eff149e999a73c52afc15fb44e3" target='_blank'>Celestial Machine Learning - Discovering the Planarity, Heliocentricity, and Orbital Equation of Mars with AI Feynman</a></td>
-          <td>
-            Zi-Yu Khoo, Gokul Rajiv, Abel Yang, Jonathan Sze Choong Low, Stéphane Bressan
-          </td>
-          <td>2023-12-19</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="We present AI Poincaré, a machine learning algorithm for autodiscovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational three-body problem, and find that it discovers not only all exactly conserved quantities, but also periodic orbits, phase transitions, and breakdown timescales for approximate conservation laws.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f3cf4756b2375cd6694267370a8d98543e781169" target='_blank'>Machine Learning Conservation Laws from Trajectories.</a></td>
-          <td>
-            Ziming Liu, Max Tegmark
-          </td>
-          <td>2021-05-06</td>
-          <td>Physical review letters</td>
-          <td>80</td>
-          <td>81</td>
-        </tr>
-    
-        <tr id="The number of satellites in orbit around Earth is increasing rapidly, with the risk of collision rising accordingly. Trends of the global population of satellites need to be analyzed to test the viability and impact of proposed rules and laws affecting the satellite population and collision avoidance strategies. This requires large scale simulations of satellites that are propagated on long timescales to compute the large amounts of actionable close encounters (called conjunctions), which could lead to collisions. Rigorously checking for conjunctions by computing future states of orbits is computationally expensive due to the large amount of objects involved and conjunction filters are thus used to remove non-conjuncting orbit pairs from the list of possible conjunctions. In this work, we explore the possibility of machine learning (ML) based conjunction filters using several algorithms such as eXtreme Gradient Boosting, TabNet and (physics-informed) neural networks and deep operator networks. To show the viability and the potential of ML based filters, these algorithms are trained to predict the future state of orbits. For the physics-informed approaches, multiple partial differential equations are set up using the Kepler equation as a basis. The empirical results demonstrate that physics-informed deep operator networks are capable of predicting the future state of orbits using these equations (RMSE: 0.136) and outperform eXtreme Gradient Boosting (RMSE: 0.568) and TabNet (RMSE: 0.459). We also propose a filter based on the trained deep operator network which is shown to outperforms the filter capability of the commonly used perigee-apogee test and the orbit path filter on a synthetic dataset, while being on average 3.2 times faster to compute than a rigorous conjunction check.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/754f540bfee6d9148c13650da01d1de68e56a6e5" target='_blank'>Machine learning meets Kepler: inverting Kepler’s equation for All vs All conjunction analysis</a></td>
-          <td>
-            Kevin Thomas Jordi Otto, Simon Burgis, K. Kersting, Reinhold Bertrand, Devendra Singh Dhami
-          </td>
-          <td>2024-05-29</td>
-          <td>Machine Learning: Science and Technology</td>
-          <td>0</td>
-          <td>8</td>
-        </tr>
-    
-        <tr id="Most problems in Earth sciences aim to do inferences about the system, where accurate predictions are just a tiny part of the whole problem. Inferences mean understanding variables relations, deriving models that are physically interpretable, that are simple parsimonious, and mathematically tractable. Machine learning models alone are excellent approximators, but very often do not respect the most elementary laws of physics, like mass or energy conservation, so consistency and confidence are compromised. In this paper, we describe the main challenges ahead in the field, and introduce several ways to live in the Physics and machine learning interplay: to encode differential equations from data, constrain data-driven models with physics-priors and dependence constraints, improve parameterizations, emulate physical models, and blend data-driven and process-based models. This is a collective long-term AI agenda towards developing and applying algorithms capable of discovering knowledge in the Earth system.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5edea84373b72e73a29b0348e388b4d458664dbd" target='_blank'>Living in the Physics and Machine Learning Interplay for Earth Observation</a></td>
-          <td>
-            Gustau Camps-Valls, D. Svendsen, Jordi Cort'es-Andr'es, 'Alvaro Moreno-Mart'inez, Adri'an P'erez-Suay, J. Adsuara, I. Mart'in, M. Piles, Jordi Munoz-Mar'i, Luca Martino
-          </td>
-          <td>2020-10-18</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>77</td>
-        </tr>
-    
-        <tr id="The Observation--Hypothesis--Prediction--Experimentation loop paradigm for scientific research has been practiced by researchers for years towards scientific discoveries. However, with data explosion in both mega-scale and milli-scale scientific research, it has been sometimes very difficult to manually analyze the data and propose new hypotheses to drive the cycle for scientific discovery. In this paper, we discuss the role of Explainable AI in scientific discovery process by demonstrating an Explainable AI-based paradigm for science discovery. The key is to use Explainable AI to help derive data or model interpretations, hypotheses, as well as scientific discoveries or insights. We show how computational and data-intensive methodology -- together with experimental and theoretical methodology -- can be seamlessly integrated for scientific research. To demonstrate the AI-based science discovery process, and to pay our respect to some of the greatest minds in human history, we show how Kepler's laws of planetary motion and Newton's law of universal gravitation can be rediscovered by (Explainable) AI based on Tycho Brahe's astronomical observation data, whose works were leading the scientific revolution in the 16-17th century. This work also highlights the important role of Explainable AI (as compared to Blackbox AI) in science discovery to help humans prevent or better prepare for the possible technological singularity that may happen in the future, since science is not only about the know how, but also the know why. Presentation of the work is available at https://slideslive.com/38986142/from-kepler-to-newton-explainable-ai-for-science-discovery.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2b1143fbed61617fcc27633dd9452a627edb5c99" target='_blank'>From Kepler to Newton: Explainable AI for Science Discovery</a></td>
-          <td>
-            Zelong Li, Jianchao Ji, Yongfeng Zhang
-          </td>
-          <td>2021-11-24</td>
-          <td>ArXiv</td>
-          <td>12</td>
-          <td>10</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/23c7b93a379c26c3738921282771e1a545538703.md b/docs/recommendations/23c7b93a379c26c3738921282771e1a545538703.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:06:58 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Solving real-world optimization tasks using physics-informed neural computing</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Optimizing the fuel cycle cost through the optimization of nuclear reactor core loading patterns involves multiple objectives and constraints, leading to a vast number of candidate solutions that cannot be explicitly solved. To advance the state-of-the-art in core reload patterns, we have developed methods based on Deep Reinforcement Learning (DRL) for both single- and multi-objective optimization. Our previous research has laid the groundwork for these approaches and demonstrated their ability to discover high-quality patterns within a reasonable time frame. On the other hand, stochastic optimization (SO) approaches are commonly used in the literature, but there is no rigorous explanation that shows which approach is better in which scenario. In this paper, we demonstrate the advantage of our RL-based approach, specifically using Proximal Policy Optimization (PPO), against the most commonly used SO-based methods: Genetic Algorithm (GA), Parallel Simulated Annealing (PSA) with mixing of states, and Tabu Search (TS), as well as an ensemble-based method, Prioritized Replay Evolutionary and Swarm Algorithm (PESA). We found that the LP scenarios derived in this paper are amenable to a global search to identify promising research directions rapidly, but then need to transition into a local search to exploit these directions efficiently and prevent getting stuck in local optima. PPO adapts its search capability via a policy with learnable weights, allowing it to function as both a global and local search method. Subsequently, we compared all algorithms against PPO in long runs, which exacerbated the differences seen in the shorter cases. Overall, the work demonstrates the statistical superiority of PPO compared to the other considered algorithms.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0541f363cd64cc0a196357699559c05301d66b61" target='_blank'>Surpassing legacy approaches to PWR core reload optimization with single-objective Reinforcement learning</a></td>
-          <td>
-            Paul Seurin, K. Shirvan
-          </td>
-          <td>2024-02-16</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>22</td>
-        </tr>
-    
-        <tr id="We present an open-source Python framework for NeuroEvolution Optimization with Reinforcement Learning (NEORL) developed at the Massachusetts Institute of Technology. NEORL offers a global optimization interface of state-of-the-art algorithms in the field of evolutionary computation, neural networks through reinforcement learning, and hybrid neuroevolution algorithms. NEORL features diverse set of algorithms, user-friendly interface, parallel computing support, automatic hyperparameter tuning, detailed documentation, and demonstration of applications in mathematical and real-world engineering optimization. NEORL encompasses various optimization problems from combinatorial, continuous, mixed discrete/continuous, to high-dimensional, expensive, and constrained engineering optimization. NEORL is tested in variety of engineering applications relevant to low carbon energy research in addressing solutions to climate change. The examples include nuclear reactor control and fuel cell power production. The results demonstrate NEORL competitiveness against other algorithms and optimization frameworks in the literature, and a potential tool to solve large-scale optimization problems. More examples and benchmarking of NEORL can be found here: https://neorl.readthedocs.io/en/latest/index.html">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/33eb8f2acbaceeef39928028d4fc19116b327233" target='_blank'>NEORL: NeuroEvolution Optimization with Reinforcement Learning</a></td>
-          <td>
-            M. Radaideh, Katelin Du, Paul Seurin, Devin Seyler, Xubo Gu, Haijiang Wang, K. Shirvan
-          </td>
-          <td>2021-12-01</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>22</td>
-        </tr>
-    
-        <tr id="Significance The scientific and engineering field has long sought an optimization method that is both efficient and accurate. While combining evolutionary algorithms with deep-learning methods offers a viable solution for complex problems, the simple combination does not achieve accurate and efficient optimization due to the nature of evolutionary principles, even with well-trained deep-learning models. We introduce a physics-supervised deep-learning optimization (PSDLO) algorithm that significantly improves convergence speed while maintaining optimization accuracy. PSDLO’s mechanism and demonstration are clearly explained and verified, presenting an ideal optimization method for various science and engineering applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ed82ec82355b994906271b5a1dd22f51f3606ba2" target='_blank'>Physics-supervised deep learning–based optimization (PSDLO) with accuracy and efficiency</a></td>
-          <td>
-            Xiaowen Li, Lige Chang, Yajun Cao, Junqiang Lu, Xiaoli Lu, Hanqing Jiang
-          </td>
-          <td>2023-08-21</td>
-          <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>2</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="This paper proposes a descent reward (DR) system to enhance agent's navigation and landing capabilities in the LunarLander-v2 environment provided by OpenAI. The DR system is evaluated with Heuristics Control, Linear Function Approximation (LFA), and Deep Q-Networks (DQN) algorithms. Results demonstrate that the DQN algorithm with DR achieves a 97% average success rate, improving 17% over the Heuristic baseline and 37% over the default reward DQN in terms of fuel consumption. Furthermore, the resilience of DQN, Double Deep Q-Networks (Double-DQN), and Dueling Deep Q-Networks (Dueling-DQN) with the proposed DR system is evaluated. Despite increased unpredictability, results show the DR system effectively augments agent learning and decision-making. The Double-DQN approach exhibits superior stability and reward achievement compared to DQN and Dueling-DQN.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b6e7434e7d08f02865c12654dd8da1440e8097c6" target='_blank'>Deep Reinforcement Learning for Unpredictability-Induced Rewards to Handle Spacecraft Landing</a></td>
-          <td>
-            Salman Shah, Nianmin Yao
-          </td>
-          <td>2023-12-08</td>
-          <td>2023 13th International Conference on Information Science and Technology (ICIST)</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="Aerobraking is used to insert a spacecraft into a low orbit around a planet through many orbital passages into its complex atmosphere. The aerobraking atmospheric passages are challenging because of the high variability of the atmospheric environment. This paper develops a parallel domain randomized deep reinforcement learning architecture for autonomous decision-making in a stochastic environment, such as aerobraking atmospheric passages. In this context, the architecture is used for planning aerobraking maneuvers to avoid the occurrence of thermal violations during the atmospheric aerobraking passages and target a final low-altitude orbit. The parallel domain randomized deep reinforcement learning architecture is designed to account for large variability of the physical model, as well as uncertain conditions. Also, the parallel approach speeds up the training process for simulation-based applications, and domain randomization improves resultant policy generalization. This framework is applied to the 2001 Mars Odyssey aerobraking campaign; with respect to the 2001 Mars Odyssey mission flight data and a Numerical Predictor Corrector (NPC)-based state-of-the-art heuristic for autonomous aerobraking, the proposed architecture outperforms the state-of-the-art heuristic algorithm with a decrease of 97.5% in the number of thermal violations. Furthermore, it yields a reduction of 98.7% in the number of thermal violations with respect to the Mars Odyssey mission flight data and requires 13.9% fewer orbits. Results also show that the proposed architecture can also learn a generalized policy in the presence of strong uncertainties, such as aggressive atmospheric density perturbations, different atmospheric density models, and a different simulator maximum step size and error accuracy.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5671f0558daa773dab04be13a10c7310c5a8e3ae" target='_blank'>Autonomous Decision-Making for Aerobraking via Parallel Randomized Deep Reinforcement Learning</a></td>
-          <td>
-            G. Falcone, Z. Putnam
-          </td>
-          <td>2023-06-01</td>
-          <td>IEEE Transactions on Aerospace and Electronic Systems</td>
-          <td>2</td>
-          <td>14</td>
-        </tr>
-    
-        <tr id="Most optimization problems require the user to select an algorithm and, to some extent, also tune it for better performance. Although intuition and knowledge about the problem can speed up these selection and fine-tuning processes, users often use trial-and-error methodologies, which can be time-consuming and inefficient. With all of that in mind and much more, the concept of "learned optimizers", "learning to learn", and "meta-learning" has been gathering attention in recent years. In this article, we propose MolOpt that uses multiagent reinforcement learning (MARL) for autonomous molecular geometry optimization (MGO). Typically MGO algorithms are hand-designed, but MolOpt uses MARL to learn a learned optimizer (policy) that can perform MGO without the need for other hand-designed optimizers. We cast MGO as a MARL problem, where each agent corresponds to a single atom in the molecule. MolOpt performs MGO by minimizing the forces on each atom of the molecule. Our experiments demonstrate the generalizing ability of MolOpt for the MGO of propane, pentane, heptane, hexane, and octane when trained on ethane, butane, and isobutane. In terms of performance, MolOpt outperforms the MDMin optimizer and demonstrates performance similar to that of the FIRE optimizer. However, it does not surpass the BFGS optimizer. The results demonstrate that MolOpt has the potential to introduce innovative advancements in MGO by providing a novel approach using reinforcement learning (RL), which may open up new research directions for MGO. Overall, this work serves as a proof-of-concept for the potential of MARL in MGO.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b56c230c9f7bb4d90c0cb6e31d8863ff2fadc6b8" target='_blank'>MolOpt: Autonomous Molecular Geometry Optimization Using Multiagent Reinforcement Learning.</a></td>
-          <td>
-            Rohit Modee, Sarvesh Mehta, Siddhartha Laghuvarapu, U. Priyakumar
-          </td>
-          <td>2023-11-27</td>
-          <td>The journal of physical chemistry. B</td>
-          <td>4</td>
-          <td>29</td>
-        </tr>
-    
-        <tr id="This article is a short introduction to AI4OPT, the NSF AI Institute for Advances in Optimization. AI4OPT fuses AI and optimization, inspired by societal challenges in supply chains, energy systems, chip design and manufacturing, and sustainable food systems. By combining machine learning and mathematical optimization, AI4OPT strives to develop AI‐assisted optimization systems that bring orders of magnitude improvements in efficiency, perform accurate uncertainty quantification, and address challenges in resiliency and sustainability. AI4OPT also applies its “teaching the teachers” philosophy to provide longitudinal educational pathways in AI for engineering.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3198a0c86b6f4b943c4abc2fd6f4457ecb7c4581" target='_blank'>AI4OPT: AI Institute for Advances in Optimization</a></td>
-          <td>
-            P. V. Hentenryck, Kevin Dalmeijer
-          </td>
-          <td>2023-07-05</td>
-          <td>AI Mag.</td>
-          <td>1</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b6a3b0b6956e496f726ffe945dc5cdae8718ba43" target='_blank'>A survey on artificial intelligence trends in spacecraft guidance dynamics and control</a></td>
-          <td>
-            D. Izzo, Marcus Märtens, Binfeng Pan
-          </td>
-          <td>2018-12-07</td>
-          <td>Astrodynamics</td>
-          <td>177</td>
-          <td>36</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
-
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diff --git a/docs/recommendations/25903eabbb1830aefa82048212e643eec660de0b.md b/docs/recommendations/25903eabbb1830aefa82048212e643eec660de0b.md
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-    Recommendations for the article <i>Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
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-  </thead>
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-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d86084808994ac54ef4840ae65295f3c0ec4decd" target='_blank'>Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations</a></td>
-          <td>
-            M. Raissi, P. Perdikaris, G. Karniadakis
-          </td>
-          <td>2019-02-01</td>
-          <td>J. Comput. Phys.</td>
-          <td>7319</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part treatise, we present our developments in the context of solving two main classes of problems: data-driven solution and data-driven discovery of partial differential equations. Depending on the nature and arrangement of the available data, we devise two distinct classes of algorithms, namely continuous time and discrete time models. The resulting neural networks form a new class of data-efficient universal function approximators that naturally encode any underlying physical laws as prior information. In this first part, we demonstrate how these networks can be used to infer solutions to partial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fa352e8e4d9ec2f4b66965dd9cea75167950152a" target='_blank'>Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations</a></td>
-          <td>
-            M. Raissi, P. Perdikaris, G. Karniadakis
-          </td>
-          <td>2017-11-28</td>
-          <td>ArXiv</td>
-          <td>753</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical models of the physical world. In the current era of abundance of data and advanced machine learning capabilities, the natural question arises: How can we automatically uncover the underlying laws of physics from high-dimensional data generated from experiments? In this work, we put forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time. Specifically, we approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks. The first network acts as a prior on the unknown solution and essentially enables us to avoid numerical differentiations which are inherently ill-conditioned and unstable. The second network represents the nonlinear dynamics and helps us distill the mechanisms that govern the evolution of a given spatiotemporal data-set. We test the effectiveness of our approach for several benchmark problems spanning a number of scientific domains and demonstrate how the proposed framework can help us accurately learn the underlying dynamics and forecast future states of the system. In particular, we study the Burgers', Korteweg-de Vries (KdV), Kuramoto-Sivashinsky, nonlinear Schr\"{o}dinger, and Navier-Stokes equations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ebcc0e71ef6a77d05e7ab064435bc2da87c55e91" target='_blank'>Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations</a></td>
-          <td>
-            M. Raissi
-          </td>
-          <td>2018-01-20</td>
-          <td>J. Mach. Learn. Res.</td>
-          <td>658</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="Partial differential equations (PDEs) play a pivotal role in mathematical analysis and modeling of dynamic processes across various disciplines of science and engineering. Machine learning (ML) techniques have emerged as a promising new approach to solving PDEs. Among them, Physics-Informed Neural Networks (PINNs) have garnered significant attention in numerous scientific and engineering studies. PINNs employ a single deep neural network to assimilate observational data with PDEs across the entire space-time of a physical system, subsequently yielding rapid solutions. However, a PINN may entail intricate analyses or computations and can be cost-intensive, depending on initial or boundary conditions and other input parameters. To address the limitations of the PINN, especially concerning resolution for nonlinear problems, the Physical-Informed Deep Operator Network (DeepONet) is introduced in this paper. The Physics-Informed DeepONet is a deep learning framework crafted to discern solution operators for any given PDEs, even in scenarios lacking paired input/output training data. The proposed framework is able to predict solutions for various types of parameterized PDEs much faster than conventional PDE solvers. Several cases confirm that this approach is effective in establishing previously unexplored paradigms for modeling/simulating nonlinear and non-equilibrium processes in science and engineering.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/54aa8e27e0e1c52997a21502817afcb71d9e8ccb" target='_blank'>Understanding on Physics-Informed DeepONet</a></td>
-          <td>
-            Sang-Min Lee
-          </td>
-          <td>2024-01-31</td>
-          <td>Journal of the Korea Academia-Industrial cooperation Society</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from scientific data thrives as a new attempt to model complex phenomena in nature, but the effectiveness of current practice is typically limited by the scarcity of data and the complexity of phenomena. Especially, the discovery of PDEs with highly nonlinear coefficients from low-quality data remains largely under-addressed. To deal with this challenge, we propose a novel physics-guided learning method, which can not only encode observation knowledge such as initial and boundary conditions but also incorporate the basic physical principles and laws to guide the model optimization. We theoretically show that our proposed method strictly reduces the coefficient estimation error of existing baselines, and is also robust against noise. Extensive experiments show that the proposed method is more robust against data noise, and can reduce the estimation error by a large margin. Moreover, all the PDEs in the experiments are correctly discovered, and for the first time we are able to discover three-dimensional PDEs with highly nonlinear coefficients.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6ba981e4ce8c6bb98c3917bb93507140c9f2b5df" target='_blank'>Physics-Guided Discovery of Highly Nonlinear Parametric Partial Differential Equations</a></td>
-          <td>
-            Yingtao Luo, Qiang Liu, Yuntian Chen, Wenbo Hu, Jun Zhu
-          </td>
-          <td>2021-06-02</td>
-          <td>Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining</td>
-          <td>2</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/43bba6a3bb186e7370366e5c899c90ca9a573820" target='_blank'>Physics Informed Extreme Learning Machine (PIELM) - A rapid method for the numerical solution of partial differential equations</a></td>
-          <td>
-            Vikas Dwivedi, B. Srinivasan
-          </td>
-          <td>2019-07-08</td>
-          <td>ArXiv</td>
-          <td>130</td>
-          <td>14</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e596988b1df3a0bc78bf72c0bfdb21c85eaab6c9" target='_blank'>Physics-informed learning of governing equations from scarce data</a></td>
-          <td>
-            Zhao Chen, Yang Liu, Hao Sun
-          </td>
-          <td>2020-05-05</td>
-          <td>Nature Communications</td>
-          <td>232</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="Significance In many physical systems, the governing equations are known with high confidence, but direct numerical solution is prohibitively expensive. Often this situation is alleviated by writing effective equations to approximate dynamics below the grid scale. This process is often impossible to perform analytically and is often ad hoc. Here we propose data-driven discretization, a method that uses machine learning to systematically derive discretizations for continuous physical systems. On a series of model problems, data-driven discretization gives accurate solutions with a dramatic drop in required resolution. The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length- and timescales. Often, it is computationally intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small-scale physics. Deriving such coarse-grained equations is notoriously difficult and often ad hoc. Here we introduce data-driven discretization, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end to end to best satisfy the equations on a low-resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in 1 spatial dimension at resolutions 4× to 8× coarser than is possible with standard finite-difference methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9a43842478bf9d1aff71e964f584af4eeb196073" target='_blank'>Learning data-driven discretizations for partial differential equations</a></td>
-          <td>
-            Yohai Bar-Sinai, Stephan Hoyer, Jason Hickey, M. Brenner
-          </td>
-          <td>2018-08-15</td>
-          <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>430</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3d6fd15fea21a3a5fff4bf294b67cb959b46008a" target='_blank'>Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations</a></td>
-          <td>
-            Benwei Wu, O. Hennigh, J. Kautz, S. Choudhry, Wonmin Byeon
-          </td>
-          <td>2022-02-24</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>91</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Graph state-space models</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series data. Fully probabilistic SSMs, however, are often found hard to train, even for smaller problems. To overcome this limitation, we propose a novel model formulation and a scalable training algorithm based on doubly stochastic variational inference and Gaussian processes. In contrast to existing work, the proposed variational approximation allows one to fully capture the latent state temporal correlations. These correlations are the key to robust training. The effectiveness of the proposed PR-SSM is evaluated on a set of real-world benchmark datasets in comparison to state-of-the-art probabilistic model learning methods. Scalability and robustness are demonstrated on a high dimensional problem.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/408570c02ba213a856bc8186c62a4e5bf91a18de" target='_blank'>Probabilistic Recurrent State-Space Models</a></td>
-          <td>
-            Andreas Doerr, Christian Daniel, Martin Schiegg, D. Nguyen-Tuong, S. Schaal, Marc Toussaint, Sebastian Trimpe
-          </td>
-          <td>2018-01-31</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>110</td>
-          <td>93</td>
-        </tr>
-    
-        <tr id="We introduce a new version of deep state-space models (DSSMs) that combines a recurrent neural network with a state-space framework to forecast time series data. The model estimates the observed series as functions of latent variables that evolve non-linearly through time. Due to the complexity and non-linearity inherent in DSSMs, previous works on DSSMs typically produced latent variables that are very difficult to interpret. Our paper focus on producing interpretable latent parameters with two key modifications. First, we simplify the predictive decoder by restricting the response variables to be a linear transformation of the latent variables plus some noise. Second, we utilize shrinkage priors on the latent variables to reduce redundancy and improve robustness. These changes make the latent variables much easier to understand and allow us to interpret the resulting latent variables as random effects in a linear mixed model. We show through two public benchmark datasets the resulting model improves forecasting performances.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b5d92a67cb7adb40d982df2f6fb6c8669d34604b" target='_blank'>Interpretable Latent Variables in Deep State Space Models</a></td>
-          <td>
-            Haoxuan Wu, David S. Matteson, M. Wells
-          </td>
-          <td>2022-03-03</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>40</td>
-        </tr>
-    
-        <tr id="Time series with long-term structure arise in a variety of contexts and capturing this temporal structure is a critical challenge in time series analysis for both inference and forecasting settings. Traditionally, state space models have been successful in providing uncertainty estimates of trajectories in the latent space. More recently, deep learning, attention-based approaches have achieved state of the art performance for sequence modeling, though often require large amounts of data and parameters to do so. We propose Stanza, a nonlinear, non-stationary state space model as an intermediate approach to fill the gap between traditional models and modern deep learning approaches for complex time series. Stanza strikes a balance between competitive forecasting accuracy and probabilistic, interpretable inference for highly structured time series. In particular, Stanza achieves forecasting accuracy competitive with deep LSTMs on real-world datasets, especially for multi-step ahead forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9c619e58d073772ff298228d47afcab625c7f37a" target='_blank'>Stanza: A Nonlinear State Space Model for Probabilistic Inference in Non-Stationary Time Series</a></td>
-          <td>
-            Anna K. Yanchenko, S. Mukherjee
-          </td>
-          <td>2020-06-11</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>31</td>
-        </tr>
-    
-        <tr id="Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational information characterizing the underlying data-generating process is unavailable and the practitioner is left with the problem of inferring from data which relational graph to use in the subsequent processing stages. We propose novel, principled - yet practical - probabilistic score-based methods that learn the relational dependencies as distributions over graphs while maximizing end-to-end the performance at task. The proposed graph learning framework is based on consolidated variance reduction techniques for Monte Carlo score-based gradient estimation, is theoretically grounded, and, as we show, effective in practice. In this paper, we focus on the time series forecasting problem and show that, by tailoring the gradient estimators to the graph learning problem, we are able to achieve state-of-the-art performance while controlling the sparsity of the learned graph and the computational scalability. We empirically assess the effectiveness of the proposed method on synthetic and real-world benchmarks, showing that the proposed solution can be used as a stand-alone graph identification procedure as well as a graph learning component of an end-to-end forecasting architecture.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0d01d21137a5af9f04e4b16a55a0f732cb8a540b" target='_blank'>Sparse Graph Learning from Spatiotemporal Time Series</a></td>
-          <td>
-            Andrea Cini, Daniele Zambon, C. Alippi
-          </td>
-          <td>2022-05-26</td>
-          <td>J. Mach. Learn. Res.</td>
-          <td>11</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a"closed-loop"variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length $\ell$ and state-space size $d$, we go from $\tilde{O}(d \ell)$ na\"ively to $\tilde{O}(d + \ell)$. In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR($p$) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a7d68b1702af08ce4dbbf2cd0b083e744ae5c6be" target='_blank'>Effectively Modeling Time Series with Simple Discrete State Spaces</a></td>
-          <td>
-            Michael Zhang, Khaled Kamal Saab, Michael Poli, Tri Dao, Karan Goel, Christopher Ré
-          </td>
-          <td>2023-03-16</td>
-          <td>ArXiv</td>
-          <td>28</td>
-          <td>43</td>
-        </tr>
-    
-        <tr id="
- 
- Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified algorithm to efficiently learn a broad class of linear and non-linear state space models, including variants where the emission and transition distributions are modeled by deep neural networks. Our learning algorithm simultaneously learns a compiled inference network and the generative model, leveraging a structured variational approximation parameterized by recurrent neural networks to mimic the posterior distribution. We apply the learning algorithm to both synthetic and real-world datasets, demonstrating its scalability and versatility. We find that using the structured approximation to the posterior results in models with significantly higher held-out likelihood.
- 
-">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2af17f153e3fd71e15db9216b972aef222f46617" target='_blank'>Structured Inference Networks for Nonlinear State Space Models</a></td>
-          <td>
-            R. G. Krishnan, Uri Shalit, D. Sontag
-          </td>
-          <td>2016-09-30</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>427</td>
-          <td>48</td>
-        </tr>
-    
-        <tr id="Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this structure to develop a computationally efficient approach to state estimation and learning in graph-structured state-space models with (partially) unknown dynamics and limited historical data. Building on recent methods that combine ideas from deep learning with principled inference in Gaussian Markov random fields (GMRF), we reformulate graph-structured state-space models as Deep GMRFs defined by simple spatial and temporal graph layers. This results in a flexible spatiotemporal prior that can be learned efficiently from a single time sequence via variational inference. Under linear Gaussian assumptions, we retain a closed-form posterior, which can be sampled efficiently using the conjugate gradient method, scaling favourably compared to classical Kalman filter based approaches">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/66173ff04bc062987a4395181001bf9b7c3eb21b" target='_blank'>Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systems</a></td>
-          <td>
-            Fiona Lippert, B. Kranstauber, E. E. V. Loon, Patrick Forr'e
-          </td>
-          <td>2023-06-14</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="Many applications, e.g., healthcare, education, call for effective methods methods for constructing predictive models from high dimensional time series data where the relationship between variables can be complex and vary over time. In such settings, the underlying system undergoes a sequence of unobserved transitions among a finite set of hidden states. Furthermore, the relationships between the observed variables and their temporal dynamics may depend on the hidden state of the system. To further complicate matters, the hidden state sequences underlying the observed data from different individuals may not be aligned relative to a common frame of reference. Against this background, we consider the novel problem of jointly learning the state-dependent inter-variable relationships as well as the pattern of transitions between hidden states from multi-variate time series data. To solve this problem, we introduce the State-Regularized Vector Autoregressive Model (SrVARM) which combines a state-regularized recurrent neural network to learn the dynamics of transitions between discrete hidden states with an augmented autoregressive model which models the inter-variable dependencies in each state using a state-dependent directed acyclic graph (DAG). We propose an efficient algorithm for training SrVARM by leveraging a recently introduced reformulation of the combinatorial problem of optimizing the DAG structure with respect to a scoring function into a continuous optimization problem. We report results of extensive experiments with simulated data as well as a real-world benchmark that show that SrVARM outperforms state-of-the-art baselines in recovering the unobserved state transitions and discovering the state-dependent relationships among variables.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4ddaa0ff15691ba148dd88c82b03547e9d2aa013" target='_blank'>SrVARM: State Regularized Vector Autoregressive Model for Joint Learning of Hidden State Transitions and State-Dependent Inter-Variable Dependencies from Multi-variate Time Series</a></td>
-          <td>
-            Tsung-Yu Hsieh, Yiwei Sun, Xianfeng Tang, Suhang Wang, Vasant G Honavar
-          </td>
-          <td>2021-04-19</td>
-          <td>Proceedings of the Web Conference 2021</td>
-          <td>8</td>
-          <td>54</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
-
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-  <i class="footer">This page was last updated on 2024-08-08 13:17:23 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Multidimensional Approximation of Nonlinear Dynamical Systems</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a dynamical system as a sum of spatial basis evolving linearly in time, thus enabling a better understanding of the physical phenomena and forecasting of future time instants. In this work we propose an extension of DMD to parameterized dynamical systems, focusing on the future forecasting of the output of interest in a parametric context. Initially all the snapshots -- for different parameters and different time instants -- are projected to a reduced space; then DMD, or one of its variants, is employed to approximate reduced snapshots for future time instants. Exploiting the low dimension of the reduced space the predicted reduced snapshots are then combined using regression techniques, thus enabling the possibility to approximate any untested parametric configuration in future. This paper depicts in detail the algorithmic core of this method; we also present and discuss three test cases for our algorithm: a simple dynamical system with a linear parameter dependency, a heat problem with nonlinear parameter dependency and a fluid dynamics problem with nonlinear parameter dependency.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5d9dff526ccb5e2adfe18d9b694dd59f358abba5" target='_blank'>A dynamic mode decomposition extension for the forecasting of parametric dynamical systems</a></td>
-          <td>
-            Francesco Andreuzzi, N. Demo, G. Rozza
-          </td>
-          <td>2021-10-18</td>
-          <td>ArXiv</td>
-          <td>15</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="In this paper we propose a model reduction and identification approach for multilinear dynamical system (MLDS) driven by noise. Compared to standard linear dynamical system based approaches which fit vector or matrix models to tensor time series, MLDS provides more natural, compact and accurate representation of tensorial data with fewer model parameters. The proposed algorithm for identifying MLDS parameters employs techniques from multilinear subspace learning: mulilinear Principal Component Analysis and multilinear regression. In addition compact array normal distribution is used to represent and estimate model error and output noise.We illustrate the benefits of the proposed approach on some real world datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5561ae4b2f4a727879648adb4db83440f42e682d" target='_blank'>Dynamic tensor time series modeling and analysis</a></td>
-          <td>
-            A. Surana, G. Patterson, I. Rajapakse
-          </td>
-          <td>2016-12-01</td>
-          <td>2016 IEEE 55th Conference on Decision and Control (CDC)</td>
-          <td>8</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="Higher-order dynamic mode decomposition (HODMD) has proved to be an efficient tool for the analysis and prediction of complex dynamical systems described by data-driven models. In the present paper, we propose a realization of HODMD that is based on the low-rank tensor decomposition of potentially high-dimensional datasets. It is used to compute the HODMD modes and eigenvalues to effectively reduce the computational complexity of the problem. The proposed extension also provides a more efficient realization of the ordinary dynamic mode decomposition with the use of the tensor-train decomposition. The high efficiency of the tensor-train-based HODMD (TT-HODMD) is illustrated by a few examples, including forecasting the load of a power system, which provides comparisons between TT-HODMD and HODMD with respect to the computing time and accuracy. The developed algorithm can be effectively used for the prediction of high-dimensional dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fa34575fd2052a29d0493b06a68dcfcaf2202f96" target='_blank'>Tensor Train Based Higher Order Dynamic Mode Decomposition for Dynamical Systems</a></td>
-          <td>
-            Keren Li, S. Utyuzhnikov
-          </td>
-          <td>2023-04-11</td>
-          <td>SSRN Electronic Journal</td>
-          <td>2</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3b44db6efdb3999b65be446114afb04720e572cc" target='_blank'>Modeling of dynamical systems through deep learning</a></td>
-          <td>
-            P. Rajendra, V. Brahmajirao
-          </td>
-          <td>2020-11-22</td>
-          <td>Biophysical Reviews</td>
-          <td>32</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards a lower-dimensional subspace; the projection onto the subspace gives the low-dimensional embedding. Training the model involves identifying the nonlinear flow and the subspace. Following the equation discovery method, we represent the vector field that defines the flow using a linear combination of dictionary elements, where each element is a pre-specified linear/nonlinear candidate function. A regularization term for the average total kinetic energy is also introduced and motivated by optimal transport theory. We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method. We also show how the DDR method can be trained using a gradient-based optimization method, where the gradients are computed using the adjoint method from optimal control theory. The DDR method is implemented and compared on synthetic and example datasets to other dimension reductions methods, including PCA, t-SNE, and Umap.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/118d777ecdb359c32649da0f7576af150d51eab4" target='_blank'>A dynamical systems based framework for dimension reduction</a></td>
-          <td>
-            Ryeongkyung Yoon, B. Osting
-          </td>
-          <td>2022-04-18</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>19</td>
-        </tr>
-    
-        <tr id="Data-driven modeling of dynamical systems has drawn much research attention recently, with the goal of approximating the underlying governing rules of a dynamical system with data-driven differential equations. Many real-world dynamical systems can be modeled as coupled oscillators, such as chemical reactors, ecological systems, integrated circuits, and mechanical systems. In those systems, the response can be described by coupled differential equations in which multi-dimensional state variables describe the timeevolution. However, in practice, the full set of state variables is often difficult or expensive to measure. This paper shows an attempt to develop a data-driven model for damped coupled oscillators from a mixed-mode response signal using neural differential equations. The univariate time-series data of the impulse response is first resampled into a multi-variate time-delayed embedding. A singular value decomposition is then applied to find the dominant orthogonal basis (oscillator modes). The decoupled modes are then modeled with parameterized neural differential equations. The unknown parameters can be learned from a segment of historical data. The proposed methodology is validated using impact testing data of an end mill in a machine tool spindle. The results demonstrate that the proposed method can effectively model damped coupled oscillators.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3c2be3a0bfe6f96b628e8a558afde40d5056bcca" target='_blank'>Learning Data-Driven Model of Damped Coupled Oscillators from System Impulse Response</a></td>
-          <td>
-            Jacob Fabro, G. Vogl, Yongzhi Qu, Reese Eischens
-          </td>
-          <td>2022-10-28</td>
-          <td>Annual Conference of the PHM Society</td>
-          <td>0</td>
-          <td>19</td>
-        </tr>
-    
-        <tr id="Unsteady fluid systems are nonlinear high-dimensional dynamical systems that may exhibit multiple complex phenomena in both time and space. Reduced Order Modeling (ROM) of fluid flows has been an active research topic in the recent decade with the primary goal to decompose complex flows into a set of features most important for future state prediction and control, typically using a dimensionality reduction technique. In this work, a novel data-driven technique based on the power of deep neural networks for ROM of the unsteady fluid flows is introduced. An autoencoder network is used for nonlinear dimension reduction and feature extraction as an alternative for singular value decomposition (SVD). Then, the extracted features are used as an input for a long short-term memory (LSTM) network to predict the velocity field at future time instances. The proposed autoencoder-LSTM method is compared with non-intrusive reduced order models based on dynamic mode decomposition (DMD) and proper orthogonal decomposition. Moreover, an autoencoder-DMD algorithm is introduced for ROM, which uses the autoencoder network for dimensionality reduction rather than SVD rank truncation. The results show that the autoencoder-LSTM method is considerably capable of predicting fluid flow evolution, where higher values for the coefficient of determination R2 are obtained using autoencoder-LSTM compared to other models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5573dfa7d03ce1dd28c298ecb0966e06c2aae8d0" target='_blank'>Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows</a></td>
-          <td>
-            Hamidreza Eivazi, H. Veisi, M. H. Naderi, V. Esfahanian
-          </td>
-          <td>2020-07-02</td>
-          <td>ArXiv</td>
-          <td>127</td>
-          <td>22</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/de3567866929da3a25754f93f917101717008833" target='_blank'>Nonlinear system identification with regularized Tensor Network B-splines</a></td>
-          <td>
-            Ridvan Karagoz, Kim Batselier
-          </td>
-          <td>2020-03-17</td>
-          <td>Autom.</td>
-          <td>17</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a9a3238808d20c5236a7c5f912c20e6dd729f88c" target='_blank'>Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation</a></td>
-          <td>
-            K. Yeo
-          </td>
-          <td>2019-06-10</td>
-          <td>J. Comput. Phys.</td>
-          <td>21</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="In recent years, we have witnessed a significant shift toward ever-more complex and ever-larger-scale systems in the majority of the grand societal challenges tackled in applied sciences. The need to comprehend and predict the dynamics of complex systems have spurred developments in large-scale simulations and a multitude of methods across several disciplines. The goals of understanding and prediction in complex dynamical systems, however, have been hindered by high dimensionality, complexity and chaotic behaviours. Recent advances in data-driven techniques and machine-learning approaches have revolutionized how we model and analyse complex systems. The integration of these techniques with dynamical systems theory opens up opportunities to tackle previously unattainable challenges in modelling and prediction of dynamical systems. While data-driven prediction methods have made great strides in recent years, it is still necessary to develop new techniques to improve their applicability to a wider range of complex systems in science and engineering. This focus issue shares recent developments in the field of complex dynamical systems with emphasis on data-driven, data-assisted and artificial intelligence-based discovery of dynamical systems. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e5aeec169d2c4d5e8e730a3c382006ba983b8709" target='_blank'>Data-driven prediction in dynamical systems: recent developments</a></td>
-          <td>
-            Amin Ghadami, B. Epureanu
-          </td>
-          <td>2022-06-20</td>
-          <td>Philosophical transactions. Series A, Mathematical, physical, and engineering sciences</td>
-          <td>41</td>
-          <td>33</td>
-        </tr>
-    
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-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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diff --git a/docs/recommendations/2c9be1e38f978f43427ea5293b3138e0c4fede71.md b/docs/recommendations/2c9be1e38f978f43427ea5293b3138e0c4fede71.md
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-    Recommendations for the article <i>Applied Koopmanism.</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches that formulate models in operator theoretic or probabilistic frameworks. Koopman spectral theory has emerged as a dominant perspective over the past decade, in which nonlinear dynamics are represented in terms of an infinite-dimensional linear operator acting on the space of all possible measurement functions of the system. This linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. However, obtaining finite-dimensional coordinate systems and embeddings in which the dynamics appear approximately linear remains a central open challenge. The success of Koopman analysis is due primarily to three key factors: 1) there exists rigorous theory connecting it to classical geometric approaches for dynamical systems, 2) the approach is formulated in terms of measurements, making it ideal for leveraging big-data and machine learning techniques, and 3) simple, yet powerful numerical algorithms, such as the dynamic mode decomposition (DMD), have been developed and extended to reduce Koopman theory to practice in real-world applications. In this review, we provide an overview of modern Koopman operator theory, describing recent theoretical and algorithmic developments and highlighting these methods with a diverse range of applications. We also discuss key advances and challenges in the rapidly growing field of machine learning that are likely to drive future developments and significantly transform the theoretical landscape of dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68b6ca45a588d538b36335b23f6969c960cf2e6e" target='_blank'>Modern Koopman Theory for Dynamical Systems</a></td>
-          <td>
-            S. Brunton, M. Budišić, E. Kaiser, J. Kutz
-          </td>
-          <td>2021-02-24</td>
-          <td>SIAM Rev.</td>
-          <td>273</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0f4b3d72f08bfadc076617850cc8a5e9395738d6" target='_blank'>Koopman Operator Dynamical Models: Learning, Analysis and Control</a></td>
-          <td>
-            Petar Bevanda, Stefan Sosnowski, S. Hirche
-          </td>
-          <td>2021-02-04</td>
-          <td>ArXiv</td>
-          <td>88</td>
-          <td>47</td>
-        </tr>
-    
-        <tr id="Introduction The end of the 20th century and the beginning of the 21st century has seen a revolutionary increase in the availability of data. Indeed, we are in the middle of the sensing revolution, where sensing is used in the broadest meaning of data acquisition. Most of this data goes unprocessed, unanalyzed, and, consequently, unused. This causes missed opportunities, in domains of vast societal importance—">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/90edc9f58779b5a32848edd2f5a8175642351b48" target='_blank'>Koopman Operator, Geometry, and Learning of Dynamical Systems</a></td>
-          <td>
-            I. Mezić
-          </td>
-          <td>2021-08-01</td>
-          <td>Notices of the American Mathematical Society</td>
-          <td>32</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="The Koopman operator is an useful analytical tool for studying dynamical systems -- both controlled and uncontrolled. For example, Koopman eigenfunctions can provide non-local stability information about the underlying dynamical system. Koopman representations of nonlinear systems are commonly calculated using machine learning methods, which seek to represent the Koopman eigenfunctions as a linear combinations of nonlinear state measurements. As such, it is important to understand whether, in principle, these eigenfunctions can be successfully obtained using machine learning and what eigenfunctions calculated in this way can tell us about the underlying system. To that end, this paper presents an analysis of continuity, stability and control limitations associated with Koopman eigenfunctions under minimal assumptions and provides a discussion that relates these properties to the ability to calculate Koopman representations with machine learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/719cbf3907aa6d2e8c2c623a9268d9ce86116223" target='_blank'>Learning Bounded Koopman Observables: Results on Stability, Continuity, and Controllability</a></td>
-          <td>
-            Craig Bakker, Thiagarajan Ramachandran, W. S. Rosenthal
-          </td>
-          <td>2020-04-30</td>
-          <td>arXiv: Dynamical Systems</td>
-          <td>3</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="This work presents a data-driven framework for learning eigenfunctions of the Koopman operator geared toward prediction and control. The method relies on the richness of the spectrum of the Koopman operator in the transient, off-attractor, regime to construct a large number of eigenfunctions such that the state (or any other observable quantity of interest) is in the span of these eigenfunctions and hence predictable in a linear fashion. Once a predictor for the uncontrolled part of the system is obtained in this way, the incorporation of control is done through a multi-step prediction error minimization, carried out by a simple linear least-squares regression. The predictor so obtained is in the form of a linear controlled dynamical system and can be readily applied within the Koopman model predictive control framework of [11] to control nonlinear dynamical systems using linear model predictive control tools. The method is entirely data-driven and based purely on convex optimization, with no reliance on neural networks or other non-convex machine learning tools. The novel eigenfunction construction method is also analyzed theoretically, proving rigorously that the family of eigenfunctions obtained is rich enough to span the space of all continuous functions. In addition, the method is extended to construct generalized eigenfunctions that also give rise Koopman invariant subspaces and hence can be used for linear prediction. Detailed numerical examples demonstrate the approach, both for prediction and feedback control.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/97629699ff9e1e67b3f4f21cab64d42f3713bfa0" target='_blank'>Learning Koopman eigenfunctions for prediction and control: the transient case</a></td>
-          <td>
-            Milan Korda, I. Mezić
-          </td>
-          <td>2018-10-20</td>
-          <td>arXiv: Optimization and Control</td>
-          <td>7</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="This article presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to construct a set of eigenfunctions such that the state (or any other observable quantity of interest) is in the span of these eigenfunctions and hence predictable in a linear fashion. The eigenfunction construction is optimization-based with no dictionary selection required. Once a predictor for the uncontrolled part of the system is obtained in this way, the incorporation of control is done through a multistep prediction error minimization, carried out by a simple linear least-squares regression. The predictor so obtained is in the form of a linear controlled dynamical system and can be readily applied within the Koopman model predictive control (MPC) framework of (M. Korda and I. Mezić, 2018) to control nonlinear dynamical systems using linear MPC tools. The method is entirely data-driven and based predominantly on convex optimization. The novel eigenfunction construction method is also analyzed theoretically, proving rigorously that the family of eigenfunctions obtained is rich enough to span the space of all continuous functions. In addition, the method is extended to construct generalized eigenfunctions that also give rise Koopman invariant subspaces and hence can be used for linear prediction. Detailed numerical examples demonstrate the approach, both for prediction and feedback control.**Code for the numerical examples is available from https://homepages.laas.fr/mkorda/Eigfuns.zip.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8f3d28be5557a1c87a80c3242d68bddb331b0cbc" target='_blank'>Optimal Construction of Koopman Eigenfunctions for Prediction and Control</a></td>
-          <td>
-            Milan Korda, I. Mezić
-          </td>
-          <td>2018-10-20</td>
-          <td>IEEE Transactions on Automatic Control</td>
-          <td>103</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/75407116e515533f3cb11b6de14449f2933638ed" target='_blank'>Estimating Koopman operators for nonlinear dynamical systems: a nonparametric approach</a></td>
-          <td>
-            Francesco Zanini, A. Chiuso
-          </td>
-          <td>2021-03-25</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system. The Koopman operator is a principled linear embedding of nonlinear dynamics and facilitates the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. In particular, PyKoopman provides tools for data-driven system identification for unforced and actuated systems that build on the equation-free dynamic mode decomposition (DMD) and its variants. In this work, we provide a brief description of the mathematical underpinnings of the Koopman operator, an overview and demonstration of the features implemented in PyKoopman (with code examples), practical advice for users, and a list of potential extensions to PyKoopman. Software is available at http://github.com/dynamicslab/pykoopman">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5a220582e1ff56332a3800470ffdc25f663f9030" target='_blank'>PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator</a></td>
-          <td>
-            Shaowu Pan, E. Kaiser, Brian M. de Silva, J. Kutz, S. Brunton
-          </td>
-          <td>2023-06-22</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="We consider the application of Koopman theory to nonlinear partial differential equations and data-driven spatio-temporal systems. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear dynamics. If such observables can be found, then the dynamic mode decomposition (DMD) algorithm can be enacted to compute a finite-dimensional approximation of the Koopman operator, including its eigenfunctions, eigenvalues, and Koopman modes. We demonstrate simple rules of thumb for selecting a parsimonious set of observables that can greatly improve the approximation of the Koopman operator. Further, we show that the clear goal in selecting observables is to place the DMD eigenvalues on the imaginary axis, thus giving an objective function for observable selection. Judiciously chosen observables lead to physically interpretable spatio-temporal features of the complex system under consideration and provide a connection to manifold learning methods. Our method provides a valuable intermediate, yet interpretable, approximation to the Koopman operator that lies between the DMD method and the computationally intensive extended DMD (EDMD). We demonstrate the impact of observable selection, including kernel methods, and construction of the Koopman operator on several canonical nonlinear PDEs: Burgers’ equation, the nonlinear Schrödinger equation, the cubic-quintic Ginzburg-Landau equation, and a reaction-diffusion system. These examples serve to highlight the most pressing and critical challenge of Koopman theory: a principled way to select appropriate observables.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1ce0ee1c0205e37c20daf33a5ad6eed187107614" target='_blank'>Applied Koopman Theory for Partial Differential Equations and Data-Driven Modeling of Spatio-Temporal Systems</a></td>
-          <td>
-            J. Kutz, J. Proctor, S. Brunton
-          </td>
-          <td>2018-12-02</td>
-          <td>Complex.</td>
-          <td>63</td>
-          <td>63</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Molecular latent space simulators</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the timescales necessary to capture the structural evolution of bio-molecules remains a daunting task. In this work we present a novel framework to advance simulation timescales by up to three orders of magnitude, by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the M\"ueller-Brown potential, the Trp Cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations and can generate, at any instant, the respective all-atom molecular trajectories. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bab880c698b850ba18c08b9d93b73ffb538a417b" target='_blank'>Accelerated Simulations of Molecular Systems through Learning of their Effective Dynamics</a></td>
-          <td>
-            Pantelis R. Vlachas, J. Zavadlav, M. Praprotnik, P. Koumoutsakos
-          </td>
-          <td>2021-02-17</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>77</td>
-        </tr>
-    
-        <tr id="Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the time scales necessary to capture the structural evolution of biomolecules remains a daunting task. In this work, we present a novel framework to advance simulation time scales by up to 3 orders of magnitude by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the Müller-Brown potential, the Trp cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations, i.e., collective variables, and can generate, at any instant, all-atom molecular trajectories consistent with the collective variables. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68c0f4d535078674fd2ce738306eb72171a0677d" target='_blank'>Accelerated Simulations of Molecular Systems through Learning of Effective Dynamics.</a></td>
-          <td>
-            Pantelis R. Vlachas, J. Zavadlav, M. Praprotnik, P. Koumoutsakos
-          </td>
-          <td>2021-12-10</td>
-          <td>Journal of chemical theory and computation</td>
-          <td>29</td>
-          <td>77</td>
-        </tr>
-    
-        <tr id="Synthetic molecular dynamics (synMD) trajectories from learned generative models have been proposed as a useful addition to the biomolecular simulation toolbox. The computational expense of explicitly integrating the equations of motion in molecular dynamics currently is a severe limit on the number and length of trajectories which can be generated for complex systems. Approximate, but more computationally efficient, generative models can be used in place of explicit integration of the equations of motion, and can produce meaningful trajectories at greatly reduced computational cost. Here, we demonstrate a very simple synMD approach using a fine-grained Markov state model (MSM) with states mapped to specific atomistic configurations, which provides an exactly solvable reference. We anticipate this simple approach will enable rapid, effective testing of enhanced sampling algorithms in highly non-trivial models for both equilibrium and non-equilibrium problems. We demonstrate the use of a MSM to generate atomistic synMD trajectories for the fast-folding miniprotein Trp-cage, at a rate of over 200 milliseconds per day on a standard workstation. We employ a non-standard clustering for MSM generation that appears to better preserve kinetic properties at shorter lag times than a conventional MSM. We also show a parallelizable workflow that backmaps discrete synMD trajectories to full-coordinate representations at dynamic resolution for efficient analysis.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d09f8cd520789fbd378a7bd90dcafc2544b6fcfc" target='_blank'>Simple synthetic molecular dynamics for efficient trajectory generation</a></td>
-          <td>
-            John D. Russo, D. Zuckerman
-          </td>
-          <td>2022-04-09</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in microscopy and tracking, there is today an abundance of experimental trajectories reflecting these dynamical laws. Inferring physical models from noisy and imperfect experimental data, however, is challenging. Because there are no inference methods that are robust and efficient, model reconstruction from experimental trajectories is a bottleneck to data-driven biophysics. In this Thesis, I present a set of tools developed to bridge this gap and permit robust and universal inference of stochastic dynamical models from experimental trajectories. These methods are rooted in an information-theoretical framework that quantifies how much can be inferred from trajectories that are short, partial and noisy. They permit the efficient inference of dynamical models for overdamped and underdamped Langevin systems, as well as the inference of entropy production rates. I finally present early applications of these techniques, as well as future research directions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/36d5a9b10d628b238c485c3e97f0ad456101dedb" target='_blank'>Learning dynamical models from stochastic trajectories</a></td>
-          <td>
-            Pierre Ronceray
-          </td>
-          <td>2024-06-04</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-sized vector indicating the membership to metastable (long-lived) states, (ii) a Markov chain that governs the transitions between metastable states and facilitates analysis of the long-time dynamics, and (iii) a generative part that samples the conditional distribution of configurations in the next time step. The model can be operated in a recursive fashion to generate trajectories to predict the system evolution from a defined starting state and propose new configurations. The DeepGenMSM is demonstrated to provide accurate estimates of the long-time kinetics and generate valid distributions for molecular dynamics (MD) benchmark systems. Remarkably, we show that DeepGenMSMs are able to make long time-steps in molecular configuration space and generate physically realistic structures in regions that were not seen in training data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5c6ee980b791766ba036cba282bcbcbcb2e5309e" target='_blank'>Deep Generative Markov State Models</a></td>
-          <td>
-            Hao Wu, Andreas Mardt, Luca Pasquali, F. Noé
-          </td>
-          <td>2018-05-19</td>
-          <td>ArXiv</td>
-          <td>54</td>
-          <td>61</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/58912e2c2aaa77d1448d51e9d9460e06a5b924b9" target='_blank'>VAMPnets for deep learning of molecular kinetics</a></td>
-          <td>
-            Andreas Mardt, Luca Pasquali, Hao Wu, F. Noé
-          </td>
-          <td>2017-10-16</td>
-          <td>Nature Communications</td>
-          <td>463</td>
-          <td>61</td>
-        </tr>
-    
-        <tr id="Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in "one shot", vast computational effort is invested for simulating these system in small steps, e.g., using Molecular Dynamics. Combining deep learning and statistical mechanics, we here develop Boltzmann Generators, that are shown to generate unbiased one-shot equilibrium samples of representative condensed matter systems and proteins. Boltzmann Generators use neural networks to learn a coordinate transformation of the complex configurational equilibrium distribution to a distribution that can be easily sampled. Accurate computation of free energy differences and discovery of new configurations are demonstrated, providing a statistical mechanics tool that can avoid rare events during sampling without prior knowledge of reaction coordinates.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9896835f050121358372254a9bce57ca117672c8" target='_blank'>Boltzmann Generators - Sampling Equilibrium States of Many-Body Systems with Deep Learning</a></td>
-          <td>
-            F. Noé, Hao Wu
-          </td>
-          <td>2018-12-04</td>
-          <td>ArXiv</td>
-          <td>24</td>
-          <td>61</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/13b52cd927d3daa5c95528b987734d97474e790c" target='_blank'>Markov field models: Scaling molecular kinetics approaches to large molecular machines.</a></td>
-          <td>
-            Tim Hempel, Simon Olsson, Frank No'e
-          </td>
-          <td>2022-06-23</td>
-          <td>Current opinion in structural biology</td>
-          <td>6</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="All-atom and coarse-grained molecular dynamics are two widely used computational tools to study the conformational states of proteins. Yet, these two simulation methods suffer from the fact that without access to supercomputing resources, the time and length scales at which these states become detectable are difficult to achieve. One alternative to such methods is based on encoding the atomistic trajectory of molecular dynamics as a shorthand version devoid of physical particles, and then learning to propagate the encoded trajectory through the use of artificial intelligence. Here we show that a simple textual representation of the frames of molecular dynamics trajectories as vectors of Ramachandran basin classes retains most of the structural information of the full atomistic representation of a protein in each frame, and can be used to generate equivalent atom-less trajectories suitable to train different types of generative neural networks. In turn, the trained generative models can be used to extend indefinitely the atom-less dynamics or to sample the conformational space of proteins from their representation in the models latent space. We define intuitively this methodology as molecular dynamics without molecules, and show that it enables to cover physically relevant states of proteins that are difficult to access with traditional molecular dynamics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/31d62c95e128caa934ca6a6c5cd5c766c6a9d541" target='_blank'>Molecular dynamics without molecules: searching the conformational space of proteins with generative neural networks</a></td>
-          <td>
-            Gregory Schwing, L. Palese, Ariel Fern'andez, L. Schwiebert, D. Gatti
-          </td>
-          <td>2022-06-09</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>33</td>
-        </tr>
-    
-  </tbody>
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-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Nonlinear Discovery of Slow Molecular Modes using Hierarchical Dynamics Encoders</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
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-  <tbody>
-    
-        <tr id="Investigating processes in complex molecular systems, which are characterized by many variables, is a crucial problem in computational physics. These systems can be reduced to a few meaningful degrees of freedom known as collective variables (CVs). However, identifying these CVs is a significant challenge, especially for systems with long-lived metastable states. This is because the information about the slow kinetics of rare transitions needs to be encoded in CVs. In this talk, we review recent advances in learning slow CVs and focus mainly on our spectral map technique, a promising deep-learning method that learns CVs based on the slowest timescales. By maximizing the spectral gap between slow and fast eigenvalues of a Markov transition matrix constructed from simulation data, our method effectively captures a simplified representation of alanine dipeptide in solvent. This practical application of our method demonstrates its ability to extract slow CVs, making it a valuable tool for analyzing complex systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8c9f4af01a841b431917e605a85746154d49529d" target='_blank'>Spectral Maps for Learning Reduced Representations of Molecular Systems</a></td>
-          <td>
-            Tuugcce Gokdemir, Jakub Rydzewski
-          </td>
-          <td>2023-11-07</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical analyses. Theoretically, we derive bounds for nonlinear TAE performance in slow mode discovery and show that in general TAEs learn a mixture of slow and maximum variance modes. Numerically, we illustrate cases where TAEs can and cannot correctly identify the leading slowest mode in two example systems: a 2D "Washington beltway" potential and the alanine dipeptide molecule in explicit water. We also compare the TAE results with those obtained using state-free reversible VAMPnets (SRVs) as a variational-based neural network approach for slow modes discovery, and show that SRVs can correctly discover slow modes where TAEs fail.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fe3850f70016ae3a31767166fb996ed0f0325fd4" target='_blank'>Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems</a></td>
-          <td>
-            Wei Chen, Hythem Sidky, Andrew L. Ferguson
-          </td>
-          <td>2019-06-02</td>
-          <td>ArXiv</td>
-          <td>31</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="Macromolecular and biomolecular folding landscapes typically contain high free energy barriers that impede efficient sampling of configurational space by standard molecular dynamics simulation. Biased sampling can artificially drive the simulation along prespecified collective variables (CVs), but success depends critically on the availability of good CVs associated with the important collective dynamical motions. Nonlinear machine learning techniques can identify such CVs but typically do not furnish an explicit relationship with the atomic coordinates necessary to perform biased sampling. In this work, we employ auto‐associative artificial neural networks (“autoencoders”) to learn nonlinear CVs that are explicit and differentiable functions of the atomic coordinates. Our approach offers substantial speedups in exploration of configurational space, and is distinguished from existing approaches by its capacity to simultaneously discover and directly accelerate along data‐driven CVs. We demonstrate the approach in simulations of alanine dipeptide and Trp‐cage, and have developed an open‐source and freely available implementation within OpenMM. © 2018 Wiley Periodicals, Inc.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c86006be8cd1c5ee6193ee31cf31d44449b9c082" target='_blank'>Molecular enhanced sampling with autoencoders: On‐the‐fly collective variable discovery and accelerated free energy landscape exploration</a></td>
-          <td>
-            Wei Chen, Andrew L. Ferguson
-          </td>
-          <td>2017-12-30</td>
-          <td>Journal of Computational Chemistry</td>
-          <td>168</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="Variational autoencoder frameworks have demonstrated success in reducing complex nonlinear dynamics in molecular simulation to a single nonlinear embedding. In this work, we illustrate how this nonlinear latent embedding can be used as a collective variable for enhanced sampling and present a simple modification that allows us to rapidly perform sampling in multiple related systems. We first demonstrate our method is able to describe the effects of force field changes in capped alanine dipeptide after learning about a model using AMBER99. We further provide a simple extension to variational dynamics encoders that allows the model to be trained in a more efficient manner on larger systems by encoding the outputs of a linear transformation using time-structure based independent component analysis (tICA). Using this technique, we show how such a model trained for one protein, the WW domain, can efficiently be transferred to perform enhanced sampling on a related mutant protein, the GTT mutation. This method shows promise for its ability to rapidly sample related systems using a single transferable collective variable, enabling us to probe the effects of variation in increasingly large systems of biophysical interest.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/69ccf867833b3564c2d2f26c49915b444eadb268" target='_blank'>Transferable Neural Networks for Enhanced Sampling of Protein Dynamics.</a></td>
-          <td>
-            Mohammad M. Sultan, H. Wayment-Steele, V. Pande
-          </td>
-          <td>2018-01-02</td>
-          <td>Journal of chemical theory and computation</td>
-          <td>94</td>
-          <td>103</td>
-        </tr>
-    
-        <tr id="The dynamics of physical systems that require high-dimensional representation can often be captured in a few meaningful degrees of freedom called collective variables (CVs). However, identifying CVs is challenging and constitutes a fundamental problem in physical chemistry. This problem is even more pronounced when CVs need to provide information about slow kinetics related to rare transitions between long-lived metastable states. To address this issue, we propose an unsupervised deep-learning method called spectral map. Our method constructs slow CVs by maximizing the spectral gap between slow and fast eigenvalues of a transition matrix estimated by an anisotropic diffusion kernel. We demonstrate our method in several high-dimensional reversible folding processes.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/17c80d75ea490a12f54d166717e9d745f7129f8d" target='_blank'>Spectral Map: Embedding Slow Kinetics in Collective Variables</a></td>
-          <td>
-            J. Rydzewski
-          </td>
-          <td>2023-06-01</td>
-          <td>The Journal of Physical Chemistry Letters</td>
-          <td>6</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the timescales necessary to capture the structural evolution of bio-molecules remains a daunting task. In this work we present a novel framework to advance simulation timescales by up to three orders of magnitude, by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the M\"ueller-Brown potential, the Trp Cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations and can generate, at any instant, the respective all-atom molecular trajectories. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bab880c698b850ba18c08b9d93b73ffb538a417b" target='_blank'>Accelerated Simulations of Molecular Systems through Learning of their Effective Dynamics</a></td>
-          <td>
-            Pantelis R. Vlachas, J. Zavadlav, M. Praprotnik, P. Koumoutsakos
-          </td>
-          <td>2021-02-17</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>77</td>
-        </tr>
-    
-        <tr id="Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the time scales necessary to capture the structural evolution of biomolecules remains a daunting task. In this work, we present a novel framework to advance simulation time scales by up to 3 orders of magnitude by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the Müller-Brown potential, the Trp cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations, i.e., collective variables, and can generate, at any instant, all-atom molecular trajectories consistent with the collective variables. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68c0f4d535078674fd2ce738306eb72171a0677d" target='_blank'>Accelerated Simulations of Molecular Systems through Learning of Effective Dynamics.</a></td>
-          <td>
-            Pantelis R. Vlachas, J. Zavadlav, M. Praprotnik, P. Koumoutsakos
-          </td>
-          <td>2021-12-10</td>
-          <td>Journal of chemical theory and computation</td>
-          <td>29</td>
-          <td>77</td>
-        </tr>
-    
-        <tr id="Abstract Abstract The convergence of free-energy calculations based on importance sampling depends heavily on the choice of collective variables (CVs), which in principle, should include the slow degrees of freedom of the biological processes to be investigated. Autoencoders (AEs), as emerging data-driven dimension reduction tools, have been utilised for discovering CVs. AEs, however, are often treated as black boxes, and what AEs actually encode during training, and whether the latent variables from encoders are suitable as CVs for further free-energy calculations remains unknown. In this contribution, we review AEs and their time-series-based variants, including time-lagged AEs (TAEs) and modified TAEs, as well as the closely related model variational approach for Markov processes networks (VAMPnets). We then show through numerical examples that AEs learn the high-variance modes instead of the slow modes. In stark contrast, time series-based models are able to capture the slow modes. Moreover, both modified TAEs with extensions from slow feature analysis and the state-free reversible VAMPnets (SRVs) can yield orthogonal multidimensional CVs. As an illustration, we employ SRVs to discover the CVs of the isomerizations of N-acetyl-N′-methylalanylamide and trialanine by iterative learning with trajectories from biased simulations. Last, through numerical experiments with anisotropic diffusion, we investigate the potential relationship of time-series-based models and committor probabilities.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0ec461f9fd4b19b52508e85f3ffb7b7e70fc5d67" target='_blank'>Chasing collective variables using temporal data-driven strategies</a></td>
-          <td>
-            Haochuan Chen, C. Chipot
-          </td>
-          <td>2023-01-06</td>
-          <td>QRB Discovery</td>
-          <td>9</td>
-          <td>54</td>
-        </tr>
-    
-        <tr id="Several enhanced sampling techniques rely on the definition of collective variables to effectively explore free energy landscapes. The existing variables that describe the progression along a reactive pathway offer an elegant solution but face a number of limitations. In this paper, we address these challenges by introducing a new path-like collective variable called the "deep-locally non-linear-embedding," which is inspired by principles of the locally linear embedding technique and is trained on a reactive trajectory. The variable mimics the ideal reaction coordinate by automatically generating a non-linear combination of features through a differentiable generalized autoencoder that combines a neural network with a continuous k-nearest neighbor selection. Among the key advantages of this method is its capability to automatically choose the metric for searching neighbors and to learn the path from state A to state B without the need to handpick landmarks a priori. We demonstrate the effectiveness of DeepLNE by showing that the progression along the path variable closely approximates the ideal reaction coordinate in toy models, such as the Müller-Brown potential and alanine dipeptide. Then, we use it in the molecular dynamics simulations of an RNA tetraloop, where we highlight its capability to accelerate transitions and estimate the free energy of folding.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/267db6e5e036b0f4bccc9e9b06085288638e31f2" target='_blank'>Deep learning path-like collective variable for enhanced sampling molecular dynamics.</a></td>
-          <td>
-            Thorben Fröhlking, Luigi Bonati, Valerio Rizzi, F. L. Gervasio
-          </td>
-          <td>2024-02-02</td>
-          <td>The Journal of chemical physics</td>
-          <td>3</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="Molecular dynamics (MD) simulations have emerged to become the back-bone of today’s computational biophysics. Simulation tools such as, NAMD, AMBER and GROMACS have accumulated more than 100,000 users. Despite this remarkable success, now also bolstered by compatibility with graphics processor units (GPUs) and exascale computers, even the most scalable simulations cannot access biologically relevant timescales - the number of numerical integration steps necessary for solving differential equations in a million-to-billion-dimensional space is computationally in-tractable. Recent advancements in Deep Learning has made it such that patterns can be found in high dimensional data. In addition, Deep Learning have also been used for simulating physical dynamics. Here, we utilize LSTMs in order to predict future molecular dynamics from current and previous timesteps, and examine how this physics-guided learning can benefit researchers in computational biophysics. In particular, we test fully connected Feed-forward Neural Networks, Recurrent Neural Networks with LSTM / GRU memory cells with TensorFlow and PyTorch frame-works trained on data from NAMD simulations to predict conformational transitions on two different biological systems. We find that non-equilibrium MD is easier to train and performance improves under the assumption that each atom is independent of all other atoms in the system. Our study represents a case study for high-dimensional data that switches stochastically between fast and slow regimes. Applications of resolving these sets will allow real-world applications in the interpretation of data from Atomic Force Microscopy experiments.">
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-          <td><a href="https://www.semanticscholar.org/paper/86de5fbe09c4381f548e1312d53f15d898c76c78" target='_blank'>Mind reading of the proteins: Deep-learning to forecast molecular dynamics</a></td>
-          <td>
-            C. Gupta, J. Cava, Daipayan Sarkar, Eric A. Wilson, J. Vant, Steven Murray, A. Singharoy, S. Karmaker
-          </td>
-          <td>2020-07-29</td>
-          <td>bioRxiv</td>
-          <td>4</td>
-          <td>23</td>
-        </tr>
-    
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-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/309c5ae93a4cabfd37747abd130866240e265b2d.md b/docs/recommendations/309c5ae93a4cabfd37747abd130866240e265b2d.md
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-    Recommendations for the article <i>Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear Dynamical Systems</i>
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-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
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-    
-        <tr id="Mathematical models of biological reactions at the system-level lead to a set of ordinary differential equations with many unknown parameters that need to be inferred using relatively few experimental measurements. Having a reliable and robust algorithm for parameter inference and prediction of the hidden dynamics has been one of the core subjects in systems biology, and is the focus of this study. We have developed a new systems-biology-informed deep learning algorithm that incorporates the system of ordinary differential equations into the neural networks. Enforcing these equations effectively adds constraints to the optimization procedure that manifests itself as an imposed structure on the observational data. Using few scattered and noisy measurements, we are able to infer the dynamics of unobserved species, external forcing, and the unknown model parameters. We have successfully tested the algorithm for three different benchmark problems. Author summary The dynamics of systems biological processes are usually modeled using ordinary differential equations (ODEs), which introduce various unknown parameters that need to be estimated efficiently from noisy measurements of concentration for a few species only. In this work, we present a new “systems-informed neural network” to infer the dynamics of experimentally unobserved species as well as the unknown parameters in the system of equations. By incorporating the system of ODEs into the neural networks, we effectively add constraints to the optimization algorithm, which makes the method robust to noisy and sparse measurements.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/33da5e93b3c9c02256c6a98f8a843ae62e27d436" target='_blank'>Systems biology informed deep learning for inferring parameters and hidden dynamics</a></td>
-          <td>
-            A. Yazdani, Lu Lu, M. Raissi, G. Karniadakis
-          </td>
-          <td>2019-12-04</td>
-          <td>PLoS Computational Biology</td>
-          <td>184</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are however difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended $\beta$-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables for the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5e660b3335f6a2a1d8592c6bfd048b1d1aaa6021" target='_blank'>Learning minimal representations of stochastic processes with variational autoencoders</a></td>
-          <td>
-            Gabriel Fern'andez-Fern'andez, Carlo Manzo, M. Lewenstein, A. Dauphin, Gorka Muñoz-Gil
-          </td>
-          <td>2023-07-21</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>93</td>
-        </tr>
-    
-        <tr id="This article presents the MAGI software package for the inference of dynamic systems. The focus of MAGI is on dynamics modeled by nonlinear ordinary differential equations with unknown parameters. While such models are widely used in science and engineering, the available experimental data for parameter estimation may be noisy and sparse. Furthermore, some system components may be entirely unobserved. MAGI solves this inference problem with the help of manifold-constrained Gaussian processes within a Bayesian statistical framework, whereas unobserved components have posed a significant challenge for existing software. We use several realistic examples to illustrate the functionality of MAGI. The user may choose to use the package in any of the R, MATLAB, and Python environments.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8ba999503769bba9ece3d5acf0ef8dcf312dc38d" target='_blank'>magi: A Package for Inference of Dynamic Systems from Noisy and Sparse Data via Manifold-Constrained Gaussian Processes</a></td>
-          <td>
-            Samuel W. K. Wong, Shihao Yang, S. Kou
-          </td>
-          <td>2022-03-11</td>
-          <td>J. Stat. Softw.</td>
-          <td>10</td>
-          <td>21</td>
-        </tr>
-    
-        <tr id="We present a machine learning framework (GP-NODE) for Bayesian model discovery from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling and Gaussian Process priors over the observed system states. This allows us to exploit temporal correlations in the observed data, and efficiently infer posterior distributions over plausible models with quantified uncertainty. The use of the Finnish Horseshoe as a sparsity-promoting prior for free model parameters also enables the discovery of parsimonious representations for the latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed GP-NODE method including predator–prey systems, systems biology and a 50-dimensional human motion dynamical system. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/26d5a4c63ca31ed5d89c3f1c9b9b9e5098975059" target='_blank'>Gaussian processes meet NeuralODEs: a Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data</a></td>
-          <td>
-            Mohamed Aziz Bhouri, P. Perdikaris
-          </td>
-          <td>2021-03-04</td>
-          <td>Philosophical Transactions of the Royal Society A</td>
-          <td>20</td>
-          <td>43</td>
-        </tr>
-    
-        <tr id="Neural Stochastic Differential Equations (NSDE) have been trained as both Variational Autoencoders, and as GANs. However, the resulting Stochastic Differential Equations can be hard to interpret or analyse due to the generic nature of the drift and diffusion fields. By restricting our NSDE to be of the form of Langevin dynamics, and training it as a VAE, we obtain NSDEs that lend themselves to more elaborate analysis and to a wider range of visualisation techniques than a generic NSDE. More specifically, we obtain an energy landscape, the minima of which are in one-to-one correspondence with latent states underlying the used data. This not only allows us to detect states underlying the data dynamics in an unsupervised manner, but also to infer the distribution of time spent in each state according to the learned SDE. More in general, restricting an NSDE to Langevin dynamics enables the use of a large set of tools from computational molecular dynamics for the analysis of the obtained results.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8ed31496eea24fb64e465cea58f1a0a4a92b4470" target='_blank'>Neural Langevin Dynamics: towards interpretable Neural Stochastic Differential Equations</a></td>
-          <td>
-            Simon Koop, M. Peletier, J. Portegies, V. Menkovski
-          </td>
-          <td>2022-11-17</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>32</td>
-        </tr>
-    
-        <tr id="Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling predictions of their temporal evolution and analyses of thermodynamic quantities, including absorbed heat, work done on the system, and entropy production. However, inferring the Langevin equation from observed trajectories remains challenging, particularly for nonlinear and high-dimensional systems. In this study, we present a comprehensive framework that employs Bayesian neural networks for inferring Langevin equations in both overdamped and underdamped regimes. Our framework first provides the drift force and diffusion matrix separately and then combines them to construct the Langevin equation. By providing a distribution of predictions instead of a single value, our approach allows us to assess prediction uncertainties, which can prevent potential misunderstandings and erroneous decisions about the system. We demonstrate the effectiveness of our framework in inferring Langevin equations for various scenarios including a neuron model and microscopic engine, highlighting its versatility and potential impact.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/547e262e26be6fd772533a4cbd6ce5ec600b8159" target='_blank'>Inferring the Langevin Equation with Uncertainty via Bayesian Neural Networks</a></td>
-          <td>
-            Youngkyoung Bae, Seungwoong Ha, Hawoong Jeong
-          </td>
-          <td>2024-02-02</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="With the rapid advances in single-cell sequencing technology, it is now feasible to conduct in-depth genetic analysis in individual cells. Study on the dynamics of single cells in response to perturbations is of great significance for understanding the functions and behaviours of living organisms. However, the acquisition of post-perturbation cellular states via biological experiments is frequently cost-prohibitive. Predicting the single-cell perturbation responses poses a critical challenge in the field of computational biology. In this work, we propose a novel deep learning method called coupled variational autoencoders (CoupleVAE), devised to predict the post-perturbation single-cell RNA-Seq data. CoupleVAE is composed of two coupled VAEs connected by a coupler, initially extracting latent features for both controlled and perturbed cells via two encoders, subsequently engaging in mutual translation within the latent space through two nonlinear mappings via a coupler, and ultimately generating controlled and perturbed data by two separate decoders to process the encoded and translated features. CoupleVAE facilitates a more intricate state transformation of single cells within the latent space. Experiments in three real datasets on infection, stimulation and cross-species prediction show that CoupleVAE surpasses the existing comparative models in effectively predicting single-cell RNA-seq data for perturbed cells, achieving superior accuracy.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/42436bd54a4b40f4d2cd584d23e12133305f40e7" target='_blank'>CoupleVAE: coupled variational autoencoders for predicting perturbational single-cell RNA sequencing data</a></td>
-          <td>
-            Yahao Wu, Jing Liu, Songyan Liu, Yanni Xiao, Shuqin Zhang, Limin Li
-          </td>
-          <td>2024-03-08</td>
-          <td>bioRxiv</td>
-          <td>0</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="End-to-end learning of dynamical systems with black-box models, such as neural ordinary differential equations (ODEs), provides a flexible framework for learning dynamics from data without prescribing a mathematical model for the dynamics. Unfortunately, this flexibility comes at the cost of understanding the dynamical system, for which ODEs are used ubiquitously. Further, experimental data are collected under various conditions (inputs), such as treatments, or grouped in some way, such as part of sub-populations. Understanding the effects of these system inputs on system outputs is crucial to have any meaningful model of a dynamical system. To that end, we propose a structured latent ODE model that explicitly captures system input variations within its latent representation. Building on a static latent variable specification, our model learns (independent) stochastic factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space. This approach provides actionable modeling through the controlled generation of time-series data for novel input combinations (or perturbations). Additionally, we propose a flexible approach for quantifying uncertainties, leveraging a quantile regression formulation. Results on challenging biological datasets show consistent improvements over competitive baselines in the controlled generation of observational data and inference of biologically meaningful system inputs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c274c48827a543ceb032855081e5362caaf53c31" target='_blank'>Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations</a></td>
-          <td>
-            Paidamoyo Chapfuwa, Sherri Rose, L. Carin, Edward Meeds, Ricardo Henao
-          </td>
-          <td>2022-02-25</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>92</td>
-        </tr>
-    
-        <tr id="We present a Bayesian framework for parameter inference in noisy, non‐stationary, nonlinear, dynamical systems. The technique is implemented in two distinct ways: (i) Lightweight implementation to be used for on‐line analysis, allowing multiple parameter estimation, optimal compensation for dynamical noise, and reconstruction by integration of the hidden dynamical variables, but with some limitations on how the noise appears in the dynamics; (ii) Full scale implementation of the technique with extensive numerical simulations (MCMC), allowing for more sophisticated reconstruction of hidden dynamical trajectories and dealing better with sources of noise external to the dynamics (measurements noise).">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8c006fc560971eed115d5a0f8bbd3a7aec7cb14f" target='_blank'>Applications of dynamical inference to the analysis of noisy biological time series with hidden dynamical variables.</a></td>
-          <td>
-            A. Duggento, D. Luchinsky, V. Smelyanskiy, M. Millonas, P. McClintock
-          </td>
-          <td>2009-05-04</td>
-          <td></td>
-          <td>0</td>
-          <td>44</td>
-        </tr>
-    
-        <tr id="Biological data often contains measurements of dynamic entities such as cells or organisms in various states of progression. However, biological systems are notoriously difficult to describe analytically due to their many interacting components, and in many cases, the technical challenge of taking longitudinal measurements. This leads to difficulties in studying the features of the dynamics, for examples the drivers of the transition. To address this problem, we present a deep neural network framework we call Dynamics Modeling Network or DyMoN. DyMoN is a neural network framework trained as a deep generative Markov model whose next state is a probability distribution based on the current state. DyMoN is well-suited to the idiosyncrasies of biological data, including noise, sparsity, and the lack of longitudinal measurements in many types of systems. Thus, DyMoN can be trained using probability distributions derived from the data in any way, such as trajectories derived via dimensionality reduction methods, and does not require longitudinal measurements. We show the advantage of learning deep models over shallow models such as Kalman filters and hidden Markov models that do not learn representations of the data, both in terms of learning embeddings of the data and also in terms training efficiency, accuracy and ability to multitask. We perform three case studies of applying DyMoN to different types of biological systems and extracting features of the dynamics in each case by examining the learned model.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/08e1e14df71651bb15302fdbc1a9ef7b31705630" target='_blank'>Modeling Dynamics of Biological Systems with Deep Generative Neural Networks</a></td>
-          <td>
-            Scott A. Gigante, D. V. Dijk, Kevin R. Moon, Alexander Strzalkowski, Guy Wolf, Smita Krishnaswamy
-          </td>
-          <td>2018-09-27</td>
-          <td>arXiv: Learning</td>
-          <td>3</td>
-          <td>26</td>
-        </tr>
-    
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Systems biology informed deep learning for inferring parameters and hidden dynamics</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/95a73387877a042e554717babbced547ee867098" target='_blank'>Parameter inference for systems biology models</a></td>
-          <td>
-            Ananya Rastogi
-          </td>
-          <td>2021-01-01</td>
-          <td>Nature Computational Science</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Physics Informed Neural Networks (PINNs) are a type of function approximators that use both data-driven supervised neural networks to learn the model of the dynamics of a physical system, and mathematical equations of the physical laws governing that system. PINNs have the benefit of being data-driven to train a model, but also of being able to assure consistency with the physics, and to extrapolate accurately beyond the range of data that currently accessible. As a result, PINNs can provide models that are more reliable while using less data. Specifically, the PINNs objective is to learn the solutions of a systems of equations using supervised learning on the available data and incorporating the knowledge of physical laws and constraints into the training process. However, solving single differential equations with a PINN may be relatively simple, solving systems of coupled differential equations may not be so simple. In this study, I present a neural network model specialized in solving differential equations of enzyme kinetics that has the main characteristic of being a demonstrative simple case of coupled equations system. The study focuses mainly on the theoretical aspects of the definition of a physics-informed loss function and shows a case study that highlights the challenges still to be overcome in solving systems of coupled differential equations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b4d6e1de7f328a123a9fdbecde40b1d5603dcdf9" target='_blank'>Learning systems of ordinary differential equations with Physics-Informed Neural Networks: the case study of enzyme kinetics</a></td>
-          <td>
-            Paola Lecca
-          </td>
-          <td>2024-02-01</td>
-          <td>Journal of Physics: Conference Series</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5db8361a4417bc02365909540dc7c3bf3442bdef" target='_blank'>Scalable Inference of Ordinary Differential Equation Models of Biochemical Processes.</a></td>
-          <td>
-            Fabian Fröhlich, Carolin Loos, J. Hasenauer
-          </td>
-          <td>2017-11-21</td>
-          <td>Methods in molecular biology</td>
-          <td>23</td>
-          <td>36</td>
-        </tr>
-    
-        <tr id="Identifying the reactions that govern a dynamical biological system is a crucial but challenging task in systems biology. In this work, we present a data-driven method to infer the underlying biochemical reaction system governing a set of observed species concentrations over time. We formulate the problem as a regression over a large, but limited, mass-action constrained reaction space and utilize sparse Bayesian inference via the regularized horseshoe prior to produce robust, interpretable biochemical reaction networks, along with uncertainty estimates of parameters. The resulting systems of chemical reactions and posteriors inform the biologist of potentially several reaction systems that can be further investigated. We demonstrate the method on two examples of recovering the dynamics of an unknown reaction system, to illustrate the benefits of improved accuracy and information obtained.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3b68c307512ff23dc5f769679ec5a46e9240c103" target='_blank'>Identification of dynamic mass-action biochemical reaction networks using sparse Bayesian methods</a></td>
-          <td>
-            Richard M. Jiang, Prashant Singh, Fredrik Wrede, A. Hellander, Linda Petzold
-          </td>
-          <td>2022-01-01</td>
-          <td>PLoS Computational Biology</td>
-          <td>10</td>
-          <td>22</td>
-        </tr>
-    
-        <tr id="We introduce a flexible, scalable Bayesian inference framework for nonlinear dynamical systems characterised by distinct and hierarchical variability at the individual, group, and population levels. Our model class is a generalisation of nonlinear mixed-effects (NLME) dynamical systems, the statistical workhorse for many experimental sciences. We cast parameter inference as stochastic optimisation of an end-to-end differentiable, block-conditional variational autoencoder. We specify the dynamics of the data-generating process as an ordinary differential equation (ODE) such that both the ODE and its solver are fully differentiable. This model class is highly flexible: the ODE right-hand sides can be a mixture of user-prescribed or “white-box” sub-components and neural network or “black-box” sub-components. Using stochastic optimisation, our amortised inference algorithm could seamlessly scale up to massive data collection pipelines (common in labs with robotic automation). Finally, our framework supports interpretability with respect to the underlying dynamics, as well as predictive generalization to unseen combinations of group components (also called “zero-shot” learning). We empirically validate our method by predicting the dynamic behaviour of bacteria that were genetically engineered to function as biosensors.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/309c5ae93a4cabfd37747abd130866240e265b2d" target='_blank'>Efficient Amortised Bayesian Inference for Hierarchical and Nonlinear Dynamical Systems</a></td>
-          <td>
-            Geoffrey Roeder, Paul K. Grant, Andrew Phillips, Neil Dalchau, Edward Meeds
-          </td>
-          <td>2019-05-24</td>
-          <td>ArXiv</td>
-          <td>21</td>
-          <td>28</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2b7ca0696fd3e37938b35c357bc68e74b262d004" target='_blank'>Data-Driven Modeling of Partially Observed Biological Systems</a></td>
-          <td>
-            Wei-Hung Su, Ching-Shan Chou, Dongbin Xiu
-          </td>
-          <td>2024-01-13</td>
-          <td>Communications on Applied Mathematics and Computation</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="The inner workings of a biological cell or a chemical reaction can be rationalized by the network of reactions, whose structure reveals the most important functional mechanisms. For complex systems, these reaction networks are not known a priori and cannot be efficiently computed with ab initio methods, therefore an important approach goal is to estimate effective reaction networks from observations, such as time series of the main species. Reaction networks estimated with standard machine learning techniques such as least-squares regression may fit the observations, but will typically contain spurious reactions. Here we extend the sparse identification of nonlinear dynamics (SINDy) method to vector-valued ansatz functions, each describing a particular reaction process. The resulting sparse tensor regression method “reactive SINDy” is able to estimate a parsimonious reaction network. We illustrate that a gene regulation network can be correctly estimated from observed time series.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8fc892b470fed3d7b2dea5598646b9e2e2e433fc" target='_blank'>Reactive SINDy: Discovering governing reactions from concentration data</a></td>
-          <td>
-            Moritz Hoffmann, C. Fröhner, F. Noé
-          </td>
-          <td>2018-10-12</td>
-          <td>bioRxiv</td>
-          <td>102</td>
-          <td>61</td>
-        </tr>
-    
-        <tr id="Artificial neural networks have changed many fields by giving scientists a strong way to model complex phenomena. They are also becoming increasingly useful for solving various difficult scientific problems. Still, people keep trying to find faster and more accurate ways to simulate dynamic systems. This research explores the transformative capabilities of physics-informed neural networks, a specialized subset of artificial neural networks, in modeling complex dynamical systems with enhanced speed and accuracy. These networks incorporate known physical laws into the learning process, ensuring predictions remain consistent with fundamental principles, which is crucial when dealing with scientific phenomena. This study focuses on optimizing the application of this specialized network for simultaneous system dynamics simulations and learning time-varying parameters, particularly when the number of unknowns in the system matches the number of undetermined parameters. Additionally, we explore scenarios with a mismatch between parameters and equations, optimizing network architecture to enhance convergence speed, computational efficiency, and accuracy in learning the time-varying parameter. Our approach enhances the algorithm’s performance and accuracy, ensuring optimal use of computational resources and yielding more precise results. Extensive experiments are conducted on four different dynamical systems: first-order irreversible chain reactions, biomass transfer, the Brusselsator model, and the Lotka-Volterra model, using synthetically generated data to validate our approach. Additionally, we apply our method to the susceptible-infected-recovered model, utilizing real-world COVID-19 data to learn the time-varying parameters of the pandemic’s spread. A comprehensive comparison between the performance of our approach and fully connected deep neural networks is presented, evaluating both accuracy and computational efficiency in parameter identification and system dynamics capture. The results demonstrate that the physics-informed neural networks outperform fully connected deep neural networks in performance, especially with increased network depth, making them ideal for real-time complex system modeling. This underscores the physics-informed neural network’s effectiveness in scientific modeling in scenarios with balanced unknowns and parameters. Furthermore, it provides a fast, accurate, and efficient alternative for analyzing dynamic systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e12ebec869b56d7d0b265027509b9e644958daae" target='_blank'>Optimizing Physics-Informed Neural Network in Dynamic System Simulation and Learning of Parameters</a></td>
-          <td>
-            Ebenezer O. Oluwasakin, Abdul Q. M. Khaliq
-          </td>
-          <td>2023-11-28</td>
-          <td>Algorithms</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Emerging concepts from scientific deep machine learning such as physics-informed neural networks (PINNs) enable a data-driven approach for the study of complex kinetic problems. We present an extended framework that combines the advantages of PINNs with the detailed consideration of experimental parameter variations for the simulation and prediction of chemical reaction kinetics. The approach is based on truncated Taylor series expansions for the underlying fundamental equations, whereby the external variations can be interpreted as perturbations of the kinetic parameters. Accordingly, our method allows for an efficient consideration of experimental parameter settings and their influence on the concentration profiles and reaction kinetics. A particular advantage of our approach, in addition to the consideration of univariate and multivariate parameter variations, is the robust model-based exploration of the parameter space to determine optimal reaction conditions in combination with advanced reaction insights. The benefits of this concept are demonstrated for higher-order chemical reactions including catalytic and oscillatory systems in combination with small amounts of training data. All predicted values show a high level of accuracy, demonstrating the broad applicability and flexibility of our approach.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/00264722dab10b6e0eee0715cbb41cd35b5b007a" target='_blank'>Scientific Deep Machine Learning Concepts for the Prediction of Concentration Profiles and Chemical Reaction Kinetics: Consideration of Reaction Conditions.</a></td>
-          <td>
-            Niklas Adebar, Julian Keupp, Victor N Emenike, Jonas Kühlborn, Lisa Vom Dahl, Robert Möckel, Jens Smiatek
-          </td>
-          <td>2024-01-25</td>
-          <td>The journal of physical chemistry. A</td>
-          <td>2</td>
-          <td>28</td>
-        </tr>
-    
-        <tr id="Parameter estimation is one of the central problems in computational modeling of biological systems. Typically, scientists must fully specify the mathematical structure of the model, often expressed as a system of ordinary differential equations, to estimate the parameters. This process poses significant challenges due to the necessity for a detailed understanding of the underlying biological mechanisms. In this paper, we present an approach for estimating model parameters and assessing their identifiability in situations where only partial knowledge of the system structure is available. The partially known model is extended into a system of Hybrid Neural Ordinary Differential Equations, which captures the unknown portions of the system using neural networks. Integrating neural networks into the model structure introduces two primary challenges for parameter estimation: the need to globally explore the search space while employing gradient-based optimization, and the assessment of parameter identifiability, which may be hindered by the expressive nature of neural networks. To overcome the first issue, we treat biological parameters as hyperparameters in the extended model, exploring the parameter search space during hyperparameter tuning. The second issue is then addressed by an a posteriori analysis of parameter identifiability, computed by introducing a variant of a well-established approach for mechanistic models. These two components are integrated into an end-to-end pipeline that is thoroughly described in the paper. We assess the effectiveness of the proposed workflow on test cases derived from three different benchmark models. These test cases have been designed to mimic real-world conditions, including the presence of noise in the training data and various levels of data availability for the system variables. Author summary Parameter estimation is a central challenge in modeling biological systems. Typically, scientists calibrate the parameters by aligning model predictions with measured data once the model structure is defined. Our paper introduces a workflow that leverages the integration between mechanistic modeling and machine learning to estimate model parameters when the model structure is not fully known. We focus mainly on analyzing the identifiability of the model parameters, which measures how confident we can be in the parameter estimates given the available experimental data and partial mechanistic understanding of the system. We assessed the effectiveness of our approach in various in silico scenarios. Our workflow represents a first step to adapting traditional methods used in fully mechanistic models to the scenario of hybrid modeling.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a064c473effb10441bd8fe1c6bde24ed0162e1e3" target='_blank'>Robust parameter estimation and identifiability analysis with Hybrid Neural Ordinary Differential Equations in Computational Biology</a></td>
-          <td>
-            Stefano Giampiccolo, Federico Reali, Anna Fochesato, Giovanni Iacca, Luca Marchetti
-          </td>
-          <td>2024-06-12</td>
-          <td>bioRxiv</td>
-          <td>0</td>
-          <td>6</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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diff --git a/docs/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220.md b/docs/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220.md
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-  <i class="footer">This page was last updated on 2024-08-08 13:17:26 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Discovery of Physics From Data: Universal Laws and Discrepancies</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically interpretable models that can (i) generalize to predict previously unobserved behaviors, (ii) provide effective forecasting predictions (extrapolation), and (iii) be certifiable. Autonomous systems will necessarily interact with changing and uncertain environments, motivating the need for models that can accurately extrapolate based on physical principles (e.g. Newton’s universal second law for classical mechanics, $F=ma$ ). Standard ML approaches have shown impressive performance for predicting dynamics in an interpolatory regime, but the resulting models often lack interpretability and fail to generalize. We build on a sparse regression framework that discovers governing dynamical systems models from data, selecting relevant terms in the dynamics from a library of possible functions. Our critically enabling innovation introduces a relaxed version of a sparse optimization framework that allows the use of non-convex sparsity promoting regularization functions and addresses three open challenges in scientific problems and data sets: (i) robust handling of outliers and corrupt data within noisy sensor measurements, (ii) parametric dependencies in candidate library functions, and (iii) the imposition of physical constraints. By explicitly addressing these open challenges, the integrated and unified algorithm developed provides a significant advancement over current state-of-the-art sparse model discovery methods. We show that the approach discovers parsimonious dynamical models on several example systems. This flexible approach can be tailored to the unique challenges associated with a wide range of applications and data sets, providing a powerful ML-based framework for learning governing models for physical systems from data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7a752ef2c71afa4566dd038b63929e75e41ab32f" target='_blank'>A Unified Sparse Optimization Framework to Learn Parsimonious Physics-Informed Models From Data</a></td>
-          <td>
-            Kathleen P. Champion, P. Zheng, A. Aravkin, S. Brunton, J. Kutz
-          </td>
-          <td>2019-06-25</td>
-          <td>IEEE Access</td>
-          <td>95</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our neural new-physics detector (NNPhD) aims to detect new physics by decomposing the force field into conservative and nonconservative components, which are represented by a Lagrangian neural network (LNN) and an unconstrained neural network, respectively, trained to minimize the force recovery error plus a constant λ times the magnitude of the predicted nonconservative force. We show that a phase transition occurs at λ=1, universally for arbitrary forces. We demonstrate that NNPhD successfully discovers new physics in toy numerical experiments, rediscovering friction (1493) from a damped double pendulum, Neptune from Uranus' orbit (1846), and gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD coupled with an integrator outperforms both an LNN and an unconstrained neural network for predicting the future of a damped double pendulum.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bb09f46438236f6e916d2ad23eca92330a41b9fb" target='_blank'>Machine-Learning Non-Conservative Dynamics for New-Physics Detection</a></td>
-          <td>
-            Ziming Liu, Bohan Wang, Qi Meng, Wei Chen, M. Tegmark, Tie-Yan Liu
-          </td>
-          <td>2021-05-31</td>
-          <td>Physical review. E</td>
-          <td>14</td>
-          <td>82</td>
-        </tr>
-    
-        <tr id="Invariants and conservation laws convey critical information about the underlying dynamics of a system, yet it is generally infeasible to find them from large-scale data without any prior knowledge or human insight. We propose ConservNet to achieve this goal, a neural network that spontaneously discovers a conserved quantity from grouped data where the members of each group share invariants, similar to a general experimental setting where trajectories from different trials are observed. As a neural network trained with a novel and intuitive loss function called noise-variance loss, ConservNet learns the hidden invariants in each group of multi-dimensional observables in a data-driven, end-to-end manner. Our model successfully discovers underlying invariants from the simulated systems having invariants as well as a real-world double pendulum trajectory. Since the model is robust to various noises and data conditions compared to baseline, our approach is directly applicable to experimental data for discovering hidden conservation laws and further, general relationships between variables.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/87648e8b1e3c94de06380ff58f39c150bc9379bb" target='_blank'>Discovering conservation laws from trajectories via machine learning</a></td>
-          <td>
-            Seungwoong Ha, Hawoong Jeong
-          </td>
-          <td>2021-02-08</td>
-          <td>ArXiv</td>
-          <td>9</td>
-          <td>43</td>
-        </tr>
-    
-        <tr id="How many free variables do we really need to build a credible model of a physical system? Currently there is no systematic approach; we appeal to some physical principles, tune free variables by comparing with canonical cases, and hope our real-world applications interpolate between them. In this work we combine two pioneering and entirely disparate pieces of mathematics: the century-old techniques of Sophus Lie for solving differential equtions and recent work initiated by Field's medallist Terence Tao on converting NP-complete combinatorical problems into neighbouring convex optimisations. We present a novel and fully systematic procedure for designing models of physical systems with necessary and just-sufficient complexity, in marked contrast with the approach to function approximation taken by neural networks and other current approaches to machine learning. Our methodology replaces the ad-hoc development of models to recover structure and understanding from observational, experimental or simulated data. At its core, our method seeks to find invariant properties of differential equations known as Lie symmetries, and for this reason we have called our algorithm the Lie Detector.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/73027ff397a011f8ffb5affb47337bfa6efbfef9" target='_blank'>The Lie Detector.</a></td>
-          <td>
-            A. Young, A. Lawrie
-          </td>
-          <td>2019-12-13</td>
-          <td>arXiv: Signal Processing</td>
-          <td>0</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d95c7f3a6ca2b98ba3c4422aabb33e3754cb1a47" target='_blank'>Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems</a></td>
-          <td>
-            Truong X. Nghiem, Ján Drgoňa, Colin N. Jones, Zoltán Nagy, Roland Schwan, Biswadip Dey, A. Chakrabarty, S. D. Cairano, J. Paulson, Andrea Carron, M. Zeilinger, Wenceslao Shaw-Cortez, D. Vrabie
-          </td>
-          <td>2023-05-31</td>
-          <td>2023 American Control Conference (ACC)</td>
-          <td>15</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse problems. We find that state-of-the-art training techniques are not well-suited to many problems that involve physical processes. The highly nonlinear behavior, common in physical processes, results in strongly varying gradients that lead first-order optimizers like SGD or Adam to compute suboptimal optimization directions. We propose a novel hybrid training approach that combines higher-order optimization methods with machine learning techniques. We take updates from a scale-invariant inverse problem solver and embed them into the gradient-descent-based learning pipeline, replacing the regular gradient of the physical process. We demonstrate the capabilities of our method on a variety of canonical physical systems, showing that it yields significant improvements on a wide range of optimization and learning problems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8070e0a6ca3fdd46e7af5ec9090643ff60f13a78" target='_blank'>Scale-invariant Learning by Physics Inversion</a></td>
-          <td>
-            Philipp Holl, V. Koltun, Nils Thuerey
-          </td>
-          <td>2021-09-30</td>
-          <td>ArXiv, DBLP</td>
-          <td>5</td>
-          <td>103</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0dfa7e909940fb1840831614e593714a5544ec02" target='_blank'>Learning continuous models for continuous physics</a></td>
-          <td>
-            A. Krishnapriyan, A. Queiruga, N. Benjamin Erichson, Michael W. Mahoney
-          </td>
-          <td>2022-02-17</td>
-          <td>Communications Physics</td>
-          <td>23</td>
-          <td>30</td>
-        </tr>
-    
-        <tr id="We present AI Poincaré, a machine learning algorithm for autodiscovering conserved quantities using trajectory data from unknown dynamical systems. We test it on five Hamiltonian systems, including the gravitational three-body problem, and find that it discovers not only all exactly conserved quantities, but also periodic orbits, phase transitions, and breakdown timescales for approximate conservation laws.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f3cf4756b2375cd6694267370a8d98543e781169" target='_blank'>Machine Learning Conservation Laws from Trajectories.</a></td>
-          <td>
-            Ziming Liu, Max Tegmark
-          </td>
-          <td>2021-05-06</td>
-          <td>Physical review letters</td>
-          <td>82</td>
-          <td>81</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9865d777203b47ab6ad919ae979714a1dbac8eb9" target='_blank'>From data to conservation laws</a></td>
-          <td>
-            F. Chirigati
-          </td>
-          <td>2023-09-01</td>
-          <td>Nature Computational Science</td>
-          <td>0</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2cd3a4931a71d74bcec53716855a3f465bca8e71" target='_blank'>Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference</a></td>
-          <td>
-            N. Sawant, B. Kramer, B. Peherstorfer
-          </td>
-          <td>2021-07-06</td>
-          <td>ArXiv</td>
-          <td>21</td>
-          <td>27</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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-    Recommendations for the article <i>Relational inductive biases, deep learning, and graph networks</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
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-    
-        <tr id="Graph neural networks (GNNs) have recently grown in popularity in the field of artificial intelligence (AI) due to their unique ability to ingest relatively unstructured data types as input data. Although some elements of the GNN architecture are conceptually similar in operation to traditional neural networks (and neural network variants), other elements represent a departure from traditional deep learning techniques. This tutorial exposes the power and novelty of GNNs to AI practitioners by collating and presenting details regarding the motivations, concepts, mathematics, and applications of the most common and performant variants of GNNs. Importantly, we present this tutorial concisely, alongside practical examples, thus providing a practical and accessible tutorial on the topic of GNNs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/28a22bea3d98b326715bcede9b0216d3f788e1b8" target='_blank'>A Practical Tutorial on Graph Neural Networks</a></td>
-          <td>
-            I. Ward, J. Joyner, C. Lickfold, Yulan Guo, Bennamoun
-          </td>
-          <td>2020-10-11</td>
-          <td>ACM Computing Surveys (CSUR)</td>
-          <td>8</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Contemporary neural networks still fall short of human-level generalization, which extends far beyond our direct experiences. In this paper, we argue that the underlying cause for this shortcoming is their inability to dynamically and flexibly bind information that is distributed throughout the network. This binding problem affects their capacity to acquire a compositional understanding of the world in terms of symbol-like entities (like objects), which is crucial for generalizing in predictable and systematic ways. To address this issue, we propose a unifying framework that revolves around forming meaningful entities from unstructured sensory inputs (segregation), maintaining this separation of information at a representational level (representation), and using these entities to construct new inferences, predictions, and behaviors (composition). Our analysis draws inspiration from a wealth of research in neuroscience and cognitive psychology, and surveys relevant mechanisms from the machine learning literature, to help identify a combination of inductive biases that allow symbolic information processing to emerge naturally in neural networks. We believe that a compositional approach to AI, in terms of grounded symbol-like representations, is of fundamental importance for realizing human-level generalization, and we hope that this paper may contribute towards that goal as a reference and inspiration.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d642868ce4325ebf3026c0aa0c497a079f112a8d" target='_blank'>On the Binding Problem in Artificial Neural Networks</a></td>
-          <td>
-            Klaus Greff, Sjoerd van Steenkiste, J. Schmidhuber
-          </td>
-          <td>2020-12-09</td>
-          <td>ArXiv</td>
-          <td>200</td>
-          <td>95</td>
-        </tr>
-    
-        <tr id="The human cognitive system exhibits remarkable flexibility and generalization capabilities, partly due to its ability to form low-dimensional, compositional representations of the environment. In contrast, standard neural network architectures often struggle with abstract reasoning tasks, overfitting, and requiring extensive data for training. This paper investigates the impact of the relational bottleneck -- a mechanism that focuses processing on relations among inputs -- on the learning of factorized representations conducive to compositional coding and the attendant flexibility of processing. We demonstrate that such a bottleneck not only improves generalization and learning efficiency, but also aligns network performance with human-like behavioral biases. Networks trained with the relational bottleneck developed orthogonal representations of feature dimensions latent in the dataset, reflecting the factorized structure thought to underlie human cognitive flexibility. Moreover, the relational network mimics human biases towards regularity without pre-specified symbolic primitives, suggesting that the bottleneck fosters the emergence of abstract representations that confer flexibility akin to symbols.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/965a57e1113f21b15ef2f62ba94f4e3db890e68c" target='_blank'>A Relational Inductive Bias for Dimensional Abstraction in Neural Networks</a></td>
-          <td>
-            Declan Campbell, Jonathan D. Cohen
-          </td>
-          <td>2024-02-28</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Neural networks have succeeded in many reasoning tasks. Empirically, these tasks require specialized network structures, e.g., Graph Neural Networks (GNNs) perform well on many such tasks, but less structured networks fail. Theoretically, there is limited understanding of why and when a network structure generalizes better than others, although they have equal expressive power. In this paper, we develop a framework to characterize which reasoning tasks a network can learn well, by studying how well its computation structure aligns with the algorithmic structure of the relevant reasoning process. We formally define this algorithmic alignment and derive a sample complexity bound that decreases with better alignment. This framework offers an explanation for the empirical success of popular reasoning models, and suggests their limitations. As an example, we unify seemingly different reasoning tasks, such as intuitive physics, visual question answering, and shortest paths, via the lens of a powerful algorithmic paradigm, dynamic programming (DP). We show that GNNs align with DP and thus are expected to solve these tasks. On several reasoning tasks, our theory is supported by empirical results.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/271b31b41782d11c5176a260f0ecdf2611b21e77" target='_blank'>What Can Neural Networks Reason About?</a></td>
-          <td>
-            Keyulu Xu, Jingling Li, Mozhi Zhang, S. Du, K. Kawarabayashi, S. Jegelka
-          </td>
-          <td>2019-05-30</td>
-          <td>ArXiv</td>
-          <td>211</td>
-          <td>47</td>
-        </tr>
-    
-        <tr id="Despite the successes of recent developments in visual AI, different shortcomings still exist; from missing exact logical reasoning, to abstract generalization abilities, to understanding complex and noisy scenes. Unfortunately, existing benchmarks, were not designed to capture more than a few of these aspects. Whereas deep learning datasets focus on visually complex data but simple visual reasoning tasks, inductive logic datasets involve complex logical learning tasks, however, lack the visual component. To address this, we propose the visual logical learning dataset, V-LoL, that seamlessly combines visual and logical challenges. Notably, we introduce the first instantiation of V-LoL, V-LoL-Trains, -- a visual rendition of a classic benchmark in symbolic AI, the Michalski train problem. By incorporating intricate visual scenes and flexible logical reasoning tasks within a versatile framework, V-LoL-Trains provides a platform for investigating a wide range of visual logical learning challenges. We evaluate a variety of AI systems including traditional symbolic AI, neural AI, as well as neuro-symbolic AI. Our evaluations demonstrate that even state-of-the-art AI faces difficulties in dealing with visual logical learning challenges, highlighting unique advantages and limitations specific to each methodology. Overall, V-LoL opens up new avenues for understanding and enhancing current abilities in visual logical learning for AI systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/51d4eafe0f3c114f0b63060c43af4c02c0d71214" target='_blank'>V-LoL: A Diagnostic Dataset for Visual Logical Learning</a></td>
-          <td>
-            Lukas Helff, Wolfgang Stammer, Hikaru Shindo, D. Dhami, K. Kersting
-          </td>
-          <td>2023-06-13</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="Recent research has highlighted the role of relational inductive biases in building learning agents that can generalize and reason in a compositional manner. However, while relational learning algorithms such as graph neural networks (GNNs) show promise, we do not understand how effectively these approaches can adapt to new tasks. In this work, we study the task of logical generalization using GNNs by designing a benchmark suite grounded in first-order logic. Our benchmark suite, GraphLog, requires that learning algorithms perform rule induction in different synthetic logics, represented as knowledge graphs. GraphLog consists of relation prediction tasks on 57 distinct logical domains. We use GraphLog to evaluate GNNs in three different setups: single-task supervised learning, multi-task pretraining, and continual learning. Unlike previous benchmarks, our approach allows us to precisely control the logical relationship between the different tasks. We find that the ability for models to generalize and adapt is strongly determined by the diversity of the logical rules they encounter during training, and our results highlight new challenges for the design of GNN models. We publicly release the dataset and code used to generate and interact with the dataset at this https URL.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7e9af8a6081dc00187bd4a6727751d1721bd7816" target='_blank'>Evaluating Logical Generalization in Graph Neural Networks</a></td>
-          <td>
-            Koustuv Sinha, Shagun Sodhani, Joelle Pineau, William L. Hamilton
-          </td>
-          <td>2020-03-14</td>
-          <td>ArXiv</td>
-          <td>21</td>
-          <td>66</td>
-        </tr>
-    
-  </tbody>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Data-driven discovery of coordinates and governing equations</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Significance Understanding dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled technology, including aircraft, combustion engines, satellites, and electrical power. This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. There are many critical data-driven problems, such as understanding cognition from neural recordings, inferring climate patterns, determining stability of financial markets, predicting and suppressing the spread of disease, and controlling turbulence for greener transportation and energy. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an important role in these efforts. Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5d150cec2775f9bc863760448f14104cc8f42368" target='_blank'>Discovering governing equations from data by sparse identification of nonlinear dynamical systems</a></td>
-          <td>
-            S. Brunton, J. Proctor, J. Kutz
-          </td>
-          <td>2015-09-11</td>
-          <td>Proceedings of the National Academy of Sciences</td>
-          <td>3168</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e596988b1df3a0bc78bf72c0bfdb21c85eaab6c9" target='_blank'>Physics-informed learning of governing equations from scarce data</a></td>
-          <td>
-            Zhao Chen, Yang Liu, Hao Sun
-          </td>
-          <td>2020-05-05</td>
-          <td>Nature Communications</td>
-          <td>234</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. Recent advances in sparse identification show encouraging success in distilling closed-form governing equations from data for a wide range of nonlinear dynamical systems. However, the fundamental bottleneck of this approach lies in the robustness and scalability with respect to data scarcity and noise. This work introduces a novel physics-informed deep learning framework to discover governing partial differential equations (PDEs) from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this approach seamlessly integrates the strengths of deep neural networks for rich representation learning, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the PDEs. The efficacy and robustness of this method are demonstrated on discovering a variety of PDE systems with different levels of data scarcity and noise. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e2acd4a2bc6af5deb02f542846766868e3f1b180" target='_blank'>Deep learning of physical laws from scarce data</a></td>
-          <td>
-            Zhao Chen, Yang Liu, Hao Sun
-          </td>
-          <td>2020-05-05</td>
-          <td>ArXiv</td>
-          <td>19</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3b44db6efdb3999b65be446114afb04720e572cc" target='_blank'>Modeling of dynamical systems through deep learning</a></td>
-          <td>
-            P. Rajendra, V. Brahmajirao
-          </td>
-          <td>2020-11-22</td>
-          <td>Biophysical Reviews</td>
-          <td>32</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under ℓ1 constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated video frames. However, it is challenging for ℓ1-based sparse inference to perform correct identification for real data due to the noisy measurements and often limited sample sizes. To address the data-driven discovery of physics in the low-data and high-noise regimes, we propose Bayesian SINDy autoencoders, which incorporate a hierarchical Bayesian Spike-and-slab Gaussian Lasso prior. Bayesian SINDy autoencoder enables the joint discovery of governing equations and coordinate systems with uncertainty estimate. To resolve the challenging computational tractability of the Bayesian hierarchical setting, we adapt an adaptive empirical Bayesian method with Stochastic Gradient Langevin Dynamics (SGLD) which gives a computationally tractable way of Bayesian posterior sampling within our framework. Bayesian SINDy autoencoder achieves better physics discovery with lower data and fewer training epochs, along with valid uncertainty quantification suggested by the experimental studies. The Bayesian SINDy autoencoder can be applied to real video data, withaccurate physics discovery which correctly identifies the governing equation and provides a close estimate for standard physics constants like gravity g, for example, in videos of a pendulum.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ea1d48d41a95a8547506f807a1307a37ec05356e" target='_blank'>Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants</a></td>
-          <td>
-            Liyao (Mars) Gao, J. Kutz
-          </td>
-          <td>2022-11-19</td>
-          <td>Proceedings of the Royal Society A</td>
-          <td>10</td>
-          <td>31</td>
-        </tr>
-    
-        <tr id="Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning-specifically deep learning-techniques have shown their capabilities in approximating dynamics from data, but a shortcoming of traditional deep learning is that there is little insight into the underlying mapping beyond its numerical output for a given input. This limits their utility in analysis beyond simple prediction. Simultaneously, a number of strategies exist which identify models based on a fixed dictionary of basis functions, but most either require some intuition or insight about the system, or are susceptible to overfitting or a lack of parsimony. Here, we present a novel approach that combines the flexibility and accuracy of deep learning approaches with the utility of symbolic solutions: a deep neural network that generates a symbolic expression for the governing equations. We first describe the architecture for our model and then show the accuracy of our algorithm across a range of classical dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eddffa1f2cf18c7ca4edbdaf01fd805f415aa4b8" target='_blank'>Symbolic regression via neural networks.</a></td>
-          <td>
-            N. Boddupalli, T. Matchen, J. Moehlis
-          </td>
-          <td>2023-08-01</td>
-          <td>Chaos</td>
-          <td>2</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1f18c5206491626d36c2271aaf491dbc945f6247" target='_blank'>Automatically discovering ordinary differential equations from data with sparse regression</a></td>
-          <td>
-            Kevin Egan, Weizhen Li, Rui Carvalho
-          </td>
-          <td>2024-01-09</td>
-          <td>Communications Physics</td>
-          <td>7</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/899995e30820d657b2e2feb791025cd6b2027e22" target='_blank'>Discovering sparse interpretable dynamics from partial observations</a></td>
-          <td>
-            Peter Y. Lu, Joan Ariño Bernad, M. Soljačić
-          </td>
-          <td>2021-07-22</td>
-          <td>Communications Physics</td>
-          <td>17</td>
-          <td>94</td>
-        </tr>
-    
-        <tr id="Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/18c6dbc4e20d80b81497e8c444e6f9a9ee1acf36" target='_blank'>Sparse Estimation for Hamiltonian Mechanics</a></td>
-          <td>
-            Yuya Note, Masahito Watanabe, Hiroaki Yoshimura, Takaharu Yaguchi, Toshiaki Omori
-          </td>
-          <td>2024-03-25</td>
-          <td>Mathematics</td>
-          <td>0</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="Distilling analytical models from data has the potential to advance our understanding and prediction of nonlinear dynamics. Although discovery of governing equations based on observed system states (e.g., trajectory time series) has revealed success in a wide range of nonlinear dynamics, uncovering the closed-form equations directly from raw videos still remains an open challenge. To this end, we introduce a novel end-to-end unsupervised deep learning framework to uncover the mathematical structure of equations that governs the dynamics of moving objects in videos. Such an architecture consists of (1) an encoder-decoder network that learns low-dimensional spatial/pixel coordinates of the moving object, (2) a learnable Spatial-Physical Transformation component that creates mapping between the extracted spatial/pixel coordinates and the latent physical states of dynamics, and (3) a numerical integrator-based sparse regression module that uncovers the parsimonious closed-form governing equations of learned physical states and, meanwhile, serves as a constraint to the autoencoder. The efficacy of the proposed method is demonstrated by uncovering the governing equations of a variety of nonlinear dynamical systems depicted by moving objects in videos. The resulting computational framework enables discovery of parsimonious interpretable model in a flexible and accessible sensing environment where only videos are available.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5ca657acba0ea3cba5a062c70eb5cb3a9aede95f" target='_blank'>Uncovering Closed-form Governing Equations of Nonlinear Dynamics from Videos</a></td>
-          <td>
-            Lele Luan, Yang Liu, Hao Sun
-          </td>
-          <td>2021-06-09</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>12</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
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diff --git a/docs/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2.md b/docs/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2.md
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-  <i class="footer">This page was last updated on 2024-08-08 13:17:17 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Chaos as an intermittently forced linear system</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="This article introduces an advanced Koopman mode decomposition (KMD) technique -- coined Featurized Koopman Mode Decomposition (FKMD) -- that uses delay embedding and a learned Mahalanobis distance to enhance analysis and prediction of high dimensional dynamical systems. The delay embedding expands the observation space to better capture underlying manifold structure, while the Mahalanobis distance adjusts observations based on the system's dynamics. This aids in featurizing KMD in cases where good features are not a priori known. We show that FKMD improves predictions for a high-dimensional linear oscillator, a high-dimensional Lorenz attractor that is partially observed, and a cell signaling problem from cancer research.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/78f159b92f2f6689b738970dc1ce3a8641b2a534" target='_blank'>Featurizing Koopman Mode Decomposition For Robust Forecasting</a></td>
-          <td>
-            D. Aristoff, J. Copperman, Nathan Mankovich, Alexander Davies
-          </td>
-          <td>2023-12-14</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="A common problem in time-series analysis is to predict dynamics with only scalar or partial observations of the underlying dynamical system. For data on a smooth compact manifold, Takens' theorem proves a time-delayed embedding of the partial state is diffeomorphic to the attractor, although for chaotic and highly nonlinear systems, learning these delay coordinate mappings is challenging. We utilize deep artificial neural networks (ANNs) to learn discrete time maps and continuous time flows of the partial state. Given training data for the full state, we also learn a reconstruction map. Thus, predictions of a time series can be made from the current state and several previous observations with embedding parameters determined from time-series analysis. The state space for time evolution is of comparable dimension to reduced order manifold models. These are advantages over recurrent neural network models, which require a high-dimensional internal state or additional memory terms and hyperparameters. We demonstrate the capacity of deep ANNs to predict chaotic behavior from a scalar observation on a manifold of dimension three via the Lorenz system. We also consider multivariate observations on the Kuramoto-Sivashinsky equation, where the observation dimension required for accurately reproducing dynamics increases with the manifold dimension via the spatial extent of the system.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e001a698302d507abbd3a818e0b0aaf84f02e418" target='_blank'>Deep learning delay coordinate dynamics for chaotic attractors from partial observable data</a></td>
-          <td>
-            Charles D. Young, M. Graham
-          </td>
-          <td>2022-11-20</td>
-          <td>Physical review. E</td>
-          <td>8</td>
-          <td>50</td>
-        </tr>
-    
-        <tr id="A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. Takens’ theorem provides conditions for when it is possible to augment partial measurements with time delayed information, resulting in an attractor that is diffeomorphic to that of the original full-state system. This diffeomorphism is typically unknown, and learning the dynamics in the embedding space has remained an open challenge for decades. Here, we design a deep autoencoder network to learn a coordinate transformation from the delay embedded space into a new space, where it is possible to represent the dynamics in a sparse, closed form. We demonstrate this approach on the Lorenz, Rössler and Lotka–Volterra systems, as well as a Lorenz analogue from a video of a chaotic waterwheel experiment. This framework combines deep learning and the sparse identification of nonlinear dynamics methods to uncover interpretable models within effective coordinates.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/37b6820d40bb884a9ae4d32c2d57357d251edd49" target='_blank'>Discovering governing equations from partial measurements with deep delay autoencoders</a></td>
-          <td>
-            Joseph Bakarji, Kathleen P. Champion, J. Nathan Kutz, S. Brunton
-          </td>
-          <td>2022-01-13</td>
-          <td>Proceedings of the Royal Society A</td>
-          <td>68</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens' delay embedding theory provides a way to transform high-dimensional spatial information into temporal information. In this work, by combining delay embedding theory and deep learning techniques, we propose a novel framework, delay-embedding-based forecast Machine (DEFM), to predict the future values of a target variable in a self-supervised and multistep-ahead manner based on high-dimensional observations. With a three-module spatiotemporal architecture, the DEFM leverages deep neural networks to effectively extract both the spatially and temporally associated information from the observed time series even with time-varying parameters or additive noise. The DEFM can accurately predict future information by transforming spatiotemporal information to the delay embeddings of a target variable. The efficacy and precision of the DEFM are substantiated through applications in three spatiotemporally chaotic systems: a 90-dimensional (90D) coupled Lorenz system, the Lorenz 96 system, and the Kuramoto-Sivashinsky equation with inhomogeneity. Additionally, the performance of the DEFM is evaluated on six real-world datasets spanning various fields. Comparative experiments with five prediction methods illustrate the superiority and robustness of the DEFM and show the great potential of the DEFM in temporal information mining and forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9daa3f8f3c122f68a62578359b06a422153cfaf6" target='_blank'>DEFM: Delay-embedding-based forecast machine for time series forecasting by spatiotemporal information transformation.</a></td>
-          <td>
-            Hao Peng, Pei Chen, R. Liu
-          </td>
-          <td>2020-05-16</td>
-          <td>Chaos</td>
-          <td>1</td>
-          <td>78</td>
-        </tr>
-    
-        <tr id="Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens' delay embedding theory provides a way to transform high-dimensional spatial information into temporal information. In this work, by combining delay embedding theory and deep learning techniques, we propose a novel framework, delay-embedding-based forecast Machine (DEFM), to predict the future values of a target variable in a self-supervised and multistep-ahead manner based on high-dimensional observations. With a three-module spatiotemporal architecture, the DEFM leverages deep neural networks to effectively extract both the spatially and temporally associated information from the observed time series even with time-varying parameters or additive noise. The DEFM can accurately predict future information by transforming spatiotemporal information to the delay embeddings of a target variable. The efficacy and precision of the DEFM are substantiated through applications in three spatiotemporally chaotic systems: a 90-dimensional (90D) coupled Lorenz system, the Lorenz 96 system, and the Kuramoto-Sivashinsky equation with inhomogeneity. Additionally, the performance of the DEFM is evaluated on six real-world datasets spanning various fields. Comparative experiments with five prediction methods illustrate the superiority and robustness of the DEFM and show the great potential of the DEFM in temporal information mining and forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9daa3f8f3c122f68a62578359b06a422153cfaf6" target='_blank'>DEFM: Delay-embedding-based forecast machine for time series forecasting by spatiotemporal information transformation.</a></td>
-          <td>
-            Hao Peng, Pei Chen, R. Liu
-          </td>
-          <td>2020-05-16</td>
-          <td>Chaos</td>
-          <td>1</td>
-          <td>78</td>
-        </tr>
-    
-        <tr id="Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based on empirical measurement is an important step in characterizing and predicting these processes. Classifying a system as chaotic usually requires estimating its largest Lyapunov exponent, which quantifies the average rate of convergence or divergence of initially close trajectories in state space, and for which a positive value is generally accepted as an operational definition of chaos. Estimating the largest Lyapunov exponent from observations of a process is especially challenging in systems affected by dynamical noise, which is the case for many models of real-world processes, in particular models of biological systems. We describe a novel method for estimating the largest Lyapunov exponent from data, based on training Deep Learning models on synthetically generated trajectories, and demonstrate that this method yields accurate and noise-robust predictions given relatively short inputs and across a range of different dynamical systems. Our method is unique in that it can analyze tree-shaped data, a ubiquitous topology in biological settings, and specifically in dynamics over lineages of cells or organisms. We also characterize the types of input information extracted by our models for their predictions, allowing for a deeper understanding into the different ways by which chaos can be analyzed in different topologies.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9fb357e57624525f27224822502061cc8fb831e1" target='_blank'>Detecting chaos in lineage-trees: A deep learning approach</a></td>
-          <td>
-            H. Rappeport, Irit Levin Reisman, Naftali Tishby, N. Balaban
-          </td>
-          <td>2021-06-08</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>56</td>
-        </tr>
-    
-        <tr id="A generally applicable robust data-driven network modeling strategy offers rapid means to predict and control complex systems. We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b0c3d159c14b0488299269c3fd62da3b9f608709" target='_blank'>Cluster-based network modeling—From snapshots to complex dynamical systems</a></td>
-          <td>
-            Daniel Fernex, B. R. Noack, R. Semaan
-          </td>
-          <td>2021-06-01</td>
-          <td>Science Advances</td>
-          <td>41</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM only assumes smoothness of the dynamics in the state space, robustly describes short- and long-term behavior and is fully automatable as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict and control complex systems in all scientific fields.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/431ea60293afebbef92f45db017299dfe379fa1f" target='_blank'>Cluster-based network modeling -- automated robust modeling of complex dynamical systems</a></td>
-          <td>
-            Daniel Fernex, B. R. Noack, R. Semaan
-          </td>
-          <td>2020-10-30</td>
-          <td>arXiv: Data Analysis, Statistics and Probability</td>
-          <td>1</td>
-          <td>49</td>
-        </tr>
-    
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-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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diff --git a/docs/recommendations/43879cf527f4918955fd55128baa6745174d8555.md b/docs/recommendations/43879cf527f4918955fd55128baa6745174d8555.md
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-    Recommendations for the article <i>Graph networks as learnable physics engines for inference and control</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
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-  <tbody>
-    
-        <tr id="Reasoning about objects, relations, and physics is central to human intelligence, and a key goal of artificial intelligence. Here we introduce the interaction network, a model which can reason about how objects in complex systems interact, supporting dynamical predictions, as well as inferences about the abstract properties of the system. Our model takes graphs as input, performs object- and relation-centric reasoning in a way that is analogous to a simulation, and is implemented using deep neural networks. We evaluate its ability to reason about several challenging physical domains: n-body problems, rigid-body collision, and non-rigid dynamics. Our results show it can be trained to accurately simulate the physical trajectories of dozens of objects over thousands of time steps, estimate abstract quantities such as energy, and generalize automatically to systems with different numbers and configurations of objects and relations. Our interaction network implementation is the first general-purpose, learnable physics engine, and a powerful general framework for reasoning about object and relations in a wide variety of complex real-world domains.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ae42c0cff384495683192b06bd985cdd7a54632a" target='_blank'>Interaction Networks for Learning about Objects, Relations and Physics</a></td>
-          <td>
-            P. Battaglia, Razvan Pascanu, Matthew Lai, Danilo Jimenez Rezende, K. Kavukcuoglu
-          </td>
-          <td>2016-12-01</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>1293</td>
-          <td>71</td>
-        </tr>
-    
-        <tr id="Endowing robots with human-like physical reasoning abilities remains challenging. We argue that existing methods often disregard spatio-temporal relations and by using Graph Neural Networks (GNNs) that incorporate a relational inductive bias, we can shift the learning process towards exploiting relations. In this work, we learn action-conditional forward dynamics models of a simulated manipulation task from visual observations involving cluttered and irregularly shaped objects. We investigate two GNN approaches and empirically assess their capability to generalize to scenarios with novel and an increasing number of objects. The first, Graph Networks (GN) based approach, considers explicitly defined edge attributes and not only does it consistently underperform an auto-encoder baseline that we modified to predict future states, our results indicate how different edge attributes can significantly influence the predictions. Consequently, we develop the Auto-Predictor that does not rely on explicitly defined edge attributes. It outperforms the baseline and the GN-based models. Overall, our results show the sensitivity of GNN-based approaches to the task representation, the efficacy of relational inductive biases and advocate choosing lightweight approaches that implicitly reason about relations over ones that leave these decisions to human designers.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e67e8500a00f2dd22537101fa76f2a60f7f1416f" target='_blank'>Learning Visual Dynamics Models of Rigid Objects using Relational Inductive Biases</a></td>
-          <td>
-            Fábio Ferreira, Lin Shao, T. Asfour, J. Bohg
-          </td>
-          <td>2019-09-09</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>54</td>
-        </tr>
-    
-        <tr id="Dynamical systems with interacting agents are universal in nature, commonly modeled by a graph of relationships between their constituents. Recently, various works have been presented to tackle the problem of inferring those relationships from the system trajectories via deep neural networks, but most of the studies assume binary or discrete types of interactions for simplicity. In the real world, the interaction kernels often involve continuous interaction strengths, which cannot be accurately approximated by discrete relations. In this work, we propose the relational attentive inference network (RAIN) to infer continuously weighted interaction graphs without any ground-truth interaction strengths. Our model employs a novel pairwise attention (PA) mechanism to refine the trajectory representations and a graph transformer to extract heterogeneous interaction weights for each pair of agents. We show that our RAIN model with the PA mechanism accurately infers continuous interaction strengths for simulated physical systems in an unsupervised manner. Further, RAIN with PA successfully predicts trajectories from motion capture data with an interpretable interaction graph, demonstrating the virtue of modeling unknown dynamics with continuous weights.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4f27abca5ea9644dd572c0f9879fecac0e60e998" target='_blank'>Learning Heterogeneous Interaction Strengths by Trajectory Prediction with Graph Neural Network</a></td>
-          <td>
-            Seungwoong Ha, Hawoong Jeong
-          </td>
-          <td>2022-08-28</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>43</td>
-        </tr>
-    
-        <tr id="Planning - the ability to analyze the structure of a problem in the large and decompose it into interrelated subproblems - is a hallmark of human intelligence. While deep reinforcement learning (RL) has shown great promise for solving relatively straightforward control tasks, it remains an open problem how to best incorporate planning into existing deep RL paradigms to handle increasingly complex environments. One prominent framework, Model-Based RL, learns a world model and plans using step-by-step virtual rollouts. This type of world model quickly diverges from reality when the planning horizon increases, thus struggling at long-horizon planning. How can we learn world models that endow agents with the ability to do temporally extended reasoning? In this work, we propose to learn graph-structured world models composed of sparse, multi-step transitions. We devise a novel algorithm to learn latent landmarks that are scattered (in terms of reachability) across the goal space as the nodes on the graph. In this same graph, the edges are the reachability estimates distilled from Q-functions. On a variety of high-dimensional continuous control tasks ranging from robotic manipulation to navigation, we demonstrate that our method, named L3P, significantly outperforms prior work, and is oftentimes the only method capable of leveraging both the robustness of model-free RL and generalization of graph-search algorithms. We believe our work is an important step towards scalable planning in reinforcement learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5cf549e26b4dce19d5bc783de83047479ce6218a" target='_blank'>World Model as a Graph: Learning Latent Landmarks for Planning</a></td>
-          <td>
-            Lunjun Zhang, Ge Yang, Bradly C. Stadie
-          </td>
-          <td>2020-11-25</td>
-          <td>ArXiv</td>
-          <td>60</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="World models for environments with many objects face a combinatorial explosion of states: as the number of objects increases, the number of possible arrangements grows exponentially. In this paper, we learn to generalize over robotic pick-and-place tasks using object-factored world models, which combat the combinatorial explosion by ensuring that predictions are equivariant to permutations of objects. Previous object-factored models were limited either by their inability to model actions, or by their inability to plan for complex manipulation tasks. We build on recent contrastive methods for training object-factored world models, which we extend to model continuous robot actions and to accurately predict the physics of robotic pick-and-place. To do so, we use a residual stack of graph neural networks that receive action information at multiple levels in both their node and edge neural networks. Crucially, our learned model can make predictions about tasks not represented in the training data. That is, we demonstrate successful zero-shot generalization to novel tasks, with only a minor decrease in model performance. Moreover, we show that an ensemble of our models can be used to plan for tasks involving up to 12 pick and place actions using heuristic search. We also demonstrate transfer to a physical robot.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0fda02b32b9f509a025d843f09d6824de9680335" target='_blank'>Factored World Models for Zero-Shot Generalization in Robotic Manipulation</a></td>
-          <td>
-            Ondrej Biza, Thomas Kipf, David Klee, Robert W. Platt, Jan-Willem van de Meent, Lawson L. S. Wong
-          </td>
-          <td>2022-02-10</td>
-          <td>ArXiv</td>
-          <td>9</td>
-          <td>25</td>
-        </tr>
-    
-        <tr id="Intelligent agents need a physical understanding of the world to predict the impact of their actions in the future. While learning-based models of the environment dynamics have contributed to significant improvements in sample efficiency compared to model-free reinforcement learning algorithms, they typically fail to generalize to system states beyond the training data, while often grounding their predictions on non-interpretable latent variables. 
-We introduce Interactive Differentiable Simulation (IDS), a differentiable physics engine, that allows for efficient, accurate inference of physical properties of rigid-body systems. Integrated into deep learning architectures, our model is able to accomplish system identification using visual input, leading to an interpretable model of the world whose parameters have physical meaning. We present experiments showing automatic task-based robot design and parameter estimation for nonlinear dynamical systems by automatically calculating gradients in IDS. When integrated into an adaptive model-predictive control algorithm, our approach exhibits orders of magnitude improvements in sample efficiency over model-free reinforcement learning algorithms on challenging nonlinear control domains.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0910a3cf9813c41ea764c89584d2957efa1159a9" target='_blank'>Interactive Differentiable Simulation</a></td>
-          <td>
-            Eric Heiden, David Millard, Hejia Zhang, G. Sukhatme
-          </td>
-          <td>2019-05-01</td>
-          <td>ArXiv</td>
-          <td>46</td>
-          <td>91</td>
-        </tr>
-    
-        <tr id="From just a glance, humans can make rich predictions about the future state of a wide range of physical systems. On the other hand, modern approaches from engineering, robotics, and graphics are often restricted to narrow domains and require direct measurements of the underlying states. We introduce the Visual Interaction Network, a general-purpose model for learning the dynamics of a physical system from raw visual observations. Our model consists of a perceptual front-end based on convolutional neural networks and a dynamics predictor based on interaction networks. Through joint training, the perceptual front-end learns to parse a dynamic visual scene into a set of factored latent object representations. The dynamics predictor learns to roll these states forward in time by computing their interactions and dynamics, producing a predicted physical trajectory of arbitrary length. We found that from just six input video frames the Visual Interaction Network can generate accurate future trajectories of hundreds of time steps on a wide range of physical systems. Our model can also be applied to scenes with invisible objects, inferring their future states from their effects on the visible objects, and can implicitly infer the unknown mass of objects. Our results demonstrate that the perceptual module and the object-based dynamics predictor module can induce factored latent representations that support accurate dynamical predictions. This work opens new opportunities for model-based decision-making and planning from raw sensory observations in complex physical environments.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/414ab203d8fc3ecfbf40d004960d3a4774830b48" target='_blank'>Visual Interaction Networks: Learning a Physics Simulator from Video</a></td>
-          <td>
-            Nicholas Watters, Daniel Zoran, T. Weber, P. Battaglia, Razvan Pascanu, A. Tacchetti
-          </td>
-          <td>2017-06-05</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>255</td>
-          <td>67</td>
-        </tr>
-    
-        <tr id="A structured understanding of our world in terms of objects, relations, and hierarchies is an important component of human cognition. Learning such a structured world model from raw sensory data remains a challenge. As a step towards this goal, we introduce Contrastively-trained Structured World Models (C-SWMs). C-SWMs utilize a contrastive approach for representation learning in environments with compositional structure. We structure each state embedding as a set of object representations and their relations, modeled by a graph neural network. This allows objects to be discovered from raw pixel observations without direct supervision as part of the learning process. We evaluate C-SWMs on compositional environments involving multiple interacting objects that can be manipulated independently by an agent, simple Atari games, and a multi-object physics simulation. Our experiments demonstrate that C-SWMs can overcome limitations of models based on pixel reconstruction and outperform typical representatives of this model class in highly structured environments, while learning interpretable object-based representations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/19b924dd9121f01165276a7afb764cf394acb80b" target='_blank'>Contrastive Learning of Structured World Models</a></td>
-          <td>
-            Thomas Kipf, Elise van der Pol, M. Welling
-          </td>
-          <td>2019-11-27</td>
-          <td>ArXiv</td>
-          <td>250</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true force vector when trained on n-body gravitational and spring-like simulations. We use symbolic regression to fit explicit algebraic equations to our trained model's message function and recover the symbolic form of Newton's law of gravitation without prior knowledge. We also show that our model generalizes better at inference time to systems with more bodies than had been experienced during training. Our approach is extensible, in principle, to any unknown interaction law learned by a graph network, and offers a valuable technique for interpreting and inferring explicit causal theories about the world from implicit knowledge captured by deep learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a6aad9ccdcb7674a3b7ab710f0a80d205834f847" target='_blank'>Learning Symbolic Physics with Graph Networks</a></td>
-          <td>
-            M. Cranmer, Rui Xu, P. Battaglia, S. Ho
-          </td>
-          <td>2019-09-12</td>
-          <td>ArXiv</td>
-          <td>77</td>
-          <td>68</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Neural Ordinary Differential Equations</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We propose Characteristic-Neural Ordinary Differential Equations (C-NODEs), a framework for extending Neural Ordinary Differential Equations (NODEs) beyond ODEs. While NODEs model the evolution of a latent variables as the solution to an ODE, C-NODE models the evolution of the latent variables as the solution of a family of first-order quasi-linear partial differential equations (PDEs) along curves on which the PDEs reduce to ODEs, referred to as characteristic curves. This in turn allows the application of the standard frameworks for solving ODEs, namely the adjoint method. Learning optimal characteristic curves for given tasks improves the performance and computational efficiency, compared to state of the art NODE models. We prove that the C-NODE framework extends the classical NODE on classification tasks by demonstrating explicit C-NODE representable functions not expressible by NODEs. Additionally, we present C-NODE-based continuous normalizing flows, which describe the density evolution of latent variables along multiple dimensions. Empirical results demonstrate the improvements provided by the proposed method for classification and density estimation on CIFAR-10, SVHN, and MNIST datasets under a similar computational budget as the existing NODE methods. The results also provide empirical evidence that the learned curves improve the efficiency of the system through a lower number of parameters and function evaluations compared with baselines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/17773066cf244e82503e7283dcf1981bfe4ef0a6" target='_blank'>Characteristic Neural Ordinary Differential Equations</a></td>
-          <td>
-            Xingzi Xu, Ali Hasan, Khalil Elkhalil, Jie Ding, V. Tarokh
-          </td>
-          <td>2021-11-25</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>62</td>
-        </tr>
-    
-        <tr id="We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural ODEs (NODEs) training and inference. HBNODEs have two properties that imply practical advantages over NODEs: (i) The adjoint state of an HBNODE also satisfies an HBNODE, accelerating both forward and backward ODE solvers, thus significantly reducing the number of function evaluations (NFEs) and improving the utility of the trained models. (ii) The spectrum of HBNODEs is well structured, enabling effective learning of long-term dependencies from complex sequential data. We verify the advantages of HBNODEs over NODEs on benchmark tasks, including image classification, learning complex dynamics, and sequential modeling. Our method requires remarkably fewer forward and backward NFEs, is more accurate, and learns long-term dependencies more effectively than the other ODE-based neural network models. Code is available at \url{https://github.com/hedixia/HeavyBallNODE}.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4c1d1114a15b501a90924653d263dd2222aa127e" target='_blank'>Heavy Ball Neural Ordinary Differential Equations</a></td>
-          <td>
-            Hedi Xia, Vai Suliafu, H. Ji, T. Nguyen, A. Bertozzi, S. Osher, Bao Wang
-          </td>
-          <td>2021-10-10</td>
-          <td>ArXiv, DBLP</td>
-          <td>44</td>
-          <td>70</td>
-        </tr>
-    
-        <tr id="Neural ordinary differential equations (NODE) present a new way of considering a deep residual network as a continuous structure by layer depth. However, it fails to overcome its representational limits, where it cannot learn all possible homeomorphisms of input data space, and therefore quickly saturates in terms of performance even as the number of layers increases. Here, we show that simply stacking Neural ODE blocks could easily improve performance by alleviating this issue. Furthermore, we suggest a more effective way of training neural ODE by using a time-evolving mixture weight on multiple ODE functions that also evolves with a separate neural ODE. We provide empirical results that are suggestive of improved performance over stacked as well as vanilla neural ODEs where we also confirm our approach can be orthogonally combined with recent advances in neural ODEs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f28e92fcbf87d2884e99dfa8143905469d2b47a3" target='_blank'>Learning Polymorphic Neural ODEs With Time-Evolving Mixture</a></td>
-          <td>
-            Tehrim Yoon, Sumin Shin, Eunho Yang
-          </td>
-          <td>2022-01-25</td>
-          <td>IEEE Transactions on Pattern Analysis and Machine Intelligence</td>
-          <td>4</td>
-          <td>29</td>
-        </tr>
-    
-        <tr id="This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and partial differential equations and their analysis who are curious to see their role in machine learning. Using three examples from machine learning and applied mathematics, we will see how neural ODEs can provide new insights into deep learning and a foundation for more efficient algorithms.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3579984410df7b486c162597584cc5179b9d3343" target='_blank'>Differential Equations for Continuous-Time Deep Learning</a></td>
-          <td>
-            Lars Ruthotto
-          </td>
-          <td>2024-01-08</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Continuous-depth learning has recently emerged as a novel perspective on deep learning, improving performance in tasks related to dynamical systems and density estimation. Core to these approaches is the neural differential equation, whose forward passes are the solutions of an initial value problem parametrized by a neural network. Unlocking the full potential of continuous-depth models requires a different set of software tools, due to peculiar differences compared to standard discrete neural networks, e.g inference must be carried out via numerical solvers. We introduce TorchDyn, a PyTorch library dedicated to continuous-depth learning, designed to elevate neural differential equations to be as accessible as regular plug-and-play deep learning primitives. This objective is achieved by identifying and subdividing different variants into common essential components, which can be combined and freely repurposed to obtain complex compositional architectures. TorchDyn further offers step-by-step tutorials and benchmarks designed to guide researchers and contributors.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7fb63e2479bc76ae72bbf67289f212a4c16f886f" target='_blank'>TorchDyn: A Neural Differential Equations Library</a></td>
-          <td>
-            Michael Poli, Stefano Massaroli, A. Yamashita, H. Asama, Jinkyoo Park
-          </td>
-          <td>2020-09-20</td>
-          <td>ArXiv</td>
-          <td>20</td>
-          <td>39</td>
-        </tr>
-    
-        <tr id="Neural ordinary differential equations (NODEs) (Chen et al., 2018) are ordinary differential equations (ODEs) with their dynamics modeled by neural networks. Continuous normalizing flows (CNFs) (Chen et al., 2018; Grathwohl et al., 2018), a class of reversible generative models which builds on NODEs and uses an instantaneous counterpart of the change of variables formula (CVF), have recently proven to achieve state-of-the-art results on density estimation and variational inference tasks. In this thesis, we review key concepts that are important to understand NODEs and CNFs, ranging from numerical ODE solvers to generative models. We derive an explicit formulation of the adjoint sensitivity method for both NODEs and CNFs using a constrained optimization framework. Furthermore, we review several classes of NODEs and prove that a particular class of hypernetwork NODEs is a universal function approximator in the discretized state. Our numerical results suggest that the ODEs arising in CNFs do not need to be solved to high precision for training and we show that training of CNFs can be made more efficient by using a tolerance scheduler that exponentially reduces the ODE solver tolerances. Moreover, we quantify the discrepancy of the CVF and the discretized instantaneous CVF for two ODE solvers. Our hope in writing this thesis is to give a comprehensive and self-contained introduction to generative modeling (with neural ordinary differential equations) and to stimulate both theoretical as well as computational future work on NODEs and CNFs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/80171fd8dbb36f4855046e7b3460f7786cb46384" target='_blank'>Generative Modeling with Neural Ordinary Differential Equations</a></td>
-          <td>
-            Tim Dockhorn
-          </td>
-          <td>2019-12-19</td>
-          <td></td>
-          <td>0</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems, enabling the analysis and prediction of complex temporal behaviors. However, how to improve the model's stability and physical interpretability remains a challenge. This paper introduces new conservation relations in Neural ODEs using Lie symmetries in both the hidden state dynamics and the back propagation dynamics. These conservation laws are then incorporated into the loss function as additional regularization terms, potentially enhancing the physical interpretability and generalizability of the model. To illustrate this method, the paper derives Lie symmetries and conservation laws in a simple Neural ODE designed to monitor charged particles in a sinusoidal electric field. New loss functions are constructed from these conservation relations, demonstrating the applicability symmetry-regularized Neural ODE in typical modeling tasks, such as data-driven discovery of dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9827f402bc2fc9561f674b5bdfc992fb7dd32e2e" target='_blank'>Symmetry-regularized neural ordinary differential equations</a></td>
-          <td>
-            Wenbo Hao
-          </td>
-          <td>2023-11-28</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="Training neural ODEs on large datasets has not been tractable due to the necessity of allowing the adaptive numerical ODE solver to refine its step size to very small values. In practice this leads to dynamics equivalent to many hundreds or even thousands of layers. In this paper, we overcome this apparent difficulty by introducing a theoretically-grounded combination of both optimal transport and stability regularizations which encourage neural ODEs to prefer simpler dynamics out of all the dynamics that solve a problem well. Simpler dynamics lead to faster convergence and to fewer discretizations of the solver, considerably decreasing wall-clock time without loss in performance. Our approach allows us to train neural ODE based generative models to the same performance as the unregularized dynamics in just over a day on one GPU, whereas unregularized dynamics can take up to 4-6 days of training time on multiple GPUs. This brings neural ODEs significantly closer to practical relevance in large-scale applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a4375125ee9900d1a5f090f433d5348601cb9989" target='_blank'>How to train your neural ODE</a></td>
-          <td>
-            Chris Finlay, J. Jacobsen, L. Nurbekyan, Adam M. Oberman
-          </td>
-          <td>2020-02-07</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>247</td>
-          <td>30</td>
-        </tr>
-    
-        <tr id="The conjoining of dynamical systems and deep learning has become a topic of great interest. In particular, neural differential equations (NDEs) demonstrate that neural networks and differential equation are two sides of the same coin. Traditional parameterised differential equations are a special case. Many popular neural network architectures, such as residual networks and recurrent networks, are discretisations. NDEs are suitable for tackling generative problems, dynamical systems, and time series (particularly in physics, finance, ...) and are thus of interest to both modern machine learning and traditional mathematical modelling. NDEs offer high-capacity function approximation, strong priors on model space, the ability to handle irregular data, memory efficiency, and a wealth of available theory on both sides. This doctoral thesis provides an in-depth survey of the field. Topics include: neural ordinary differential equations (e.g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e.g. for learning functions of irregular time series); and neural stochastic differential equations (e.g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions). Further topics include: numerical methods for NDEs (e.g. reversible differential equations solvers, backpropagation through differential equations, Brownian reconstruction); symbolic regression for dynamical systems (e.g. via regularised evolution); and deep implicit models (e.g. deep equilibrium models, differentiable optimisation). We anticipate this thesis will be of interest to anyone interested in the marriage of deep learning with dynamical systems, and hope it will provide a useful reference for the current state of the art.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1f7ba0832203ab808fc8d6706836c591754b79da" target='_blank'>On Neural Differential Equations</a></td>
-          <td>
-            Patrick Kidger
-          </td>
-          <td>2022-02-04</td>
-          <td>ArXiv</td>
-          <td>161</td>
-          <td>12</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba.md b/docs/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba.md
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-  <i class="footer">This page was last updated on 2024-08-08 13:16:38 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Graph-Guided Network for Irregularly Sampled Multivariate Time Series</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Real-world applications often involve irregular time series, for which the time intervals between successive observations are non-uniform. Irregularity across multiple features in a multi-variate time series further results in a different subset of features at any given time (i.e., asynchronicity). Existing pre-training schemes for time-series, however, often assume regularity of time series and make no special treatment of irregularity. We argue that such irregularity offers insight about domain property of the data—for example, frequency of hospital visits may signal patient health condition—that can guide representation learning. In this work, we propose PrimeNet to learn a self-supervised representation for irregular multivariate time-series. Specifically, we design a time sensitive contrastive learning and data reconstruction task to pre-train a model. Irregular time-series exhibits considerable variations in sampling density over time. Hence, our triplet generation strategy follows the density of the original data points, preserving its native irregularity. Moreover, the sampling density variation over time makes data reconstruction difficult for different regions. Therefore, we design a data masking technique that always masks a constant time duration to accommodate reconstruction for regions of different sampling density. We learn with these tasks using unlabeled data to build a pre-trained model and fine-tune on a downstream task with limited labeled data, in contrast with existing fully supervised approach for irregular time-series, requiring large amounts of labeled data. Experiment results show that PrimeNet significantly outperforms state-of-the-art methods on naturally irregular and asynchronous data from Healthcare and IoT applications for several downstream tasks, including classification, interpolation, and regression.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/70e5e9bd353d1b1e54b4eebd3a67b58026a13dff" target='_blank'>PrimeNet: Pre-training for Irregular Multivariate Time Series</a></td>
-          <td>
-            Ranak Roy Chowdhury, Jiacheng Li, Xiyuan Zhang, Dezhi Hong, Rajesh K. Gupta, Jingbo Shang
-          </td>
-          <td>2023-06-26</td>
-          <td>DBLP</td>
-          <td>9</td>
-          <td>16</td>
-        </tr>
-    
-        <tr id="Irregularly-sampled time series (ITS) are native to high-impact domains like healthcare, where measurements are collected over time at uneven intervals. However, for many classification problems, only small portions of long time series are often relevant to the class label. In this case, existing ITS models often fail to classify long series since they rely on careful imputation, which easily over- or under-samples the relevant regions. Using this insight, we then propose CAT, a model that classifies multivariate ITS by explicitly seeking highly-relevant portions of an input series' timeline. CAT achieves this by integrating three components: (1) A Moment Network learns to seek relevant moments in an ITS's continuous timeline using reinforcement learning. (2) A Receptor Network models the temporal dynamics of both observations and their timing localized around predicted moments. (3) A recurrent Transition Model models the sequence of transitions between these moments, cultivating a representation with which the series is classified. Using synthetic and real data, we find that CAT outperforms ten state-of-the-art methods by finding short signals in long irregular time series.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6f0f354fc0a8f864d7646c41d06fdcbc65a8d55d" target='_blank'>Finding Short Signals in Long Irregular Time Series with Continuous-Time Attention Policy Networks</a></td>
-          <td>
-            Thomas Hartvigsen, Jidapa Thadajarassiri, Xiangnan Kong, Elke A. Rundensteiner
-          </td>
-          <td>2023-02-08</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="Prevalent in many real-world settings such as healthcare, irregular time series are challenging to formulate predictions from. It is difficult to infer the value of a feature at any given time when observations are sporadic, as it could take on a range of values depending on when it was last observed. To characterize this uncertainty we present EDICT, a strategy that learns an evidential distribution over irregular time series in continuous time. This distribution enables well-calibrated and flexible inference of partially observed features at any time of interest, while expanding uncertainty temporally for sparse, irregular observations. We demonstrate that EDICT attains competitive performance on challenging time series classification tasks and enabling uncertainty-guided inference when encountering noisy data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5a4149fcbf11abc14e349a75f2e0672e876b7faf" target='_blank'>Continuous Time Evidential Distributions for Irregular Time Series</a></td>
-          <td>
-            Taylor W. Killian, Haoran Zhang, Thomas Hartvigsen, Ava P. Amini
-          </td>
-          <td>2023-07-25</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="Irregularly sampled time series are increasingly prevalent, particularly in medical domains. While various specialized methods have been developed to handle these irregularities, effectively modeling their complex dynamics and pronounced sparsity remains a challenge. This paper introduces a novel perspective by converting irregularly sampled time series into line graph images, then utilizing powerful pre-trained vision transformers for time series classification in the same way as image classification. This method not only largely simplifies specialized algorithm designs but also presents the potential to serve as a universal framework for time series modeling. Remarkably, despite its simplicity, our approach outperforms state-of-the-art specialized algorithms on several popular healthcare and human activity datasets. Especially in the rigorous leave-sensors-out setting where a portion of variables is omitted during testing, our method exhibits strong robustness against varying degrees of missing observations, achieving an impressive improvement of 42.8% in absolute F1 score points over leading specialized baselines even with half the variables masked. Code and data are available at https://github.com/Leezekun/ViTST">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3f4bd6e35eca865b0226f1bc0da9fc5f0dc948a8" target='_blank'>Time Series as Images: Vision Transformer for Irregularly Sampled Time Series</a></td>
-          <td>
-            Zekun Li, SHIYANG LI, Xifeng Yan
-          </td>
-          <td>2023-03-01</td>
-          <td>ArXiv</td>
-          <td>8</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="Irregularly sampled time series are increasingly prevalent, particularly in medical domains. While various specialized methods have been developed to handle these irregularities, effectively modeling their complex dynamics and pronounced sparsity remains a challenge. This paper introduces a novel perspective by converting irregularly sampled time series into line graph images, then utilizing powerful pre-trained vision transformers for time series classification in the same way as image classification. This method not only largely simplifies specialized algorithm designs but also presents the potential to serve as a universal framework for time series modeling. Remarkably, despite its simplicity, our approach outperforms state-of-the-art specialized algorithms on several popular healthcare and human activity datasets. Especially in the rigorous leave-sensors-out setting where a portion of variables is omitted during testing, our method exhibits strong robustness against varying degrees of missing observations, achieving an impressive improvement of 42.8% in absolute F1 score points over leading specialized baselines even with half the variables masked. Code and data are available at https://github.com/Leezekun/ViTST">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3f4bd6e35eca865b0226f1bc0da9fc5f0dc948a8" target='_blank'>Time Series as Images: Vision Transformer for Irregularly Sampled Time Series</a></td>
-          <td>
-            Zekun Li, SHIYANG LI, Xifeng Yan
-          </td>
-          <td>2023-03-01</td>
-          <td>ArXiv</td>
-          <td>8</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="To analyze multivariate time series, most previous methods assume regular subsampling of time series, where the interval between adjacent measurements and the number of samples remain unchanged. Practically, data collection systems could produce irregularly sampled time series due to sensor failures and interventions. However, existing methods designed for regularly sampled multivariate time series cannot directly handle irregularity owing to misalignment along both temporal and variate dimensions. To fill this gap, we propose Compatible Transformer (CoFormer), a transformer-based encoder to achieve comprehensive temporal-interaction feature learning for each individual sample in irregular multivariate time series. In CoFormer, we view each sample as a unique variate-time point and leverage intra-variate/inter-variate attentions to learn sample-wise temporal/interaction features based on intra-variate/inter-variate neighbors. With CoFormer as the core, we can analyze irregularly sampled multivariate time series for many downstream tasks, including classification and prediction. We conduct extensive experiments on 3 real-world datasets and validate that the proposed CoFormer significantly and consistently outperforms existing methods. Code will be avilable at https://github.com/MediaBrain-SJTU/CoFormer.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f6f708484a85b2b96d6f6764724b950cab167bb7" target='_blank'>Compatible Transformer for Irregularly Sampled Multivariate Time Series</a></td>
-          <td>
-            Yuxi Wei, Juntong Peng, Tong He, Chenxin Xu, Jian Zhang, Shirui Pan, Siheng Chen
-          </td>
-          <td>2023-10-17</td>
-          <td>2023 IEEE International Conference on Data Mining (ICDM)</td>
-          <td>0</td>
-          <td>8</td>
-        </tr>
-    
-        <tr id="Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In this paper, we consider irregular sampling from the perspective of missing data. We model observed irregularly-sampled time series data as a sequence of index-value pairs sampled from a continuous but unobserved function. We introduce an encoder-decoder framework for learning from such generic indexed sequences. We propose learning methods for this framework based on variational autoencoders and generative adversarial networks. For continuous irregularly-sampled time series, we introduce continuous convolutional layers that can efficiently interface with existing neural network architectures. Experiments show that our models are able to achieve competitive or better classification results on irregularly-sampled multivariate time series compared to recent RNN models while offering significantly faster training times.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7651d6498f437e30d31e354933b93f52791b6542" target='_blank'>Learning from Irregularly-Sampled Time Series: A Missing Data Perspective</a></td>
-          <td>
-            Steven Cheng-Xian Li, Benjamin M Marlin
-          </td>
-          <td>2020-07-12</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>47</td>
-          <td>32</td>
-        </tr>
-    
-        <tr id="We consider a sequence of related multivariate time series learning tasks, such as predicting failures for different instances of a machine from time series of multi-sensor data, or activity recognition tasks over different individuals from multiple wearable sensors. We focus on two under-explored practical challenges arising in such settings: (i) Each task may have a different subset of sensors, i.e., providing different partial observations of the underlying ‘system’. This restriction can be due to different manufacturers in the former case, and people wearing more or less measurement devices in the latter (ii) We are not allowed to store or re-access data from a task once it has been observed at the task level. This may be due to privacy considerations in the case of people, or legal restrictions placed by machine owners. Nevertheless, we would like to (a) improve performance on subsequent tasks using experience from completed tasks as well as (b) continue to perform better on past tasks, e.g., update the model and improve predictions on even the first machine after learning from subsequently observed ones. We note that existing continual learning methods do not take into account variability in input dimensions arising due to different subsets of sensors being available across tasks, and struggle to adapt to such variable input dimensions (VID) tasks. In this work, we address this shortcoming of existing methods. To this end, we learn task-specific generative models and classifiers, and use these to augment data for target tasks. Since the input dimensions across tasks vary, we propose a novel conditioning module based on graph neural networks to aid a standard recurrent neural network. We evaluate the efficacy of the proposed approach on three publicly available datasets corresponding to two activity recognition tasks (classification) and one prognostics task (regression). We demonstrate that it is possible to significantly enhance the performance on future and previous tasks while learning continuously from VID tasks without storing data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/72846d22118ef02bff11330dd28f408fde72d98b" target='_blank'>Continual Learning for Multivariate Time Series Tasks with Variable Input Dimensions</a></td>
-          <td>
-            Vibhor Gupta, Jyoti Narwariya, Pankaj Malhotra, L. Vig, Gautam M. Shroff
-          </td>
-          <td>2021-12-01</td>
-          <td>2021 IEEE International Conference on Data Mining (ICDM)</td>
-          <td>15</td>
-          <td>27</td>
-        </tr>
-    
-        <tr id="Multivariate time series (MTS) data are becoming increasingly ubiquitous in diverse domains, e.g., IoT systems, health informatics, and 5G networks. To obtain an effective representation of MTS data, it is not only essential to consider unpredictable dynamics and highly variable lengths of these data but also important to address the irregularities in the sampling rates of MTS. Existing parametric approaches rely on manual hyperparameter tuning and may cost a huge amount of labor effort. Therefore, it is desirable to learn the representation automatically and efficiently. To this end, we propose an autonomous representation learning approach for multivariate time series (TimeAutoML) with irregular sampling rates and variable lengths. As opposed to previous works, we first present a representation learning pipeline in which the configuration and hyperparameter optimization are fully automatic and can be tailored for various tasks, e.g., anomaly detection, clustering, etc. Next, a negative sample generation approach and an auxiliary classification task are developed and integrated within TimeAutoML to enhance its representation capability. Extensive empirical studies on real-world datasets demonstrate that the proposed TimeAutoML outperforms competing approaches on various tasks by a large margin. In fact, it achieves the best anomaly detection performance among all comparison algorithms on 78 out of all 85 UCR datasets, acquiring up to 20% performance improvement in terms of AUC score.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/60773c01dd3c76be0e1d3bc429cf474e5f9d8519" target='_blank'>TimeAutoML: Autonomous Representation Learning for Multivariate Irregularly Sampled Time Series</a></td>
-          <td>
-            Yang Jiao, Kai Yang, Shaoyu Dou, Pan Luo, Sijia Liu, Dongjin Song
-          </td>
-          <td>2020-10-04</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>22</td>
-        </tr>
-    
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
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diff --git a/docs/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01.md b/docs/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01.md
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-    Recommendations for the article <i>SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4cb7ffb5dfa4330c7fcc70afce6f8129c1699c42" target='_blank'>Sparse identification of Lagrangian for nonlinear dynamical systems via proximal gradient method</a></td>
-          <td>
-            Adam Purnomo, M. Hayashibe
-          </td>
-          <td>2022-09-04</td>
-          <td>Scientific Reports</td>
-          <td>2</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that violate basic physical laws. This work proposes a novel method for the Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI). SINDy-SI is an iterative method that uses Sum-of-Squares (SOS) programming to learn optimally fitted models while guaranteeing that the learned model satisfies side information, such as symmetry's and physical laws. Guided by the principle of Occam's razor, that the simplest or most regularized best fitted model is typically the superior choice, during each iteration SINDy-SI prunes the basis functions associated with small coefficients, yielding a sparse dynamical model upon termination. Through several numerical experiments we will show how the combination of side information constraints and sparse polynomial representation cultivates dynamical models that obey known physical laws while displaying impressive generalized performance beyond the training set.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/13a6b8f2d60ef8006dfe6e6bed42df96f773a323" target='_blank'>Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI)</a></td>
-          <td>
-            Gabriel F. Machado, Morgan Jones
-          </td>
-          <td>2023-10-06</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/433ba35ced5d3f47fa2688c81a60363a74193449" target='_blank'>PySINDy: A comprehensive Python package for robust sparse system identification</a></td>
-          <td>
-            A. Kaptanoglu, Brian M. de Silva, Urban Fasel, Kadierdan Kaheman, Jared L. Callaham, Charles B. Delahunt, Kathleen P. Champion, Jean-Christophe Loiseau, J. Kutz, S. Brunton
-          </td>
-          <td>2021-11-12</td>
-          <td>J. Open Source Softw.</td>
-          <td>109</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Data-driven modeling frameworks that adopt sparse regression techniques, such as sparse identification of nonlinear dynamics (SINDy) and its modifications, are developed to resolve difficulties in extracting underlying dynamics from experimental data. In contrast to neural-network-based methods, these methods are designed to obtain white-box analytical models. In this work, we incorporate the concept of SINDy and knowledge in the field of classical mechanics to identify interpretable and sparse expressions of total energy and the Lagrangian that shelters the hidden dynamics. Moreover, our method (hereafter referred as Lagrangian-SINDy) is developed to use knowledge of simple systems that form the system being analyzed to ensure the likelihood of correct results and to improve the learning pace. Lagrangian-SINDy is highly accurate in discovering interpretable dynamics via energy-related physical quantities. Its performance is validated with three popular multi-DOF nonlinear dynamical systems, namely the spherical pendulum, double pendulum and cart-pendulum system. Comparisons with other SINDy-based methods are made and Lagrangian-SINDy is found to provide the most compact analytical models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7d7e107bcb40ed9596642ff12cc60f33f3eb47e2" target='_blank'>Discovering Interpretable Dynamics by Sparsity Promotion on Energy and the Lagrangian</a></td>
-          <td>
-            H. Chu, M. Hayashibe
-          </td>
-          <td>2020-01-31</td>
-          <td>IEEE Robotics and Automation Letters</td>
-          <td>23</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1f18c5206491626d36c2271aaf491dbc945f6247" target='_blank'>Automatically discovering ordinary differential equations from data with sparse regression</a></td>
-          <td>
-            Kevin Egan, Weizhen Li, Rui Carvalho
-          </td>
-          <td>2024-01-09</td>
-          <td>Communications Physics</td>
-          <td>7</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/22dc1c64c6423f738f2c63b7945f7b7f2fbf958d" target='_blank'>Derivative-Based SINDy (DSINDy): Addressing the Challenge of Discovering Governing Equations from Noisy Data</a></td>
-          <td>
-            J. Wentz, A. Doostan
-          </td>
-          <td>2022-11-10</td>
-          <td>SSRN Electronic Journal</td>
-          <td>8</td>
-          <td>33</td>
-        </tr>
-    
-        <tr id="The discovery of governing equations from data has been an active field of research for decades. One widely used methodology for this purpose is sparse regression for nonlinear dynamics, known as SINDy. Despite several attempts, noisy and scarce data still pose a severe challenge to the success of the SINDy approach. In this work, we discuss a robust method to discover nonlinear governing equations from noisy and scarce data. To do this, we make use of neural networks to learn an implicit representation based on measurement data so that not only it produces the output in the vicinity of the measurements but also the time-evolution of output can be described by a dynamical system. Additionally, we learn such a dynamic system in the spirit of the SINDy framework. Leveraging the implicit representation using neural networks, we obtain the derivative information -- required for SINDy -- using an automatic differentiation tool. To enhance the robustness of our methodology, we further incorporate an integral condition on the output of the implicit networks. Furthermore, we extend our methodology to handle data collected from multiple initial conditions. We demonstrate the efficiency of the proposed methodology to discover governing equations under noisy and scarce data regimes by means of several examples and compare its performance with existing methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7a3166991a8c4161d83c4cdb27033c02f3135cc0" target='_blank'>A Robust SINDy Approach by Combining Neural Networks and an Integral Form</a></td>
-          <td>
-            A. Forootani, P. Goyal, P. Benner
-          </td>
-          <td>2023-09-13</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>14</td>
-        </tr>
-    
-        <tr id="Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (\sindy) framework, which uses sparse regression to identify governing equations from data. This study introduces an enhanced method, Nested SINDy, that aims to increase the expressivity of the SINDy approach thanks to a nested structure. Indeed, traditional symbolic regression and system identification methods often fail with complex systems that cannot be easily described analytically. Nested SINDy builds on the SINDy framework by introducing additional layers before and after the core SINDy layer. This allows the method to identify symbolic representations for a wider range of systems, including those with compositions and products of functions. We demonstrate the ability of the Nested SINDy approach to accurately find symbolic expressions for simple systems, such as basic trigonometric functions, and sparse (false but accurate) analytical representations for more complex systems. Our results highlight Nested SINDy's potential as a tool for symbolic regression, surpassing the traditional SINDy approach in terms of expressivity. However, we also note the challenges in the optimization process for Nested SINDy and suggest future research directions, including the designing of a more robust methodology for the optimization process. This study proves that Nested SINDy can effectively discover symbolic representations of dynamical systems from data, offering new opportunities for understanding complex systems through data-driven methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5ef8aa10b07c62bde12d142106068d2ffd9e7414" target='_blank'>Generalizing the SINDy approach with nested neural networks</a></td>
-          <td>
-            Camilla Fiorini, Cl'ement Flint, Louis Fostier, Emmanuel Franck, Reyhaneh Hashemi, Victor Michel-Dansac, Wassim Tenachi
-          </td>
-          <td>2024-04-24</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/99877062e70fae24c531d58aa880fa443ec10c9b" target='_blank'>SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study</a></td>
-          <td>
-            Aurelio Raffa Ugolini, Valentina Breschi, Andrea Manzoni, M. Tanelli
-          </td>
-          <td>2024-03-01</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7be51140c9c66207fc1baa0ca92a691726cbd900" target='_blank'>Weak SINDy For Partial Differential Equations</a></td>
-          <td>
-            D. Messenger, D. Bortz
-          </td>
-          <td>2020-07-06</td>
-          <td>Journal of computational physics</td>
-          <td>119</td>
-          <td>19</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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diff --git a/docs/recommendations/4a111f7a3b56d0468f13104999844885157ef17d.md b/docs/recommendations/4a111f7a3b56d0468f13104999844885157ef17d.md
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-  <i class="footer">This page was last updated on 2024-08-08 13:16:48 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Unified Training of Universal Time Series Forecasting Transformers</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4fb78450650894091b0a55b5504a8b0a6f3dec37" target='_blank'>Chronos: Learning the Language of Time Series</a></td>
-          <td>
-            Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, Yuyang Wang
-          </td>
-          <td>2024-03-12</td>
-          <td>ArXiv</td>
-          <td>23</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world data-scarce scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progress has been achieved with the emergence of large language models, exhibiting unprecedented abilities such as few-shot generalization, scalability, and task generality, which are however absent in small deep models. To change the status quo of training scenario-specific small models from scratch, this paper aims at the early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), which is generative pre-trained by next token prediction and adapted to various downstream tasks with promising capabilities as an LTSM. Code and datasets are available at: https://github.com/thuml/Large-Time-Series-Model.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/73f58b90697f957832f5090946894480849dea3a" target='_blank'>Timer: Generative Pre-trained Transformers Are Large Time Series Models</a></td>
-          <td>
-            Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
-          </td>
-          <td>2024-02-04</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history. Our channel-independent patch time series Transformer (PatchTST) can improve the long-term forecasting accuracy significantly when compared with that of SOTA Transformer-based models. We also apply our model to self-supervised pre-training tasks and attain excellent fine-tuning performance, which outperforms supervised training on large datasets. Transferring of masked pre-trained representation on one dataset to others also produces SOTA forecasting accuracy. Code is available at: https://github.com/yuqinie98/PatchTST.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/dad15404d372a23b4b3bf9a63b3124693df3c85e" target='_blank'>A Time Series is Worth 64 Words: Long-term Forecasting with Transformers</a></td>
-          <td>
-            Yuqi Nie, Nam H. Nguyen, Phanwadee Sinthong, J. Kalagnanam
-          </td>
-          <td>2022-11-27</td>
-          <td>ArXiv</td>
-          <td>479</td>
-          <td>34</td>
-        </tr>
-    
-        <tr id="Time series forecasting is a critical and challenging task in practical application. Recent advancements in pre-trained foundation models for time series forecasting have gained significant interest. However, current methods often overlook the multi-scale nature of time series, which is essential for accurate forecasting. To address this, we propose HiMTM, a hierarchical multi-scale masked time series modeling with self-distillation for long-term forecasting. HiMTM integrates four key components: (1) hierarchical multi-scale transformer (HMT) to capture temporal information at different scales; (2) decoupled encoder-decoder (DED) that directs the encoder towards feature extraction while the decoder focuses on pretext tasks; (3) hierarchical self-distillation (HSD) for multi-stage feature-level supervision signals during pre-training; and (4) cross-scale attention fine-tuning (CSA-FT) to capture dependencies between different scales for downstream tasks. These components collectively enhance multi-scale feature extraction in masked time series modeling, improving forecasting accuracy. Extensive experiments on seven mainstream datasets show that HiMTM surpasses state-of-the-art self-supervised and end-to-end learning methods by a considerable margin of 3.16-68.54\%. Additionally, HiMTM outperforms the latest robust self-supervised learning method, PatchTST, in cross-domain forecasting by a significant margin of 2.3\%. The effectiveness of HiMTM is further demonstrated through its application in natural gas demand forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d945eae22457648e191742c37bcad88a114ce703" target='_blank'>HiMTM: Hierarchical Multi-Scale Masked Time Series Modeling with Self-Distillation for Long-Term Forecasting</a></td>
-          <td>
-            Shubao Zhao, Ming Jin, Zhaoxiang Hou, Che-Sheng Yang, Zengxiang Li, Qingsong Wen, Yi Wang
-          </td>
-          <td>2024-01-10</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>5</td>
-        </tr>
-    
-        <tr id="The Transformer is a highly successful deep learning model that has revolutionised the world of artificial neural networks, first in natural language processing and later in computer vision. This model is based on the attention mechanism and is able to capture complex semantic relationships between a variety of patterns present in the input data. Precisely because of these characteristics, the Transformer has recently been exploited for time series forecasting problems, assuming a natural adaptability to the domain of continuous numerical series. Despite the acclaimed results in the literature, some works have raised doubts about the robustness and effectiveness of this approach. In this paper, we further investigate the effectiveness of Transformer-based models applied to the domain of time series forecasting, demonstrate their limitations, and propose a set of alternative models that are better performing and significantly less complex. In particular, we empirically show how simplifying Transformer-based forecasting models almost always leads to an improvement, reaching state of the art performance. We also propose shallow models without the attention mechanism, which compete with the overall state of the art in long time series forecasting, and demonstrate their ability to accurately predict time series over extremely long windows. From a methodological perspective, we show how it is always necessary to use a simple baseline to verify the effectiveness of proposed models, and finally, we conclude the paper with a reflection on recent research paths and the opportunity to follow trends and hypes even where it may not be necessary.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b98bc7d48357932537fc9ba6035e3b6bd1018ae6" target='_blank'>Two Steps Forward and One Behind: Rethinking Time Series Forecasting with Deep Learning</a></td>
-          <td>
-            Riccardo Ughi, Eugenio Lomurno, Matteo Matteucci
-          </td>
-          <td>2023-04-10</td>
-          <td>ArXiv, DBLP</td>
-          <td>1</td>
-          <td>5</td>
-        </tr>
-    
-        <tr id="Time series has been left behind in the era of pre-training and transfer learning. While research in the fields of natural language processing and computer vision are enjoying progressively larger datasets to train massive models, the most popular time series datasets consist of only tens of thousands of time steps, limiting our ability to study the effectiveness of pre-training and scaling. Recent studies have also cast doubt on the need for expressive models and scale. To alleviate these issues, we introduce three large-scale time series forecasting datasets from the cloud operations (CloudOps) domain, the largest having billions of observations, enabling further study into pre-training and scaling of time series models. We build the empirical groundwork for studying pre-training and scaling of time series models and pave the way for future research by identifying a promising candidate architecture. We show that it is a strong zero-shot baseline and benefits from further scaling, both in model and dataset size. Accompanying these datasets and results is a suite of comprehensive benchmark results comparing classical and deep learning baselines to our pre-trained method - achieving a 27% reduction in error on the largest dataset. Code and datasets can be found https://github.com/SalesforceAIResearch/pretrain-time-series-cloudops.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/dbd6463cfff26861f6f3ea8e8d19eff4e6331904" target='_blank'>Pushing the Limits of Pre-training for Time Series Forecasting in the CloudOps Domain</a></td>
-          <td>
-            Gerald Woo, Chenghao Liu, Akshat Kumar, Doyen Sahoo
-          </td>
-          <td>2023-10-08</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>22</td>
-        </tr>
-    
-        <tr id="Time Series Forecasting plays a crucial role in various fields such as industrial equipment maintenance, meteorology, energy consumption, traffic flow and financial investment. However, despite their considerable advantages over traditional statistical approaches, current deep learning-based predictive models often exhibit a significant deviation between their forecasting outcomes and the ground truth. This discrepancy is largely due to an insufficient emphasis on extracting the sequence's latent information, particularly its global information within the frequency domain and the relationship between different variables. To address this issue, we propose a novel model Frequency-domain Attention In Two Horizons, which decomposes time series into trend and seasonal components using a multi-scale sequence adaptive decomposition and fusion architecture, and processes them separately. FAITH utilizes Frequency Channel feature Extraction Module and Frequency Temporal feature Extraction Module to capture inter-channel relationships and temporal global information in the sequence, significantly improving its ability to handle long-term dependencies and complex patterns. Furthermore, FAITH achieves theoretically linear complexity by modifying the time-frequency domain transformation method, effectively reducing computational costs. Extensive experiments on 6 benchmarks for long-term forecasting and 3 benchmarks for short-term forecasting demonstrate that FAITH outperforms existing models in many fields, such as electricity, weather and traffic, proving its effectiveness and superiority both in long-term and short-term time series forecasting tasks. Our codes and data are available at https://github.com/LRQ577/FAITH.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ca89b6de0dbe31f523495727dc83f8ab5d2ae1c3" target='_blank'>FAITH: Frequency-domain Attention In Two Horizons for Time Series Forecasting</a></td>
-          <td>
-            Ruiqi Li, Maowei Jiang, Kai Wang, Kaiduo Feng, Quangao Liu, Yue Sun, Xiufang Zhou
-          </td>
-          <td>2024-05-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>2</td>
-        </tr>
-    
-  </tbody>
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-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/4e837965494c4edbec4d30832d31ba5639996da8.md b/docs/recommendations/4e837965494c4edbec4d30832d31ba5639996da8.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:06:47 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Deep learning prediction of patient response time course from early data via neural-pharmacokinetic/pharmacodynamic modelling</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Nonlinear mixed effect (NLME) models are the gold standard for the analysis of patient response following drug exposure. However, these types of models are complex and time‐consuming to develop. There is great interest in the adoption of machine‐learning methods, but most implementations cannot be reliably extrapolated to treatment strategies outside of the training data. In order to solve this problem, we propose the deep compartment model (DCM), a combination of neural networks and ordinary differential equations. Using simulated datasets of different sizes, we show that our model remains accurate when training on small data sets. Furthermore, using a real‐world data set of patients with hemophilia A receiving factor VIII concentrate while undergoing surgery, we show that our model more accurately predicts a priori drug concentrations compared to a previous NLME model. In addition, we show that our model correctly describes the changing drug concentration over time. By adopting pharmacokinetic principles, the DCM allows for simulation of different treatment strategies and enables therapeutic drug monitoring.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9d61f6031526a07caee1c8ff98f7aec3dcc0e8a7" target='_blank'>Deep compartment models: A deep learning approach for the reliable prediction of time‐series data in pharmacokinetic modeling</a></td>
-          <td>
-            A. Janssen, F. Leebeek, M. Cnossen, R. Mathôt
-          </td>
-          <td>2022-05-27</td>
-          <td>CPT: Pharmacometrics & Systems Pharmacology</td>
-          <td>13</td>
-          <td>47</td>
-        </tr>
-    
-        <tr id="The advent of machine learning has led to innovative approaches in dealing with clinical data. Among these, Neural Ordinary Differential Equations (Neural ODEs), hybrid models merging mechanistic with deep learning models have shown promise in accurately modeling continuous dynamical systems. Although initial applications of Neural ODEs in the field of model-informed drug development and clinical pharmacology are becoming evident, applying these models to actual clinical trial datasets-characterized by sparse and irregularly timed measurements-poses several challenges. Traditional models often have limitations with sparse data, highlighting the urgent need to address this issue, potentially through the use of assumptions. This review examines the fundamentals of Neural ODEs, their ability to handle sparse and irregular data, and their applications in model-informed drug development.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d55a1a4acc93d905399f2126e7beb524fd64ec38" target='_blank'>Bridging pharmacology and neural networks: A deep dive into neural ordinary differential equations.</a></td>
-          <td>
-            Idris Bachali Losada, N. Terranova
-          </td>
-          <td>2024-07-11</td>
-          <td>CPT: pharmacometrics & systems pharmacology</td>
-          <td>0</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6b9e53c14cb42fbbf2cf83f8d3216cae3454e22f" target='_blank'>Neural-ODE for pharmacokinetics modeling and its advantage to alternative machine learning models in predicting new dosing regimens</a></td>
-          <td>
-            James Lu, Kaiwen Deng, Xinyuan Zhang, Gengbo Liu, Y. Guan
-          </td>
-          <td>2021-06-30</td>
-          <td>iScience</td>
-          <td>54</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="Modeling the time-series of high-dimensional, longitudinal data is important for predicting patient disease progression. However, existing neural network based approaches that learn representations of patient state, while very flexible, are susceptible to overfitting. We propose a deep generative model that makes use of a novel attention-based neural architecture inspired by the physics of how treatments affect disease state. The result is a scalable and accurate model of high-dimensional patient biomarkers as they vary over time. Our proposed model yields significant improvements in generalization and, on real-world clinical data, provides interpretable insights into the dynamics of cancer progression.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/32deb99e701749871af165676d9321642b1bd738" target='_blank'>Neural Pharmacodynamic State Space Modeling</a></td>
-          <td>
-            Zeshan Hussain, R. G. Krishnan, D. Sontag
-          </td>
-          <td>2021-02-22</td>
-          <td>ArXiv, DBLP</td>
-          <td>8</td>
-          <td>48</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/41f08a0f0e68812316548323db2b809f94474314" target='_blank'>Machine learning for pharmacokinetic/pharmacodynamic modeling.</a></td>
-          <td>
-            Albert Tang
-          </td>
-          <td>2023-01-01</td>
-          <td>Journal of pharmaceutical sciences</td>
-          <td>4</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fb6dc40c018f42d7750cea04fcf109340b5b508a" target='_blank'>Study of drug assimilation in human system using physics informed neural networks</a></td>
-          <td>
-            Kanupriya Goswami, Arpana Sharma, Madhu Pruthi, Richa Gupta
-          </td>
-          <td>2021-10-08</td>
-          <td>International Journal of Information Technology</td>
-          <td>7</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Pharmacometric models are pivotal across drug discovery and development, playing a decisive role in determining the progression of candidate molecules. However, the derivation of mathematical equations governing the system is a labor-intensive trial-and-error process, often constrained by tight timelines. In this study, we introduce PKINNs, a novel purely data-driven pharmacokinetic-informed neural network model. PKINNs efficiently discovers and models intrinsic multi-compartment-based pharmacometric structures, reliably forecasting their derivatives. The resulting models are both interpretable and explainable through Symbolic Regression methods. Our computational framework demonstrates the potential for closed-form model discovery in pharmacometric applications, addressing the labor-intensive nature of traditional model derivation. With the increasing availability of large datasets, this framework holds the potential to significantly enhance model-informed drug discovery.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1ecec2c77f9d85a4e75c8a8de808c4d916ca0015" target='_blank'>Discovering intrinsic multi-compartment pharmacometric models using Physics Informed Neural Networks</a></td>
-          <td>
-            I. Nasim, Adam Nasim
-          </td>
-          <td>2024-04-30</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c5953e5cee3b374ed2705efca252b1b44e0fe928" target='_blank'>Exploring Transformer Model in Longitudinal Pharmacokinetic/Pharmacodynamic Analyses and Comparing with Alternative Natural Language Processing Models.</a></td>
-          <td>
-            Yiming Cheng, Hongxiang Hu, Xin Dong, Xiaoran Hao, Yan Li
-          </td>
-          <td>2024-02-01</td>
-          <td>Journal of pharmaceutical sciences</td>
-          <td>0</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d3bf13f68e8df5be2212e7986959d08cd4995221" target='_blank'>Low-dimensional neural ODEs and their application in pharmacokinetics</a></td>
-          <td>
-            Dominic Stefan Bräm, U. Nahum, J. Schropp, M. Pfister, Gilbert Koch
-          </td>
-          <td>2023-10-14</td>
-          <td>Journal of Pharmacokinetics and Pharmacodynamics</td>
-          <td>5</td>
-          <td>3</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/4fd23f18cfb2105ccadda5a51fed13063d611fff.md b/docs/recommendations/4fd23f18cfb2105ccadda5a51fed13063d611fff.md
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-    Recommendations for the article <i>Learning 3D Particle-based Simulators from RGB-D Videos</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="From just a glance, humans can make rich predictions about the future state of a wide range of physical systems. On the other hand, modern approaches from engineering, robotics, and graphics are often restricted to narrow domains and require direct measurements of the underlying states. We introduce the Visual Interaction Network, a general-purpose model for learning the dynamics of a physical system from raw visual observations. Our model consists of a perceptual front-end based on convolutional neural networks and a dynamics predictor based on interaction networks. Through joint training, the perceptual front-end learns to parse a dynamic visual scene into a set of factored latent object representations. The dynamics predictor learns to roll these states forward in time by computing their interactions and dynamics, producing a predicted physical trajectory of arbitrary length. We found that from just six input video frames the Visual Interaction Network can generate accurate future trajectories of hundreds of time steps on a wide range of physical systems. Our model can also be applied to scenes with invisible objects, inferring their future states from their effects on the visible objects, and can implicitly infer the unknown mass of objects. Our results demonstrate that the perceptual module and the object-based dynamics predictor module can induce factored latent representations that support accurate dynamical predictions. This work opens new opportunities for model-based decision-making and planning from raw sensory observations in complex physical environments.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/414ab203d8fc3ecfbf40d004960d3a4774830b48" target='_blank'>Visual Interaction Networks: Learning a Physics Simulator from Video</a></td>
-          <td>
-            Nicholas Watters, Daniel Zoran, T. Weber, P. Battaglia, Razvan Pascanu, A. Tacchetti
-          </td>
-          <td>2017-06-05</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>255</td>
-          <td>67</td>
-        </tr>
-    
-        <tr id="Given a visual scene, humans have strong intuitions about how a scene can evolve over time under given actions. The intuition, often termed visual intuitive physics, is a critical ability that allows us to make effective plans to manipulate the scene to achieve desired outcomes without relying on extensive trial and error. In this paper, we present a framework capable of learning 3D-grounded visual intuitive physics models from videos of complex scenes with fluids. Our method is composed of a conditional Neural Radiance Field (NeRF)-style visual frontend and a 3D point-based dynamics prediction backend, using which we can impose strong relational and structural inductive bias to capture the structure of the underlying environment. Unlike existing intuitive point-based dynamics works that rely on the supervision of dense point trajectory from simulators, we relax the requirements and only assume access to multi-view RGB images and (imperfect) instance masks acquired using color prior. This enables the proposed model to handle scenarios where accurate point estimation and tracking are hard or impossible. We generate datasets including three challenging scenarios involving fluid, granular materials, and rigid objects in the simulation. The datasets do not include any dense particle information so most previous 3D-based intuitive physics pipelines can barely deal with that. We show our model can make long-horizon future predictions by learning from raw images and significantly outperforms models that do not employ an explicit 3D representation space. We also show that once trained, our model can achieve strong generalization in complex scenarios under extrapolate settings.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f3f1592ff282fbf58864c243510eb4a425f3fc70" target='_blank'>3D-IntPhys: Towards More Generalized 3D-grounded Visual Intuitive Physics under Challenging Scenes</a></td>
-          <td>
-            Haotian Xue, A. Torralba, J. Tenenbaum, Daniel L. K. Yamins, Yunzhu Li, H. Tung
-          </td>
-          <td>2023-04-22</td>
-          <td>2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)</td>
-          <td>5</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="For autonomous skill acquisition, robots have to learn about the physical rules governing the 3D world dynamics from their own past experience to predict and reason about plausible future outcomes. To this end, we propose a transformation-based 3D video prediction (T3VIP) approach that explicitly models the 3D motion by decomposing a scene into its object parts and predicting their corresponding rigid transformations. Our model is fully unsupervised, captures the stochastic nature of the real world, and the observational cues in image and point cloud domains constitute its learning signals. To fully leverage all the 2D and 3D observational signals, we equip our model with automatic hyperparameter optimization (HPO) to interpret the best way of learning from them. To the best of our knowledge, our model is the first generative model that provides an RGB-D video prediction of the future for a static camera. Our extensive evaluation with simulated and real-world datasets demonstrates that our formulation leads to interpretable 3D models that predict future depth videos while achieving on-par performance with 2D models on RGB video prediction. Moreover, we demonstrate that our model outperforms 2D baselines on visuomotor control. Videos, code, dataset, and pre-trained models are available at http://t3vip.cs.uni-freiburg.de.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/18c4b8d0c878e91542c3277201f4eb50fee3a4b3" target='_blank'>T3VIP: Transformation-based $3\mathrm{D}$ Video Prediction</a></td>
-          <td>
-            Iman Nematollahi, Erick Rosete-Beas, Seyed Mahdi B. Azad, Raghunandan Rajan, F. Hutter, Wolfram Burgard
-          </td>
-          <td>2022-09-19</td>
-          <td>2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)</td>
-          <td>2</td>
-          <td>121</td>
-        </tr>
-    
-        <tr id="For autonomous skill acquisition, robots have to learn about the physical rules governing the 3D world dynamics from their own past experience to predict and reason about plausible future outcomes. To this end, we propose a transformation-based 3D video prediction (T3VIP) approach that explicitly models the 3D motion by decomposing a scene into its object parts and predicting their corresponding rigid transformations. Our model is fully unsupervised, captures the stochastic nature of the real world, and the observational cues in image and point cloud domains constitute its learning signals. To fully leverage all the 2D and 3D observational signals, we equip our model with automatic hyperparameter optimization (HPO) to interpret the best way of learning from them. To the best of our knowledge, our model is the first generative model that provides an RGB-D video prediction of the future for a static camera. Our extensive evaluation with simulated and real-world datasets demonstrates that our formulation leads to interpretable 3D models that predict future depth videos while achieving on-par performance with 2D models on RGB video prediction. Moreover, we demonstrate that our model outperforms 2D baselines on visuomotor control. Videos, code, dataset, and pre-trained models are available at http://t3vip.cs.uni-freiburg.de.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/18c4b8d0c878e91542c3277201f4eb50fee3a4b3" target='_blank'>T3VIP: Transformation-based $3\mathrm{D}$ Video Prediction</a></td>
-          <td>
-            Iman Nematollahi, Erick Rosete-Beas, Seyed Mahdi B. Azad, Raghunandan Rajan, F. Hutter, Wolfram Burgard
-          </td>
-          <td>2022-09-19</td>
-          <td>2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)</td>
-          <td>2</td>
-          <td>121</td>
-        </tr>
-    
-        <tr id="When humans observe a physical system, they can easily locate objects, understand their interactions, and anticipate future behavior, even in settings with complicated and previously unseen interactions. For computers, however, learning such models from videos in an unsupervised fashion is an unsolved research problem. In this paper, we present STOVE, a novel state-space model for videos, which explicitly reasons about objects and their positions, velocities, and interactions. It is constructed by combining an image model and a dynamics model in compositional manner and improves on previous work by reusing the dynamics model for inference, accelerating and regularizing training. STOVE predicts videos with convincing physical behavior over hundreds of timesteps, outperforms previous unsupervised models, and even approaches the performance of supervised baselines. We further demonstrate the strength of our model as a simulator for sample efficient model-based control in a task with heavily interacting objects.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f87c63cd336f859007a2c07744fb24f8ec466932" target='_blank'>Structured Object-Aware Physics Prediction for Video Modeling and Planning</a></td>
-          <td>
-            Jannik Kossen, Karl Stelzner, Marcel Hussing, C. Voelcker, K. Kersting
-          </td>
-          <td>2019-10-06</td>
-          <td>ArXiv</td>
-          <td>67</td>
-          <td>58</td>
-        </tr>
-    
-        <tr id="Constructing simulation scenes that are both visually and physically realistic is a problem of practical interest in domains ranging from robotics to computer vision. This problem has become even more relevant as researchers wielding large data-hungry learning methods seek new sources of training data for physical decision-making systems. However, building simulation models is often still done by hand. A graphic designer and a simulation engineer work with predefined assets to construct rich scenes with realistic dynamic and kinematic properties. While this may scale to small numbers of scenes, to achieve the generalization properties that are required for data-driven robotic control, we require a pipeline that is able to synthesize large numbers of realistic scenes, complete with 'natural' kinematic and dynamic structures. To attack this problem, we develop models for inferring structure and generating simulation scenes from natural images, allowing for scalable scene generation from web-scale datasets. To train these image-to-simulation models, we show how controllable text-to-image generative models can be used in generating paired training data that allows for modeling of the inverse problem, mapping from realistic images back to complete scene models. We show how this paradigm allows us to build large datasets of scenes in simulation with semantic and physical realism. We present an integrated end-to-end pipeline that generates simulation scenes complete with articulated kinematic and dynamic structures from real-world images and use these for training robotic control policies. We then robustly deploy in the real world for tasks like articulated object manipulation. In doing so, our work provides both a pipeline for large-scale generation of simulation environments and an integrated system for training robust robotic control policies in the resulting environments.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a0217c22848ac2effc93dba58e8813faa57a8011" target='_blank'>URDFormer: A Pipeline for Constructing Articulated Simulation Environments from Real-World Images</a></td>
-          <td>
-            Zoey Chen, Aaron Walsman, Marius Memmel, Kaichun Mo, Alex Fang, Karthikeya Vemuri, Alan Wu, Dieter Fox, Abhishek Gupta
-          </td>
-          <td>2024-05-19</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="A key challenge for an agent learning to interact with the world is to reason about physical properties of objects and to foresee their dynamics under the effect of applied forces. In order to scale learning through interaction to many objects and scenes, robots should be able to improve their own performance from real-world experience without requiring human supervision. To this end, we propose a novel approach for modeling the dynamics of a robot’s interactions directly from unlabeled 3D point clouds and images. Unlike previous approaches, our method does not require ground-truth data associations provided by a tracker or any pre-trained perception network. To learn from unlabeled real-world interaction data, we enforce consistency of estimated 3D clouds, actions and 2D images with observed ones. Our joint forward and inverse network learns to segment a scene into salient object parts and predicts their 3D motion under the effect of applied actions. Moreover, our object-centric model outputs action-conditioned 3D scene flow, object masks and 2D optical flow as emergent properties. Our extensive evaluation both in simulation and with real-world data demonstrates that our formulation leads to effective, interpretable models that can be used for visuomotor control and planning. Videos, code and dataset are available at http://hind4sight.cs.uni-freiburg.de">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f3268665dd71fc2738f8bd86bb95dda36fc47bc9" target='_blank'>Hindsight for Foresight: Unsupervised Structured Dynamics Models from Physical Interaction</a></td>
-          <td>
-            Iman Nematollahi, Oier Mees, Lukás Hermann, Wolfram Burgard
-          </td>
-          <td>2020-08-02</td>
-          <td>2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)</td>
-          <td>14</td>
-          <td>121</td>
-        </tr>
-    
-        <tr id="We aim to perform unsupervised discovery of objects and their states such as location and velocity, as well as physical system parameters such as mass and gravity from video -- given only the differential equations governing the scene dynamics. Existing physical scene understanding methods require either object state supervision, or do not integrate with differentiable physics to learn interpretable system parameters and states. We address this problem through a $\textit{physics-as-inverse-graphics}$ approach that brings together vision-as-inverse-graphics and differentiable physics engines. This framework allows us to perform long term extrapolative video prediction, as well as vision-based model-predictive control. Our approach significantly outperforms related unsupervised methods in long-term future frame prediction of systems with interacting objects (such as ball-spring or 3-body gravitational systems). We further show the value of this tight vision-physics integration by demonstrating data-efficient learning of vision-actuated model-based control for a pendulum system. The controller's interpretability also provides unique capabilities in goal-driven control and physical reasoning for zero-data adaptation.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2ac26ffe14d264fad2cf26632fab86e49a06b03e" target='_blank'>Physics-as-Inverse-Graphics: Joint Unsupervised Learning of Objects and Physics from Video</a></td>
-          <td>
-            Miguel Jaques, Michael Burke, Timothy M. Hospedales
-          </td>
-          <td>2019-05-27</td>
-          <td>ArXiv</td>
-          <td>18</td>
-          <td>70</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Physics-informed machine learning</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Physics-informed machine learning (PIML) refers to the emerging area of extracting physically relevant solutions to complex multiscale modeling problems lacking sufficient quantity and veracity of data with learning models informed by physically relevant prior information. This work discusses the recent critical advancements in the PIML domain. Novel methods and applications of domain decomposition in physics-informed neural networks (PINNs) in particular are highlighted. Additionally, we explore recent works toward utilizing neural operator learning to intuit relationships in physics systems traditionally modeled by sets of complex governing equations and solved with expensive differentiation techniques. Finally, expansive applications of traditional physics-informed machine learning and potential limitations are discussed. In addition to summarizing recent work, we propose a novel taxonomic structure to catalog physics-informed machine learning based on how the physics-information is derived and injected into the machine learning process. The taxonomy assumes the explicit objectives of facilitating interdisciplinary collaboration in methodology, thereby promoting a wider characterization of what types of physics problems are served by the physics-informed learning machines and assisting in identifying suitable targets for future work. To summarize, the major twofold goal of this work is to summarize recent advancements and introduce a taxonomic catalog for applications of physics-informed machine learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c02bcf76b42448750eb510a96bfba6c18e6c84ce" target='_blank'>A Taxonomic Survey of Physics-Informed Machine Learning</a></td>
-          <td>
-            J. Pateras, P. Rana, Preetam Ghosh
-          </td>
-          <td>2023-06-07</td>
-          <td>Applied Sciences</td>
-          <td>7</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="Abstract Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some instances, the objective is to discover part of the hidden physics from the available data, and PIML has been shown to be particularly effective for such problems for which conventional methods may fail. Unlike commercial machine learning where training of deep neural networks requires big data, in PIML big data are not available. Instead, we can train such networks from additional information obtained by employing the physical laws and evaluating them at random points in the space–time domain. Such PIML integrates multimodality and multifidelity data with mathematical models, and implements them using neural networks or graph networks. Here, we review some of the prevailing trends in embedding physics into machine learning, using physics-informed neural networks (PINNs) based primarily on feed-forward neural networks and automatic differentiation. For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs). We present representative examples for both forward and inverse problems and discuss what advances are needed to scale up PINNs, PIGNs and more broadly GNNs for large-scale engineering problems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b30c496f3eae005a948eb2b6dff4db69e39958f0" target='_blank'>Scalable algorithms for physics-informed neural and graph networks</a></td>
-          <td>
-            K. Shukla, Mengjia Xu, N. Trask, G. Karniadakis
-          </td>
-          <td>2022-05-16</td>
-          <td>Data-Centric Engineering</td>
-          <td>26</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="Numerous physics theories are rooted in partial differential equations (PDEs). However, the increasingly intricate physics equations, especially those that lack analytic solutions or closed forms, have impeded the further development of physics. Computationally solving PDEs by classic numerical approaches suffers from the trade-off between accuracy and efficiency and is not applicable to the empirical data generated by unknown latent PDEs. To overcome this challenge, we present KoopmanLab, an efficient module of the Koopman neural operator (KNO) family, for learning PDEs without analytic solutions or closed forms. Our module consists of multiple variants of the KNO, a kind of mesh-independent neural-network-based PDE solvers developed following the dynamic system theory. The compact variants of KNO can accurately solve PDEs with small model sizes, while the large variants of KNO are more competitive in predicting highly complicated dynamic systems govern by unknown, high-dimensional, and non-linear PDEs. All variants are validated by mesh-independent and long-term prediction experiments implemented on representative PDEs (e.g., the Navier–Stokes equation and the Bateman–Burgers equation in fluid mechanics) and ERA5 (i.e., one of the largest high-resolution global-scale climate datasets in earth physics). These demonstrations suggest the potential of KoopmanLab to be a fundamental tool in diverse physics studies related to equations or dynamic systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1ea73ffbdc09eab4c8dd3c4a8f234bf88effdd11" target='_blank'>KoopmanLab: machine learning for solving complex physics equations</a></td>
-          <td>
-            Wei Xiong, Muyuan Ma, Ziyang Zhang, Pei Sun, Yang Tian
-          </td>
-          <td>2023-01-03</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="
- Advancements in computing power have recently made it possible to utilize machine learning and deep learning to push scientific computing forward in a range of disciplines, such as fluid mechanics, solid mechanics, materials science, etc. The incorporation of neural networks is particularly crucial in this hybridization process. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data is sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multi-physics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multi-physics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities are presented in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bc9ae66c84e31839015dd30c0bd76548bf1b7a5c" target='_blank'>Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks and Operators in Scientific Computing: Fluid and Solid Mechanics</a></td>
-          <td>
-            Salah A. Faroughi, Nikhil M. Pawar, Célio Fernandes, M. Raissi, Subasish Das, N. Kalantari, S. K. Mahjour
-          </td>
-          <td>2024-01-08</td>
-          <td>J. Comput. Inf. Sci. Eng.</td>
-          <td>22</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id=" Physics-Informed Neural Networks (PINNs) represent a groundbreaking approach wherein neural networks (NNs) integrate model equations, such as Partial Differential Equations (PDEs), within their architecture. This innovation has become instrumental in solving diverse problem sets including PDEs, fractional equations, integral-differential equations, and stochastic PDEs. It's a versatile multi-task learning framework that tasks NNs with fitting observed data while simultaneously minimizing PDE residuals. This paper delves into the landscape of PINNs, aiming to delineate their inherent strengths and weaknesses. Beyond exploring the fundamental characteristics of these networks, this review endeavors to encompass a wider spectrum of collocation-based physics-informed neural networks, extending beyond the core PINN model. Variants like physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN) constitute pivotal aspects of this exploration. The study accentuates a predominant focus in research on tailoring PINNs through diverse strategies: adapting activation functions, refining gradient optimization techniques, innovating neural network structures, and enhancing loss function architectures. Despite the extensive applicability demonstrated by PINNs, surpassing classical numerical methods like Finite Element Method (FEM) in certain contexts, the review highlights ongoing opportunities for advancement. Notably, there are persisting theoretical challenges that demand resolution, ensuring the continued evolution and refinement of this revolutionary approach.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d724afae8cafd27a64fb7f6418c81436eaf2f6cc" target='_blank'>Machine Learning Through Physics–Informed Neural Networks: Progress and Challenges</a></td>
-          <td>
-            Klapa Antonion, Xiao Wang, M. Raissi, Laurn Joshie
-          </td>
-          <td>2024-01-20</td>
-          <td>Academic Journal of Science and Technology</td>
-          <td>2</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="Partial differential equations (PDEs) play a pivotal role in mathematical analysis and modeling of dynamic processes across various disciplines of science and engineering. Machine learning (ML) techniques have emerged as a promising new approach to solving PDEs. Among them, Physics-Informed Neural Networks (PINNs) have garnered significant attention in numerous scientific and engineering studies. PINNs employ a single deep neural network to assimilate observational data with PDEs across the entire space-time of a physical system, subsequently yielding rapid solutions. However, a PINN may entail intricate analyses or computations and can be cost-intensive, depending on initial or boundary conditions and other input parameters. To address the limitations of the PINN, especially concerning resolution for nonlinear problems, the Physical-Informed Deep Operator Network (DeepONet) is introduced in this paper. The Physics-Informed DeepONet is a deep learning framework crafted to discern solution operators for any given PDEs, even in scenarios lacking paired input/output training data. The proposed framework is able to predict solutions for various types of parameterized PDEs much faster than conventional PDE solvers. Several cases confirm that this approach is effective in establishing previously unexplored paradigms for modeling/simulating nonlinear and non-equilibrium processes in science and engineering.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/54aa8e27e0e1c52997a21502817afcb71d9e8ccb" target='_blank'>Understanding on Physics-Informed DeepONet</a></td>
-          <td>
-            Sang-Min Lee
-          </td>
-          <td>2024-01-31</td>
-          <td>Journal of the Korea Academia-Industrial cooperation Society</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="Recent breakthroughs in computing power have made it feasible to use machine learning and deep learning to advance scientific computing in many fields, including fluid mechanics, solid mechanics, materials science, etc. Neural networks, in particular, play a central role in this hybridization. Due to their intrinsic architecture, conventional neural networks cannot be successfully trained and scoped when data is sparse, which is the case in many scientific and engineering domains. Nonetheless, neural networks provide a solid foundation to respect physics-driven or knowledge-based constraints during training. Generally speaking, there are three distinct neural network frameworks to enforce the underlying physics: (i) physics-guided neural networks (PgNNs), (ii) physics-informed neural networks (PiNNs), and (iii) physics-encoded neural networks (PeNNs). These methods provide distinct advantages for accelerating the numerical modeling of complex multiscale multi-physics phenomena. In addition, the recent developments in neural operators (NOs) add another dimension to these new simulation paradigms, especially when the real-time prediction of complex multi-physics systems is required. All these models also come with their own unique drawbacks and limitations that call for further fundamental research. This study aims to present a review of the four neural network frameworks (i.e., PgNNs, PiNNs, PeNNs, and NOs) used in scientific computing research. The state-of-the-art architectures and their applications are reviewed, limitations are discussed, and future research opportunities in terms of improving algorithms, considering causalities, expanding applications, and coupling scientific and deep learning solvers are presented. This critical review provides researchers and engineers with a solid starting point to comprehend how to integrate different layers of physics into neural networks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/759a38745575ef3ef1a67f7128d5e00fd8a303f0" target='_blank'>Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing</a></td>
-          <td>
-            Salah A. Faroughi, N. Pawar, C. Fernandes, Subasish Das, N. Kalantari, S. K. Mahjour
-          </td>
-          <td>2022-11-14</td>
-          <td>ArXiv</td>
-          <td>31</td>
-          <td>29</td>
-        </tr>
-    
-        <tr id="We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator learning. These bounds guarantee that PINNs and (physics-informed) DeepONets or FNOs will efficiently approximate the underlying solution or solution operator of generic partial differential equations (PDEs). Our framework utilizes existing neural network approximation results to obtain bounds on more involved learning architectures for PDEs. We illustrate the general framework by deriving the first rigorous bounds on the approximation error of physics-informed operator learning and by showing that PINNs (and physics-informed DeepONets and FNOs) mitigate the curse of dimensionality in approximating nonlinear parabolic PDEs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a1d9a2ca8002ba984357c156b4a7339eda219e2f" target='_blank'>Generic bounds on the approximation error for physics-informed (and) operator learning</a></td>
-          <td>
-            Tim De Ryck, Siddhartha Mishra
-          </td>
-          <td>2022-05-23</td>
-          <td>ArXiv</td>
-          <td>48</td>
-          <td>10</td>
-        </tr>
-    
-        <tr id="Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e5858daa78db0cd950891018505e0e63c41b90ee" target='_blank'>Scientific machine learning for closure models in multiscale problems: a review</a></td>
-          <td>
-            Benjamin Sanderse, P. Stinis, R. Maulik, Shady E. Ahmed
-          </td>
-          <td>2024-03-05</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>21</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>VAMPnets for deep learning of molecular kinetics</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f8a6341496701a0d7fdaa50e6a5aa157236a0ff8" target='_blank'>Author Correction: VAMPnets for deep learning of molecular kinetics</a></td>
-          <td>
-            Andreas Mardt, Luca Pasquali, Hao Wu, F. Noé
-          </td>
-          <td>2018-10-22</td>
-          <td>Nature Communications</td>
-          <td>24</td>
-          <td>61</td>
-        </tr>
-    
-        <tr id="Recent advances in computational power and algorithms have enabled molecular dynamics (MD) simulations to reach greater time scales. However, for observing conformational transitions associated with biomolecular processes, MD simulations still have limitations. Several enhanced sampling techniques seek to address this challenge, including the weighted ensemble (WE) method, which samples transitions between metastable states using many weighted trajectories to estimate kinetic rate constants. However, initial sampling of the potential energy surface has a significant impact on the performance of WE, i.e., convergence and efficiency. We therefore introduce deep-learned kinetic modeling approaches that extract statistically relevant information from short MD trajectories to provide a well-sampled initial state distribution for WE simulations. This hybrid approach overcomes any statistical bias to the system, as it runs short unbiased MD trajectories and identifies meaningful metastable states of the system. It is shown to provide a more refined free energy landscape closer to the steady state that could efficiently sample kinetic properties such as rate constants.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c4d9b7166a2ac580c195d72f64489b3f4e0b9c23" target='_blank'>DeepWEST: Deep Learning of Kinetic Models with the Weighted Ensemble Simulation Toolkit for Enhanced Sampling.</a></td>
-          <td>
-            Anupam Anand Ojha, Saumya Thakur, Surl-Hee Ahn, Rommie E. Amaro
-          </td>
-          <td>2023-01-31</td>
-          <td>Journal of chemical theory and computation</td>
-          <td>7</td>
-          <td>53</td>
-        </tr>
-    
-        <tr id="Finding a low dimensional representation of data from long-timescale trajectories of biomolecular processes, such as protein folding or ligand-receptor binding, is of fundamental importance, and kinetic models, such as Markov modeling, have proven useful in describing the kinetics of these systems. Recently, an unsupervised machine learning technique called VAMPNet was introduced to learn the low dimensional representation and the linear dynamical model in an end-to-end manner. VAMPNet is based on the variational approach for Markov processes and relies on neural networks to learn the coarse-grained dynamics. In this paper, we combine VAMPNet and graph neural networks to generate an end-to-end framework to efficiently learn high-level dynamics and metastable states from the long-timescale molecular dynamics trajectories. This method bears the advantages of graph representation learning and uses graph message passing operations to generate an embedding for each datapoint, which is used in the VAMPNet to generate a coarse-grained dynamical model. This type of molecular representation results in a higher resolution and a more interpretable Markov model than the standard VAMPNet, enabling a more detailed kinetic study of the biomolecular processes. Our GraphVAMPNet approach is also enhanced with an attention mechanism to find the important residues for classification into different metastable states.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e15c87cfb4d2b1f82076331f9c58085598440e46" target='_blank'>GraphVAMPNet, using graph neural networks and variational approach to markov processes for dynamical modeling of biomolecules</a></td>
-          <td>
-            Mahdi Ghorbani, Samarjeet Prasad, Jeffery B. Klauda, B. Brooks
-          </td>
-          <td>2022-01-12</td>
-          <td>The Journal of chemical physics</td>
-          <td>22</td>
-          <td>64</td>
-        </tr>
-    
-        <tr id="Molecular dynamics (MD) simulations have emerged to become the back-bone of today’s computational biophysics. Simulation tools such as, NAMD, AMBER and GROMACS have accumulated more than 100,000 users. Despite this remarkable success, now also bolstered by compatibility with graphics processor units (GPUs) and exascale computers, even the most scalable simulations cannot access biologically relevant timescales - the number of numerical integration steps necessary for solving differential equations in a million-to-billion-dimensional space is computationally in-tractable. Recent advancements in Deep Learning has made it such that patterns can be found in high dimensional data. In addition, Deep Learning have also been used for simulating physical dynamics. Here, we utilize LSTMs in order to predict future molecular dynamics from current and previous timesteps, and examine how this physics-guided learning can benefit researchers in computational biophysics. In particular, we test fully connected Feed-forward Neural Networks, Recurrent Neural Networks with LSTM / GRU memory cells with TensorFlow and PyTorch frame-works trained on data from NAMD simulations to predict conformational transitions on two different biological systems. We find that non-equilibrium MD is easier to train and performance improves under the assumption that each atom is independent of all other atoms in the system. Our study represents a case study for high-dimensional data that switches stochastically between fast and slow regimes. Applications of resolving these sets will allow real-world applications in the interpretation of data from Atomic Force Microscopy experiments.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/86de5fbe09c4381f548e1312d53f15d898c76c78" target='_blank'>Mind reading of the proteins: Deep-learning to forecast molecular dynamics</a></td>
-          <td>
-            C. Gupta, J. Cava, Daipayan Sarkar, Eric A. Wilson, J. Vant, Steven Murray, A. Singharoy, S. Karmaker
-          </td>
-          <td>2020-07-29</td>
-          <td>bioRxiv</td>
-          <td>4</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="The success of enhanced sampling molecular simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational dynamics of a system. It is challenging to intuit these slow CVs for all but the simplest molecular systems, and their data-driven discovery directly from molecular simulation trajectories has been a central focus of the molecular simulation community to both unveil the important physical mechanisms and drive enhanced sampling. In this work, we introduce state-free reversible VAMPnets (SRV) as a deep learning architecture that learns nonlinear CV approximants to the leading slow eigenfunctions of the spectral decomposition of the transfer operator that evolves equilibrium-scaled probability distributions through time. Orthogonality of the learned CVs is naturally imposed within network training without added regularization. The CVs are inherently explicit and differentiable functions of the input coordinates making them well-suited to use in enhanced sampling calculations. We demonstrate the utility of SRVs in capturing parsimonious nonlinear representations of complex system dynamics in applications to 1D and 2D toy systems where the true eigenfunctions are exactly calculable and to molecular dynamics simulations of alanine dipeptide and the WW domain protein.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2e7163e31e9b32cec11005678bae9e1dbeb6d573" target='_blank'>Nonlinear Discovery of Slow Molecular Modes using Hierarchical Dynamics Encoders</a></td>
-          <td>
-            Wei Chen, Hythem Sidky, Andrew L. Ferguson
-          </td>
-          <td>2019-02-09</td>
-          <td>The Journal of chemical physics</td>
-          <td>77</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="Small integration time steps limit molecular dynamics (MD) simulations to millisecond time scales. Markov state models (MSMs) and equation-free approaches learn low-dimensional kinetic models from MD simulation data by performing configurational or dynamical coarse-graining of the state space. The learned kinetic models enable the efficient generation of dynamical trajectories over vastly longer time scales than are accessible by MD, but the discretization of configurational space and/or absence of a means to reconstruct molecular configurations precludes the generation of continuous atomistic molecular trajectories. We propose latent space simulators (LSS) to learn kinetic models for continuous atomistic simulation trajectories by training three deep learning networks to (i) learn the slow collective variables of the molecular system, (ii) propagate the system dynamics within this slow latent space, and (iii) generatively reconstruct molecular configurations. We demonstrate the approach in an application to Trp-cage miniprotein to produce novel ultra-long synthetic folding trajectories that accurately reproduce atomistic molecular structure, thermodynamics, and kinetics at six orders of magnitude lower cost than MD. The dramatically lower cost of trajectory generation enables greatly improved sampling and greatly reduced statistical uncertainties in estimated thermodynamic averages and kinetic rates.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2d3000d245988a02d3c1060211e9d89c67147b49" target='_blank'>Molecular latent space simulators</a></td>
-          <td>
-            Hythem Sidky, Wei Chen, Andrew L. Ferguson
-          </td>
-          <td>2020-07-01</td>
-          <td>Chemical Science</td>
-          <td>31</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="Machine learning (ML) has emerged as a pervasive tool in science, engineering, and beyond. Its success has also led to several synergies with molecular dynamics (MD) simulations, which we use to identify and characterize the major metastable states of molecular systems. Typically, we aim to determine the relative stabilities of these states and how rapidly they interchange. This information allows mechanistic descriptions of molecular mechanisms, enables a quantitative comparison with experiments, and facilitates their rational design. ML impacts all aspects of MD simulations – from analyzing the data and accelerating sampling to defining more efficient or more accurate simulation models. This chapter focuses on three fundamental problems in MD simulations: accurately parameterizing coarse-grained force fields, sampling thermodynamically stable states, and analyzing the exchange kinetics between those states. In addition, we outline several state-of-the-art neural network architectures and show how they are combined with physics-motivated learning objectives to solve MD-specific problems. Finally, we highlight open questions and challenges in the field and give some perspective on future developments.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/50c74a10fcddb0e41a5a00b965383fdc52534eec" target='_blank'>Machine Learning in Molecular Dynamics Simulations of Biomolecular Systems</a></td>
-          <td>
-            Christopher Kolloff, Simon Olsson
-          </td>
-          <td>2022-05-06</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/13b52cd927d3daa5c95528b987734d97474e790c" target='_blank'>Markov field models: Scaling molecular kinetics approaches to large molecular machines.</a></td>
-          <td>
-            Tim Hempel, Simon Olsson, Frank No'e
-          </td>
-          <td>2022-06-23</td>
-          <td>Current opinion in structural biology</td>
-          <td>6</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="Capturing the time evolution and predicting future kinetic states of physicochemical systems present significant challenges due to the precision and computational effort required. In this study, we demonstrate that the transformer, a machine learning model renowned for machine translation and natural language processing, can be effectively adapted to predict the dynamical state-to-state transition kinetics of biologically relevant physicochemical systems. Specifically, by using sequences of time-discretized states from Molecular Dynamics (MD) simulation trajectories as input, we show that a transformer can learn the complex syntactic and semantic relationships within the trajectory. This enables this generative pre-trained transformer (GPT) to predict kinetically accurate sequences of future states for a diverse set of models and biomolecules of varying complexity. Remarkably, the GPT can predict future states much faster than traditional MD simulations. We show that it is particularly adept at forecasting the time evolution of an out-of-equilibrium active system that do not maintain detailed balance. An analysis of self-attention mechanism inherent in transformers is found to hold crucial role for capturing the long-range correlations necessary for accurate state-to-state transition predictions. Together, our results highlight the ability of transformer based machine learning model in generating future states of physicochemical systems with statistical precision.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3f68df42b37752017ad05438942ecb38a7e24c6e" target='_blank'>Predicting Future Kinetic States of Physicochemical Systems Using Generative Pre-trained Transformer</a></td>
-          <td>
-            Palash Bera, Jagannath Mondal
-          </td>
-          <td>2024-06-19</td>
-          <td>bioRxiv</td>
-          <td>0</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="Markov state models (MSMs) are a powerful framework for analyzing dynamical systems, such as molecular dynamics (MD) simulations, that have gained widespread use over the past several decades. This perspective offers an overview of the MSM field to date, presented for a general audience as a timeline of key developments in the field. We sequentially address early studies that motivated the method, canonical papers that established the use of MSMs for MD analysis, and subsequent advances in software and analysis protocols. The derivation of a variational principle for MSMs in 2013 signified a turning point from expertise-driving MSM building to a systematic, objective protocol. The variational approach, combined with best practices for model selection and open-source software, enabled a wide range of MSM analysis for applications such as protein folding and allostery, ligand binding, and protein-protein association. To conclude, the current frontiers of methods development are highlighted, as well as exciting applications in experimental design and drug discovery.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/260f212da0cf8b3309f0ab3a130a0ad22993892e" target='_blank'>Markov State Models: From an Art to a Science.</a></td>
-          <td>
-            B. Husic, V. Pande
-          </td>
-          <td>2018-02-02</td>
-          <td>Journal of the American Chemical Society</td>
-          <td>584</td>
-          <td>103</td>
-        </tr>
-    
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-        <th>Citation count</th>
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-    Recommendations for the article <i>Domain Adaptation for Time Series Under Feature and Label Shifts</i>
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-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
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-        <th>Publication Date</th>
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-    
-        <tr id="Unsupervised Domain Adaptation (UDA) aims to harness labeled source data to train models for unlabeled target data. Despite extensive research in domains like computer vision and natural language processing, UDA remains underexplored for time series data, which has widespread real-world applications ranging from medicine and manufacturing to earth observation and human activity recognition. Our paper addresses this gap by introducing a comprehensive benchmark for evaluating UDA techniques for time series classification, with a focus on deep learning methods. We provide seven new benchmark datasets covering various domain shifts and temporal dynamics, facilitating fair and standardized UDA method assessments with state of the art neural network backbones (e.g. Inception) for time series data. This benchmark offers insights into the strengths and limitations of the evaluated approaches while preserving the unsupervised nature of domain adaptation, making it directly applicable to practical problems. Our paper serves as a vital resource for researchers and practitioners, advancing domain adaptation solutions for time series data and fostering innovation in this critical field. The implementation code of this benchmark is available at https://github.com/EricssonResearch/UDA-4-TSC.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0f5f7b22ebc4dbbb2a0d3ba1e19e4659a7b0bcb5" target='_blank'>Deep Unsupervised Domain Adaptation for Time Series Classification: a Benchmark</a></td>
-          <td>
-            Hassan Ismail Fawaz, Ganesh Del Grosso, Tanguy Kerdoncuff, Aurelie Boisbunon, Illyyne Saffar
-          </td>
-          <td>2023-12-15</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>5</td>
-        </tr>
-    
-        <tr id="Unsupervised domain adaptation methods aim at generalizing well on unlabeled test data that may have a different (shifted) distribution from the training data. Such methods are typically developed on image data, and their application to time series data is less explored. Existing works on time series domain adaptation suffer from inconsistencies in evaluation schemes, datasets, and backbone neural network architectures. Moreover, labeled target data are often used for model selection, which violates the fundamental assumption of unsupervised domain adaptation. To address these issues, we develop a benchmarking evaluation suite (AdaTime) to systematically and fairly evaluate different domain adaptation methods on time series data. Specifically, we standardize the backbone neural network architectures and benchmarking datasets, while also exploring more realistic model selection approaches that can work with no labeled data or just a few labeled samples. Our evaluation includes adapting state-of-the-art visual domain adaptation methods to time series data as well as the recent methods specifically developed for time series data. We conduct extensive experiments to evaluate 11 state-of-the-art methods on five representative datasets spanning 50 cross-domain scenarios. Our results suggest that with careful selection of hyper-parameters, visual domain adaptation methods are competitive with methods proposed for time series domain adaptation. In addition, we find that hyper-parameters could be selected based on realistic model selection approaches. Our work unveils practical insights for applying domain adaptation methods on time series data and builds a solid foundation for future works in the field. The code is available at github.com/emadeldeen24/AdaTime.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4fce5494c4c00fbf0cabab2744d024d0f8039007" target='_blank'>ADATIME: A Benchmarking Suite for Domain Adaptation on Time Series Data</a></td>
-          <td>
-            Mohamed Ragab, Emadeldeen Eldele, Wee Ling Tan, Chuan-Sheng Foo, Zhenghua Chen, Min Wu, C. Kwoh, Xiaoli Li
-          </td>
-          <td>2022-03-15</td>
-          <td>ACM Transactions on Knowledge Discovery from Data</td>
-          <td>38</td>
-          <td>36</td>
-        </tr>
-    
-        <tr id="Domain generalization methods aim to learn models robust to domain shift with data from a limited number of source domains and without access to target domain samples during training. Popular domain alignment methods for domain generalization seek to extract domain-invariant features by minimizing the discrepancy between feature distributions across all domains, disregarding inter-domain relationships. In this paper, we instead propose a novel representation learning methodology that selectively enforces prediction consistency between source domains estimated to be closely-related. Specifically, we hypothesize that domains share different class-informative representations, so instead of aligning all domains which can cause negative transfer, we only regularize the discrepancy between closely-related domains. We apply our method to time-series classification tasks and conduct comprehensive experiments on three public real-world datasets. Our method significantly improves over the baseline and achieves better or competitive performance in comparison with state-of-the-art methods in terms of both accuracy and model calibration.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4a1938c9fd3db160a34b8673afd6ba51f8c151f6" target='_blank'>Domain Generalization via Selective Consistency Regularization for Time Series Classification</a></td>
-          <td>
-            Wenyu Zhang, Mohamed Ragab, Chuan-Sheng Foo
-          </td>
-          <td>2022-06-16</td>
-          <td>2022 26th International Conference on Pattern Recognition (ICPR)</td>
-          <td>0</td>
-          <td>25</td>
-        </tr>
-    
-        <tr id="Recently, deep neural networks have gained increasing popularity in the field of time series forecasting. A primary reason for their success is their ability to effectively capture complex temporal dynamics across multiple related time series. The advantages of these deep forecasters only start to emerge in the presence of a sufficient amount of data. This poses a challenge for typical forecasting problems in practice, where there is a limited number of time series or observations per time series, or both. To cope with this data scarcity issue, we propose a novel domain adaptation framework, Domain Adaptation Forecaster (DAF). DAF leverages statistical strengths from a relevant domain with abundant data samples (source) to improve the performance on the domain of interest with limited data (target). In particular, we use an attention-based shared module with a domain discriminator across domains and private modules for individual domains. We induce domain-invariant latent features (queries and keys) and retrain domain-specific features (values) simultaneously to enable joint training of forecasters on source and target domains. A main insight is that our design of aligning keys allows the target domain to leverage source time series even with different characteristics. Extensive experiments on various domains demonstrate that our proposed method outperforms state-of-the-art baselines on synthetic and real-world datasets, and ablation studies verify the effectiveness of our design choices.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/82332f1b4199814269d7ae317ec7917859540ea0" target='_blank'>Domain Adaptation for Time Series Forecasting via Attention Sharing</a></td>
-          <td>
-            Xiaoyong Jin, Youngsuk Park, Danielle C. Maddix, Bernie Wang, Xifeng Yan
-          </td>
-          <td>2021-02-13</td>
-          <td>ArXiv, DBLP</td>
-          <td>56</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="In many real-world scenarios, machine learning models fall short in prediction performance due to data characteristics changing from training on one source domain to testing on a target domain. There has been extensive research to address this problem with Domain Adaptation (DA) for learning domain invariant features. However, when considering advances for time series, those methods remain limited to the use of hard parameter sharing (HPS) between source and target models, and the use of domain adaptation objective function. To address these challenges, we propose a soft parameter sharing (SPS) DA architecture with representation learning while modeling the relation as non-linear between parameters of source and target models and modeling the adaptation loss function as the squared Maximum Mean Discrepancy (MMD). The proposed architecture advances the state-of-the-art for time series in the context of activity recognition and in fields with other modalities, where SPS has been limited to a linear relation. An additional contribution of our work is to provide a study that demonstrates the strengths and limitations of HPS versus SPS. Experiment results showed the success of the method in three domain adaptation cases of multivariate time series activity recognition with different users and sensors.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/932f3f370dc502d1edb018b0b7a4be28de719ed6" target='_blank'>Domain Adaptation with Representation Learning and Nonlinear Relation for Time Series</a></td>
-          <td>
-            A. Hussein, Hazem Hajj
-          </td>
-          <td>2022-02-15</td>
-          <td>ACM Transactions on Internet of Things</td>
-          <td>11</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="While large volumes of unlabeled data are usually available, associated labels are often scarce. The unsupervised domain adaptation problem aims at exploiting labels from a source domain to classify data from a related, yet different, target domain. When time series are at stake, new difficulties arise as temporal shifts may appear in addition to the standard feature distribution shift. In this paper, we introduce the Match-And-Deform (MAD) approach that aims at finding correspondences between the source and target time series while allowing temporal distortions. The associated optimization problem simultaneously aligns the series thanks to an optimal transport loss and the time stamps through dynamic time warping. When embedded into a deep neural network, MAD helps learning new representations of time series that both align the domains and maximize the discriminative power of the network. Empirical studies on benchmark datasets and remote sensing data demonstrate that MAD makes meaningful sample-to-sample pairing and time shift estimation, reaching similar or better classification performance than state-of-the-art deep time series domain adaptation strategies.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2e5a111c55cb603e88a99034ada50dc147e23009" target='_blank'>Match-And-Deform: Time Series Domain Adaptation through Optimal Transport and Temporal Alignment</a></td>
-          <td>
-            Franccois Painblanc, L. Chapel, N. Courty, Chloé Friguet, Charlotte Pelletier, R. Tavenard
-          </td>
-          <td>2023-08-24</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>33</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/5d150cec2775f9bc863760448f14104cc8f42368.md b/docs/recommendations/5d150cec2775f9bc863760448f14104cc8f42368.md
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-  <i class="footer">This page was last updated on 2024-08-08 13:17:12 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Discovering governing equations from data by sparse identification of nonlinear dynamical systems</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
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-  <tbody>
-    
-        <tr id="Significance Governing equations are essential to the study of physical systems, providing models that can generalize to predict previously unseen behaviors. There are many systems of interest across disciplines where large quantities of data have been collected, but the underlying governing equations remain unknown. This work introduces an approach to discover governing models from data. The proposed method addresses a key limitation of prior approaches by simultaneously discovering coordinates that admit a parsimonious dynamical model. Developing parsimonious and interpretable governing models has the potential to transform our understanding of complex systems, including in neuroscience, biology, and climate science. The discovery of governing equations from scientific data has the potential to transform data-rich fields that lack well-characterized quantitative descriptions. Advances in sparse regression are currently enabling the tractable identification of both the structure and parameters of a nonlinear dynamical system from data. The resulting models have the fewest terms necessary to describe the dynamics, balancing model complexity with descriptive ability, and thus promoting interpretability and generalizability. This provides an algorithmic approach to Occam’s razor for model discovery. However, this approach fundamentally relies on an effective coordinate system in which the dynamics have a simple representation. In this work, we design a custom deep autoencoder network to discover a coordinate transformation into a reduced space where the dynamics may be sparsely represented. Thus, we simultaneously learn the governing equations and the associated coordinate system. We demonstrate this approach on several example high-dimensional systems with low-dimensional behavior. The resulting modeling framework combines the strengths of deep neural networks for flexible representation and sparse identification of nonlinear dynamics (SINDy) for parsimonious models. This method places the discovery of coordinates and models on an equal footing.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3c9961153493370500020c81527b3548c96f81e0" target='_blank'>Data-driven discovery of coordinates and governing equations</a></td>
-          <td>
-            Kathleen P. Champion, Bethany Lusch, J. Kutz, S. Brunton
-          </td>
-          <td>2019-03-29</td>
-          <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>595</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1f18c5206491626d36c2271aaf491dbc945f6247" target='_blank'>Automatically discovering ordinary differential equations from data with sparse regression</a></td>
-          <td>
-            Kevin Egan, Weizhen Li, Rui Carvalho
-          </td>
-          <td>2024-01-09</td>
-          <td>Communications Physics</td>
-          <td>7</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Estimating governing equations from observed time-series data is crucial for understanding dynamical systems. From the perspective of system comprehension, the demand for accurate estimation and interpretable results has been particularly emphasized. Herein, we propose a novel data-driven method for estimating the governing equations of dynamical systems based on machine learning with high accuracy and interpretability. The proposed method enhances the estimation accuracy for dynamical systems using sparse modeling by incorporating physical constraints derived from Hamiltonian mechanics. Unlike conventional approaches used for estimating governing equations for dynamical systems, we employ a sparse representation of Hamiltonian, allowing for the estimation. Using noisy observational data, the proposed method demonstrates a capability to achieve accurate parameter estimation and extraction of essential nonlinear terms. In addition, it is shown that estimations based on energy conservation principles exhibit superior accuracy in long-term predictions. These results collectively indicate that the proposed method accurately estimates dynamical systems while maintaining interpretability.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/18c6dbc4e20d80b81497e8c444e6f9a9ee1acf36" target='_blank'>Sparse Estimation for Hamiltonian Mechanics</a></td>
-          <td>
-            Yuya Note, Masahito Watanabe, Hiroaki Yoshimura, Takaharu Yaguchi, Toshiaki Omori
-          </td>
-          <td>2024-03-25</td>
-          <td>Mathematics</td>
-          <td>0</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e596988b1df3a0bc78bf72c0bfdb21c85eaab6c9" target='_blank'>Physics-informed learning of governing equations from scarce data</a></td>
-          <td>
-            Zhao Chen, Yang Liu, Hao Sun
-          </td>
-          <td>2020-05-05</td>
-          <td>Nature Communications</td>
-          <td>234</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="Discovering the partial differential equations underlying spatio-temporal datasets from very limited and highly noisy observations is of paramount interest in many scientific fields. However, it remains an open question to know when model discovery algorithms based on sparse regression can actually recover the underlying physical processes. In this work, we show the design matrices used to infer the equations by sparse regression can violate the irrepresentability condition (IRC) of the Lasso, even when derived from analytical PDE solutions (i.e. without additional noise). Sparse regression techniques which can recover the true underlying model under violated IRC conditions are therefore required, leading to the introduction of the randomised adaptive Lasso. We show once the latter is integrated within the deep learning model discovery framework DeepMod, a wide variety of nonlinear and chaotic canonical PDEs can be recovered: (1) up to $\mathcal{O}(2)$ higher noise-to-sample ratios than state-of-the-art algorithms, (2) with a single set of hyperparameters, which paves the road towards truly automated model discovery.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/45633bde87d3fecdb0ef577036f2465e70c51f24" target='_blank'>Sparsistent Model Discovery</a></td>
-          <td>
-            Georges Tod, G. Both, R. Kusters
-          </td>
-          <td>2021-06-22</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. Recent advances in sparse identification show encouraging success in distilling closed-form governing equations from data for a wide range of nonlinear dynamical systems. However, the fundamental bottleneck of this approach lies in the robustness and scalability with respect to data scarcity and noise. This work introduces a novel physics-informed deep learning framework to discover governing partial differential equations (PDEs) from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this approach seamlessly integrates the strengths of deep neural networks for rich representation learning, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the PDEs. The efficacy and robustness of this method are demonstrated on discovering a variety of PDE systems with different levels of data scarcity and noise. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e2acd4a2bc6af5deb02f542846766868e3f1b180" target='_blank'>Deep learning of physical laws from scarce data</a></td>
-          <td>
-            Zhao Chen, Yang Liu, Hao Sun
-          </td>
-          <td>2020-05-05</td>
-          <td>ArXiv</td>
-          <td>19</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="In this work, we blend machine learning and dictionary-based learning with numerical analysis tools to discover differential equations from noisy and sparsely sampled measurement data of time-dependent processes. We use the fact that given a dictionary containing large candidate nonlinear functions, dynamical models can often be described by a few appropriately chosen basis functions. As a result, we obtain parsimonious models that can be better interpreted by practitioners, and potentially generalize better beyond the sampling regime than black-box modelling. In this work, we integrate a numerical integration framework with dictionary learning that yields differential equations without requiring or approximating derivative information at any stage. Hence, it is utterly effective for corrupted and sparsely sampled data. We discuss its extension to governing equations, containing rational nonlinearities that typically appear in biological networks. Moreover, we generalized the method to governing equations subject to parameter variations and externally controlled inputs. We demonstrate the efficiency of the method to discover a number of diverse differential equations using noisy measurements, including a model describing neural dynamics, chaotic Lorenz model, Michaelis–Menten kinetics and a parameterized Hopf normal form.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5430c642bf5e56ce52dbfa94a9b3f4035b3222d1" target='_blank'>Discovery of nonlinear dynamical systems using a Runge–Kutta inspired dictionary-based sparse regression approach</a></td>
-          <td>
-            P. Goyal, P. Benner
-          </td>
-          <td>2021-05-11</td>
-          <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>37</td>
-          <td>53</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/01dc5b357be8d15e52cfad61a421b2b27a6e73d4" target='_blank'>Exploiting sparsity and equation-free architectures in complex systems</a></td>
-          <td>
-            J. Proctor, S. Brunton, Bingni W. Brunton, J. Kutz
-          </td>
-          <td>2014-12-10</td>
-          <td>The European Physical Journal Special Topics</td>
-          <td>64</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f066f56b839bc2b5bf188c44767582440c6ea850" target='_blank'>Exploiting sparsity and equation-free architectures in complex systems</a></td>
-          <td>
-            J. Proctor, S. Brunton, Bingni W. Brunton, J. Kutz
-          </td>
-          <td>2014-12-01</td>
-          <td>The European Physical Journal Special Topics</td>
-          <td>7</td>
-          <td>63</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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diff --git a/docs/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c.md b/docs/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c.md
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-    Recommendations for the article <i>Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression</i>
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-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f51873e0fe8affb3e33af0c8a2ca9594a3b393a1" target='_blank'>Automated discovery of fundamental variables hidden in experimental data</a></td>
-          <td>
-            Boyuan Chen, Kuang Huang, Sunand Raghupathi, I. Chandratreya, Qi Du, H. Lipson
-          </td>
-          <td>2022-07-01</td>
-          <td>Nature Computational Science</td>
-          <td>66</td>
-          <td>20</td>
-        </tr>
-    
-        <tr id="Technological advancements have substantially increased computational power and data availability, enabling the application of powerful machine-learning (ML) techniques across various fields. However, our ability to leverage ML methods for scientific discovery, {\it i.e.} to obtain fundamental and formalized knowledge about natural processes, is still in its infancy. In this review, we explore how the scientific community can increasingly leverage ML techniques to achieve scientific discoveries. We observe that the applicability and opportunity of ML depends strongly on the nature of the problem domain, and whether we have full ({\it e.g.}, turbulence), partial ({\it e.g.}, computational biochemistry), or no ({\it e.g.}, neuroscience) {\it a-priori} knowledge about the governing equations and physical properties of the system. Although challenges remain, principled use of ML is opening up new avenues for fundamental scientific discoveries. Throughout these diverse fields, there is a theme that ML is enabling researchers to embrace complexity in observational data that was previously intractable to classic analysis and numerical investigations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f7214e1640b55a726c771c629c873920245e0839" target='_blank'>Opportunities for machine learning in scientific discovery</a></td>
-          <td>
-            Ricardo Vinuesa, Jean Rabault, Hossein Azizpour, Stefan Bauer, Bingni W. Brunton, Arne Elofsson, Elias Jarlebring, Hedvig Kjellstrom, Stefano Markidis, David Marlevi, Paola Cinnella, S. Brunton
-          </td>
-          <td>2024-05-07</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/84d75025e7a847d86cd0bf6308cce4d9a3883c7c" target='_blank'>DeepMoD: Deep learning for model discovery in noisy data</a></td>
-          <td>
-            G. Both, Subham Choudhury, P. Sens, R. Kusters
-          </td>
-          <td>2019-04-20</td>
-          <td>J. Comput. Phys.</td>
-          <td>100</td>
-          <td>34</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/899995e30820d657b2e2feb791025cd6b2027e22" target='_blank'>Discovering sparse interpretable dynamics from partial observations</a></td>
-          <td>
-            Peter Y. Lu, Joan Ariño Bernad, M. Soljačić
-          </td>
-          <td>2021-07-22</td>
-          <td>Communications Physics</td>
-          <td>17</td>
-          <td>94</td>
-        </tr>
-    
-        <tr id="The extraction of models from data (in a sense, the “understanding” of the physical laws giving rise to the data) is a fundamental cognitive as well as scientific challenge. We show a geometric/analytic learning algorithm capable of creating minimal descriptions of parametrically dependent unknown nonlinear dynamical systems. This is accomplished by the data-driven discovery of useful intrinsic-state variables and parameters in terms of which one can empirically model the underlying dynamics. We discuss an informed observation geometry that enables us to formulate models without first principles as well as without closed form equations. (See pp. E7865–E7874.)">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d2df6b9b2ee1bdef1834c343bb952182a7807bda" target='_blank'>PNAS Plus Significance Statements</a></td>
-          <td>
-            Ronald R. Coifman, David A. Kessler, A. Goodkind
-          </td>
-          <td>2017-09-19</td>
-          <td>Proceedings of the National Academy of Sciences</td>
-          <td>40</td>
-          <td>13</td>
-        </tr>
-    
-        <tr id="All physical laws are described as relationships between state variables that give a complete and non-redundant description of the relevant system dynamics. However, despite the prevalence of computing power and AI, the process of identifying the hidden state variables themselves has resisted automation. Most data-driven methods for modeling physical phenomena still assume that observed data streams already correspond to relevant state variables. A key challenge is to identify the possible sets of state variables from scratch, given only high-dimensional observational data. Here we propose a new principle for determining how many state variables an observed system is likely to have, and what these variables might be, directly from video streams. We demonstrate the effectiveness of this approach using video recordings of a variety of physical dynamical systems, ranging from elastic double pendulums to fire flames. Without any prior knowledge of the underlying physics, our algorithm discovers the intrinsic dimension of the observed dynamics and identifies candidate sets of state variables. We suggest that this approach could help catalyze the understanding, prediction and control of increasingly complex systems. Project website is at: https://www.cs.columbia.edu/~bchen/neural-state-variables">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a0d7a5cfc804f90ba8ae80f8cf786d0ad7fe1d17" target='_blank'>Discovering State Variables Hidden in Experimental Data</a></td>
-          <td>
-            Boyuan Chen, Kuang Huang, Sunand Raghupathi, I. Chandratreya, Qi Du, Hod Lipson
-          </td>
-          <td>2021-12-20</td>
-          <td>ArXiv</td>
-          <td>11</td>
-          <td>72</td>
-        </tr>
-    
-        <tr id="High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete and noisy. Deep-learning approaches have been shown suitable for such super-resolution tasks. However, a high number of high-resolution examples is needed, which may not be available for many cases. Moreover, the obtained predictions may lack in complying with the physical principles, e.g. mass and momentum conservation. Physics-informed deep learning provides frameworks for integrating data and physical laws for learning. In this study, we apply physics-informed neural networks (PINNs) for super-resolution of flow-field data both in time and space from a limited set of noisy measurements without having any high-resolution reference data. Our objective is to obtain a continuous solution of the problem, providing a physically-consistent prediction at any point in the solution domain. We demonstrate the applicability of PINNs for the super-resolution of flow-field data in time and space through three canonical cases: Burgers’ equation, two-dimensional vortex shedding behind a circular cylinder and the minimal turbulent channel flow. The robustness of the models is also investigated by adding synthetic Gaussian noise. Furthermore, we show the capabilities of PINNs to improve the resolution and reduce the noise in a real experimental dataset consisting of hot-wire-anemometry measurements. Our results show the adequate capabilities of PINNs in the context of data augmentation for experiments in fluid mechanics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ecf61b26615fc12f9edc4826dd81a23ac0d72f37" target='_blank'>Physics-informed deep-learning applications to experimental fluid mechanics</a></td>
-          <td>
-            Hamidreza Eivazi, Yuning Wang, R. Vinuesa
-          </td>
-          <td>2022-03-29</td>
-          <td>Measurement Science and Technology</td>
-          <td>21</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/606824bebf4e444fca9b988823883f1ec99f19ec" target='_blank'>A physics-informed operator regression framework for extracting data-driven continuum models</a></td>
-          <td>
-            Ravi G. Patel, N. Trask, M. Wood, E. Cyr
-          </td>
-          <td>2020-09-25</td>
-          <td>ArXiv</td>
-          <td>84</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/138138aeee75f8f5a6f2f22575bc4d0354138e5d" target='_blank'>Data-Driven Discovery of Coarse-Grained Equations</a></td>
-          <td>
-            Joseph Bakarji, D. Tartakovsky
-          </td>
-          <td>2020-01-30</td>
-          <td>J. Comput. Phys.</td>
-          <td>31</td>
-          <td>47</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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diff --git a/docs/recommendations/643ac3ef063c77eb02a3d52637c11fe028bfae28.md b/docs/recommendations/643ac3ef063c77eb02a3d52637c11fe028bfae28.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:06:25 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Discovering Symbolic Models from Deep Learning with Inductive Biases</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true force vector when trained on n-body gravitational and spring-like simulations. We use symbolic regression to fit explicit algebraic equations to our trained model's message function and recover the symbolic form of Newton's law of gravitation without prior knowledge. We also show that our model generalizes better at inference time to systems with more bodies than had been experienced during training. Our approach is extensible, in principle, to any unknown interaction law learned by a graph network, and offers a valuable technique for interpreting and inferring explicit causal theories about the world from implicit knowledge captured by deep learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a6aad9ccdcb7674a3b7ab710f0a80d205834f847" target='_blank'>Learning Symbolic Physics with Graph Networks</a></td>
-          <td>
-            M. Cranmer, Rui Xu, P. Battaglia, S. Ho
-          </td>
-          <td>2019-09-12</td>
-          <td>ArXiv</td>
-          <td>77</td>
-          <td>68</td>
-        </tr>
-    
-        <tr id="Symbolic regression (SR) is the study of algorithms that automate the search for analytic expressions that fit data. While recent advances in deep learning have generated renewed interest in such approaches, the development of SR methods has not been focused on physics, where we have important additional constraints due to the units associated with our data. Here we present Φ-SO, a physical symbolic optimization framework for recovering analytical symbolic expressions from physics data using deep reinforcement learning techniques by learning units constraints. Our system is built, from the ground up, to propose solutions where the physical units are consistent by construction. This is useful not only in eliminating physically impossible solutions but also because the grammatical rules of dimensional analysis enormously restrict the freedom of the equation generator, thus vastly improving performance. The algorithm can be used to fit noiseless data, which can be useful, for instance, when attempting to derive an analytical property of a physical model, and it can also be used to obtain analytical approximations of noisy data. We test our machinery on a standard benchmark of equations from the Feynman Lectures on Physics and other physics textbooks, achieving state-of-the-art performance in the presence of noise (exceeding 0.1%) and show that it is robust even in the presence of substantial (10%) noise. We showcase its abilities on a panel of examples from astrophysics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0597e979716c2488f82e607fbf4fae37d14b8a30" target='_blank'>Deep Symbolic Regression for Physics Guided by Units Constraints: Toward the Automated Discovery of Physical Laws</a></td>
-          <td>
-            Wassim Tenachi, R. Ibata, F. Diakogiannis
-          </td>
-          <td>2023-03-06</td>
-          <td>The Astrophysical Journal</td>
-          <td>32</td>
-          <td>70</td>
-        </tr>
-    
-        <tr id="We consider the problem of learning free-form symbolic expressions from raw data, such as that produced by an experiment in any scientific domain. Accurate and interpretable models of scientific phenomena are the cornerstone of scientific research. Simple yet interpretable models, such as linear or logistic regression and decision trees often lack predictive accuracy. Alternatively, accurate blackbox models such as deep neural networks provide high predictive accuracy, but do not readily admit human understanding in a way that would enrich the scientific theory of the phenomenon. Many great breakthroughs in science revolve around the development of parsimonious equational models with high predictive accuracy, such as Newton's laws, universal gravitation, and Maxwell's equations. Previous work on automating the search of equational models from data combine domain-specific heuristics as well as computationally expensive techniques, such as genetic programming and Monte-Carlo search. We develop a deep neural network (MACSYMA) to address the symbolic regression problem as an end-to-end supervised learning problem. MACSYMA can generate symbolic expressions that describe a dataset. The computational complexity of the task is reduced to the feedforward computation of a neural network. We train our neural network on a synthetic dataset consisting of data tables of varying length and varying levels of noise, for which the neural network must learn to produce the correct symbolic expression token by token. Finally, we validate our technique by running on a public dataset from behavioral science.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7b039955d66e0cfd5b217f7fd8338ea0cf02cc29" target='_blank'>Accelerating Understanding of Scientific Experiments with End to End Symbolic Regression</a></td>
-          <td>
-            N. Aréchiga, Francine Chen, Yan-Ying Chen, Yanxia Zhang, Rumen Iliev, Heishiro Toyoda, Kent Lyons
-          </td>
-          <td>2021-12-07</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>16</td>
-        </tr>
-    
-        <tr id="While physics conveys knowledge of nature built from an interplay between observations and theory, it has been considered less importantly in deep neural networks. Especially, there are few works leveraging physics behaviors when the knowledge is given less explicitly. In this work, we propose a novel architecture called Differentiable Physics-informed Graph Networks (DPGN) to incorporate implicit physics knowledge which is given from domain experts by informing it in latent space. Using the concept of DPGN, we demonstrate that climate prediction tasks are significantly improved. Besides the experiment results, we validate the effectiveness of the proposed module and provide further applications of DPGN, such as inductive learning and multistep predictions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/820d3142ceec2ddb57e3f117610873454d0b4540" target='_blank'>Differentiable Physics-informed Graph Networks</a></td>
-          <td>
-            Sungyong Seo, Yan Liu
-          </td>
-          <td>2019-02-08</td>
-          <td>ArXiv</td>
-          <td>63</td>
-          <td>13</td>
-        </tr>
-    
-        <tr id="We present an approach for using machine learning to automatically discover the governing equations and unknown properties (in this case, masses) of real physical systems from observations. We train a ‘graph neural network’ to simulate the dynamics of our Solar System’s Sun, planets, and large moons from 30 years of trajectory data. We then use symbolic regression to correctly infer an analytical expression for the force law implicitly learned by the neural network, which our results showed is equivalent to Newton’s law of gravitation. The key assumptions our method makes are translational and rotational equivariance, and Newton’s second and third laws of motion. It did not, however, require any assumptions about the masses of planets and moons or physical constants, but nonetheless, they, too, were accurately inferred with our method. Naturally, the classical law of gravitation has been known since Isaac Newton, but our results demonstrate that our method can discover unknown laws and hidden properties from observed data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2232751169e57a14723bfffb4ab26aa0e0e3839a" target='_blank'>Rediscovering orbital mechanics with machine learning</a></td>
-          <td>
-            P. Lemos, N. Jeffrey, M. Cranmer, S. Ho, P. Battaglia
-          </td>
-          <td>2022-02-04</td>
-          <td>Machine Learning: Science and Technology</td>
-          <td>55</td>
-          <td>46</td>
-        </tr>
-    
-        <tr id="Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent deep generative SR methods have shown promising results. However, these methods face difficulties in processing high-dimensional problems and learning constants due to the large search space, and they don't scale well to unseen problems. In this work, we propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR. Instead of searching for expressions within a large search space, we explore symbolic networks with various structures, guided by reinforcement learning, and optimize them to identify expressions that better-fitting the data. Based on extensive numerical experiments on low-dimensional public standard benchmarks and the well-known SRBench with more variables, DySymNet shows clear superiority over several representative baseline models. Open source code is available at https://github.com/AILWQ/DySymNet.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/96558b4ff44919fc1b09d51bdcb9f469f0c768ad" target='_blank'>A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Data</a></td>
-          <td>
-            Wenqiang Li, Weijun Li, Lina Yu, Min Wu, Jingyi Liu, Yanjie Li
-          </td>
-          <td>2023-09-24</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>20</td>
-        </tr>
-    
-        <tr id="Despite the success of neural networks at solving concrete physics problems, their use as a general-purpose tool for scientific discovery is still in its infancy. Here, we approach this problem by modeling a neural network architecture after the human physical reasoning process, which has similarities to representation learning. This allows us to make progress towards the long-term goal of machine-assisted scientific discovery from experimental data without making prior assumptions about the system. We apply this method to toy examples and show that the network finds the physically relevant parameters, exploits conservation laws to make predictions, and can help to gain conceptual insights, e.g., Copernicus' conclusion that the solar system is heliocentric.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7b2e20a3cdf96fc0bcddf6bd6576e5d5e09f17ec" target='_blank'>Discovering physical concepts with neural networks</a></td>
-          <td>
-            Raban Iten, Tony Metger, H. Wilming, L. D. Rio, R. Renner
-          </td>
-          <td>2018-07-27</td>
-          <td>Physical review letters</td>
-          <td>355</td>
-          <td>69</td>
-        </tr>
-    
-        <tr id="Symbolic regression (SR) aims to discover concise closed-form mathematical equations from data, a task fundamental to scientific discovery. However, the problem is highly challenging because closed-form equations lie in a complex combinatorial search space. Existing methods, ranging from heuristic search to reinforcement learning, fail to scale with the number of input variables. We make the observation that closed-form equations often have structural characteristics and invariances (e.g., the commutative law) that could be further exploited to build more effective symbolic regression solutions. Motivated by this observation, our key contribution is to leverage pre-trained deep generative models to capture the intrinsic regularities of equations, thereby providing a solid foundation for subsequent optimization steps. We show that our novel formalism unifies several prominent approaches of symbolic regression and offers a new perspective to justify and improve on the previous ad hoc designs, such as the usage of cross-entropy loss during pre-training. Specifically, we propose an instantiation of our framework, Deep Generative Symbolic Regression (DGSR). In our experiments, we show that DGSR achieves a higher recovery rate of true equations in the setting of a larger number of input variables, and it is more computationally efficient at inference time than state-of-the-art RL symbolic regression solutions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cda10f395932f2d16ce925d3d91dc4368416a656" target='_blank'>Deep Generative Symbolic Regression</a></td>
-          <td>
-            Samuel Holt, Zhaozhi Qian, M. Schaar
-          </td>
-          <td>2023-12-30</td>
-          <td>ArXiv</td>
-          <td>16</td>
-          <td>64</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
-
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diff --git a/docs/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37.md b/docs/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37.md
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-  <i class="footer">This page was last updated on 2024-08-08 13:16:54 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Self-Supervised Contrastive Pre-Training For Time Series via Time-Frequency Consistency</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
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-  <tbody>
-    
-        <tr id="Medical time series are sequential data collected over time that measures health-related signals, such as electroencephalography (EEG), electrocardiography (ECG), and intensive care unit (ICU) readings. Analyzing medical time series and identifying the latent patterns and trends that lead to uncovering highly valuable insights for enhancing diagnosis, treatment, risk assessment, and disease progression. However, data mining in medical time series is heavily limited by the sample annotation which is time-consuming and labor-intensive, and expert-depending. To mitigate this challenge, the emerging self-supervised contrastive learning, which has shown great success since 2020, is a promising solution. Contrastive learning aims to learn representative embeddings by contrasting positive and negative samples without the requirement for explicit labels. Here, we conducted a systematic review of how contrastive learning alleviates the label scarcity in medical time series based on PRISMA standards. We searched the studies in five scientific databases (IEEE, ACM, Scopus, Google Scholar, and PubMed) and retrieved 1908 papers based on the inclusion criteria. After applying excluding criteria, and screening at title, abstract, and full text levels, we carefully reviewed 43 papers in this area. Specifically, this paper outlines the pipeline of contrastive learning, including pre-training, fine-tuning, and testing. We provide a comprehensive summary of the various augmentations applied to medical time series data, the architectures of pre-training encoders, the types of fine-tuning classifiers and clusters, and the popular contrastive loss functions. Moreover, we present an overview of the different data types used in medical time series, highlight the medical applications of interest, and provide a comprehensive table of 51 public datasets that have been utilized in this field. In addition, this paper will provide a discussion on the promising future scopes such as providing guidance for effective augmentation design, developing a unified framework for analyzing hierarchical time series, and investigating methods for processing multimodal data. Despite being in its early stages, self-supervised contrastive learning has shown great potential in overcoming the need for expert-created annotations in the research of medical time series.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5db7888e68bb23fe1db8d8c434b5d7de543a1f0c" target='_blank'>Self-Supervised Contrastive Learning for Medical Time Series: A Systematic Review</a></td>
-          <td>
-            Ziyu Liu, A. Alavi, Minyi Li, X. Zhang
-          </td>
-          <td>2023-04-23</td>
-          <td>Sensors (Basel, Switzerland)</td>
-          <td>20</td>
-          <td>77</td>
-        </tr>
-    
-        <tr id="Time series is a typical data type in numerous domains; however, labeling large amounts of time series data can be costly and time-consuming. Learning effective representation from unlabeled time series data is a challenging task. Contrastive learning stands out as a promising method to acquire representations of unlabeled time series data. Therefore, we propose a self-supervised time-series representation learning framework via Time-Frequency Fusion Contrasting (TF-FC) to learn time-series representation from unlabeled data. Specifically, TF-FC combines time-domain augmentation with frequency-domain augmentation to generate the diverse samples. For time-domain augmentation, the raw time series data pass through the time-domain augmentation bank (such as jitter, scaling, permutation, and masking) and get time-domain augmentation data. For frequency-domain augmentation, first, the raw time series undergoes conversion into frequency domain data following Fast Fourier Transform (FFT) analysis. Then, the frequency data passes through the frequency-domain augmentation bank (such as low pass filter, remove frequency, add frequency, and phase shift) and gets frequency-domain augmentation data. The fusion method of time-domain augmentation data and frequency-domain augmentation data is kernel PCA, which is useful for extracting nonlinear features in high-dimensional spaces. By capturing both the time and frequency domains of the time series, the proposed approach is able to extract more informative features from the data, enhancing the model's capacity to distinguish between different time series. To verify the effectiveness of the TF-FC method, we conducted experiments on four time series domain datasets (i.e., SleepEEG, HAR, Gesture, and Epilepsy). Experimental results show that TF-FC significantly improves in recognition accuracy compared with other SOTA methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/51190de29ec8ff369f3082560caa7c46fc2885b5" target='_blank'>Time-series representation learning via Time-Frequency Fusion Contrasting</a></td>
-          <td>
-            Wenbo Zhao, Ling Fan
-          </td>
-          <td>2024-06-12</td>
-          <td>Frontiers in Artificial Intelligence</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Limited availability of labeled physiological data often prohibits the use of powerful supervised deep learning models in the biomedical machine intelligence domain. We approach this problem and propose a novel encoding framework that relies on self-supervised learning with momentum contrast to learn representations from multivariate time-series of various physiological domains without needing labels. Our model uses a transformer architecture that can be easily adapted to classification problems by optimizing a linear output classification layer. We experimentally evaluate our framework using two publicly available physiological datasets from different domains, i.e., human activity recognition from embedded inertial sensory and emotion recognition from electroencephalography. We show that our self-supervised learning approach can indeed learn discriminative features which can be exploited in downstream classification tasks. Our work enables the development of domain-agnostic intelligent systems that can effectively analyze multivariate time-series data from physiological domains.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6095c33f35505cca934e44c0f50bcac52135c299" target='_blank'>TS-MoCo: Time-Series Momentum Contrast for Self-Supervised Physiological Representation Learning</a></td>
-          <td>
-            Philipp Hallgarten, David Bethge, Ozan Özdenizci, T. Große-Puppendahl, Enkelejda Kasneci
-          </td>
-          <td>2023-06-10</td>
-          <td>2023 31st European Signal Processing Conference (EUSIPCO)</td>
-          <td>0</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="Significant progress has been made in representation learning, especially with recent success on self-supervised contrastive learning. However, for time series with less intuitive or semantic meaning, sampling bias may be inevitably encountered in unsupervised approaches. Although supervised contrastive learning has shown superior performance by leveraging label information, it may also suffer from class collapse. In this study, we consider a realistic scenario in industry with limited annotation information available. A supervised contrastive framework is developed for high-frequency time series representation and classification, wherein a novel variant of supervised contrastive loss is proposed to include multiple augmentations while induce spread within each class. Experiments on four mainstream public datasets as well as a series of sensitivity and ablation analyses demonstrate that the learned representations are effective and robust compared with the direct supervised learning and self-supervised learning, notably under the minimal few-shot situation.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a2056f5affe509b50e41612057ca9cca143ef97a" target='_blank'>Supervised Contrastive Few-Shot Learning for High-Frequency Time Series</a></td>
-          <td>
-            X. Chen, Cheng Ge, Mingxing Wang, Jin Wang
-          </td>
-          <td>2023-06-26</td>
-          <td>DBLP</td>
-          <td>2</td>
-          <td>139</td>
-        </tr>
-    
-        <tr id="Contrastive representation learning is crucial in medical time series analysis as it alleviates dependency on labor-intensive, domain-specific, and scarce expert annotations. However, existing contrastive learning methods primarily focus on one single data level, which fails to fully exploit the intricate nature of medical time series. To address this issue, we present COMET, an innovative hierarchical framework that leverages data consistencies at all inherent levels in medical time series. Our meticulously designed model systematically captures data consistency from four potential levels: observation, sample, trial, and patient levels. By developing contrastive loss at multiple levels, we can learn effective representations that preserve comprehensive data consistency, maximizing information utilization in a self-supervised manner. We conduct experiments in the challenging patient-independent setting. We compare COMET against six baselines using three diverse datasets, which include ECG signals for myocardial infarction and EEG signals for Alzheimer's and Parkinson's diseases. The results demonstrate that COMET consistently outperforms all baselines, particularly in setup with 10% and 1% labeled data fractions across all datasets. These results underscore the significant impact of our framework in advancing contrastive representation learning techniques for medical time series. The source code is available at https://github.com/DL4mHealth/COMET.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9331fe5ae1d8c16a36037dd0f0378ccac7d5f230" target='_blank'>Contrast Everything: A Hierarchical Contrastive Framework for Medical Time-Series</a></td>
-          <td>
-            Yihe Wang, Yu Han, Haishuai Wang, Xiang Zhang
-          </td>
-          <td>2023-10-21</td>
-          <td>ArXiv</td>
-          <td>18</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Unsupervised domain adaptation (UDA) provides a strategy for improving machine learning performance in data-rich (target) domains where ground truth labels are inaccessible but can be found in related (source) domains. In cases where meta-domain information such as label distributions is available, weak supervision can further boost performance. We propose a novel framework, CALDA, to tackle these two problems. CALDA synergistically combines the principles of contrastive learning and adversarial learning to robustly support multi-source UDA (MS-UDA) for time series data. Similar to prior methods, CALDA utilizes adversarial learning to align source and target feature representations. Unlike prior approaches, CALDA additionally leverages cross-source label information across domains. CALDA pulls examples with the same label close to each other, while pushing apart examples with different labels, reshaping the space through contrastive learning. Unlike prior contrastive adaptation methods, CALDA requires neither data augmentation nor pseudo labeling, which may be more challenging for time series. We empirically validate our proposed approach. Based on results from human activity recognition, electromyography, and synthetic datasets, we find utilizing cross-source information improves performance over prior time series and contrastive methods. Weak supervision further improves performance, even in the presence of noise, allowing CALDA to offer generalizable strategies for MS-UDA.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/73e8e82f2ee312d71d69ca48af933817eb4758c7" target='_blank'>CALDA: Improving Multi-Source Time Series Domain Adaptation With Contrastive Adversarial Learning</a></td>
-          <td>
-            Garrett Wilson, J. Doppa, D. Cook
-          </td>
-          <td>2021-09-30</td>
-          <td>IEEE Transactions on Pattern Analysis and Machine Intelligence</td>
-          <td>14</td>
-          <td>72</td>
-        </tr>
-    
-        <tr id="To improve the accuracy of clinical multivariate time series (MTS) classification (such as EEG and ECG) by a novel self-supervised paradigm that directly captures the dynamics between the different time series learned together to optimize the classification task. Labels in clinical datasets are very often insufficient. One way to address this challenge is leveraging self-supervision. This paradigm attempts to identify a supervisory signal inherent within a dataset to serve as a surrogate label. We present a novel form of self-supervision: dynamics of clinical MTS. Unlike other self-supervision methods, such as masking, that are intuitive but still heuristic, we suggest to learn a representation justified by Koopman theory. The latter was shown useful for representing clinical time series and can be used as a form of surrogate task to improve the clinical MTS classification. In the ECG task, we show that our proposed framework achieved higher sensitivity and specificity than the state-of-the-art (SOTA) baseline over numerous common diagnoses. For EEG abnormality classification, our proposed framework also achieved higher sensitivity and specificity than the SOTA baseline. All results are statistically significant. Our technique yields reliable clinical diagnosis in an empirical study employing signals from thousands of patients in multiple clinical tasks employing two types of clinical-grade sensors (ECG and EEG) as compared to the state-of-the-art machine learning. Leveraging time-series-dynamics self-supervision can help mitigate the lack of labels in clinical datasets used for training machine learning algorithms and significantly improve their performance. Specifically, the ECG system presented in this work is being trialed in hospitals, used by top cardiologists for patient diagnosis and treatment. We believe that the deployment of such cutting-edge technology will significantly improve the accuracy and speed of cardiac assessments.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/de72c6226ecbc7150dc3e634ca983d001808e6b0" target='_blank'>Self-supervised Classification of Clinical Multivariate Time Series using Time Series Dynamics</a></td>
-          <td>
-            Yakir Yehuda, Daniel Freedman, Kira Radinsky
-          </td>
-          <td>2023-08-04</td>
-          <td>Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining</td>
-          <td>0</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="Monitoring and recognizing patterns in continuous sensing data is crucial for many practical applications. These real-world time-series data are often nonstationary, characterized by varying statistical and spectral properties over time. This poses a significant challenge in developing learning models that can effectively generalize across different distributions. In this work, based on our observation that nonstationary statistics are intrinsically linked to the phase information, we propose a time-series learning framework, PhASER. It consists of three novel elements: 1) phase augmentation that diversifies non-stationarity while preserving discriminatory semantics, 2) separate feature encoding by viewing time-varying magnitude and phase as independent modalities, and 3) feature broadcasting by incorporating phase with a novel residual connection for inherent regularization to enhance distribution invariant learning. Upon extensive evaluation on 5 datasets from human activity recognition, sleep-stage classification, and gesture recognition against 10 state-of-the-art baseline methods, we demonstrate that PhASER consistently outperforms the best baselines by an average of 5% and up to 13% in some cases. Moreover, PhASER's principles can be applied broadly to boost the generalization ability of existing time series classification models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8afaf2f41bc85fd8c0413754fa9ccc2b1e9303d5" target='_blank'>Phase-driven Domain Generalizable Learning for Nonstationary Time Series</a></td>
-          <td>
-            Payal Mohapatra, Lixu Wang, Qi Zhu
-          </td>
-          <td>2024-02-05</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="Recent contrastive methods show significant improvement in self-supervised learning in several domains. In particular, contrastive methods are most effective where data augmentation can be easily constructed e.g. in computer vision. However, they are less successful in domains without established data transformations such as time series data. In this paper, we propose a novel self-supervised learning framework that combines contrastive learning with neural processes. It relies on recent advances in neural processes to perform time series forecasting. This allows to generate augmented versions of data by employing a set of various sampling functions and, hence, avoid manually designed augmentations. We extend conventional neural processes and propose a new contrastive loss to learn times series representations in a self-supervised setup. Therefore, unlike previous self-supervised methods, our augmentation pipeline is task-agnostic, enabling our method to perform well across various applications. In particular, a ResNet with a linear classifier trained using our approach is able to outperform state-of-the-art techniques across industrial, medical and audio datasets improving accuracy over 10% in ECG periodic data. We further demonstrate that our self-supervised representations are more efficient in the latent space, improving multiple clustering indexes and that fine-tuning our method on 10% of labels achieves results competitive to fully-supervised learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3f20f3b72be3b57f375bc5116a34f750554ec2a2" target='_blank'>Contrastive Neural Processes for Self-Supervised Learning</a></td>
-          <td>
-            Konstantinos Kallidromitis, Denis A. Gudovskiy, Kozuka Kazuki, Ohama Iku, Luca Rigazio
-          </td>
-          <td>2021-10-24</td>
-          <td>ArXiv, DBLP</td>
-          <td>10</td>
-          <td>13</td>
-        </tr>
-    
-        <tr id="Learning representations from unlabeled time series data is a challenging problem. Most existing self-supervised and unsupervised approaches in the time-series domain fall short in capturing low-and high-frequency features at the same time. As a result, the generalization ability of the learned representations remains limited. Furthermore, some of these methods employ large-scale models like transformers or rely on computationally expensive techniques such as contrastive learning. To tackle these problems, we propose a noncontrastive self-supervised learning (SSL) approach that efficiently captures low-and high-frequency features in a cost-effective manner. The proposed framework comprises a Siamese configuration of a deep neural network with two weight-sharing branches which are followed by low-and high-frequency feature extraction modules. The two branches of the proposed network allow bootstrapping of the latent representation by taking two different augmented views of raw time series data as input. The augmented views are created by applying random transformations sampled from a single set of augmentations. The low-and high-frequency feature extraction modules of the proposed network contain a combination of multilayer perceptron (MLP) and temporal convolutional network (TCN) heads, respectively, which capture the temporal dependencies from the raw input data at various scales due to the varying receptive fields. To demonstrate the robustness of our model, we performed extensive experiments and ablation studies on five real-world time-series datasets. Our method achieves state-of-art performance on all the considered datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4b65c76f7f28e7ba3ea44ebb1b3e4355a148d0de" target='_blank'>Large Scale Time-Series Representation Learning via Simultaneous Low and High Frequency Feature Bootstrapping</a></td>
-          <td>
-            Vandan Gorade, Azad Singh, Deepak Mishra
-          </td>
-          <td>2022-04-24</td>
-          <td>IEEE transactions on neural networks and learning systems</td>
-          <td>4</td>
-          <td>5</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/68b6ca45a588d538b36335b23f6969c960cf2e6e.md b/docs/recommendations/68b6ca45a588d538b36335b23f6969c960cf2e6e.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:07:15 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Modern Koopman Theory for Dynamical Systems</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/75407116e515533f3cb11b6de14449f2933638ed" target='_blank'>Estimating Koopman operators for nonlinear dynamical systems: a nonparametric approach</a></td>
-          <td>
-            Francesco Zanini, A. Chiuso
-          </td>
-          <td>2021-03-25</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0f4b3d72f08bfadc076617850cc8a5e9395738d6" target='_blank'>Koopman Operator Dynamical Models: Learning, Analysis and Control</a></td>
-          <td>
-            Petar Bevanda, Stefan Sosnowski, S. Hirche
-          </td>
-          <td>2021-02-04</td>
-          <td>ArXiv</td>
-          <td>88</td>
-          <td>47</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3ea99ee3b9d78f3a81076b19637bae9a53236cb0" target='_blank'>Data-Driven Approximations of Dynamical Systems Operators for Control</a></td>
-          <td>
-            E. Kaiser, J. Kutz, S. Brunton
-          </td>
-          <td>2019-02-26</td>
-          <td>Lecture Notes in Control and Information Sciences</td>
-          <td>37</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often need to prepare nonlinear observables manually according to the underlying dynamics, which is not always possible since we may not have any a priori knowledge about them. In this paper, we propose a fully data-driven method for Koopman spectral analysis based on the principle of learning Koopman invariant subspaces from observed data. To this end, we propose minimization of the residual sum of squares of linear least-squares regression to estimate a set of functions that transforms data into a form in which the linear regression fits well. We introduce an implementation with neural networks and evaluate performance empirically using nonlinear dynamical systems and applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/49ee811e5c7af5980d3dfe791f6b18e0080ad566" target='_blank'>Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition</a></td>
-          <td>
-            Naoya Takeishi, Y. Kawahara, T. Yairi
-          </td>
-          <td>2017-10-12</td>
-          <td>ArXiv</td>
-          <td>326</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning for widely used dynamic mode decomposition algorithms. While such methods have proven to be remarkably useful in the analysis of time-series data, the resulting linear models must generally be of high order to accurately approximate fundamentally nonlinear behaviors. This issue poses an inherent risk of overfitting to training data thereby limiting predictive capabilities. By contrast, this work explores strategies for nonlinear data-driven estimation of the action of the Koopman operator. General strategies that yield nonlinear models are presented for systems both with and without control. Subsequent projection of the resulting nonlinear equations onto a low-rank basis yields a low order representation for the underlying dynamical system. In both computational and experimental examples considered in this work, linear estimators of the Koopman operator are generally only able to provide short-term predictions for the observable dynamics while comparable nonlinear estimators provide accurate predictions on substantially longer timescales and replicate infinite-time behaviors that linear predictors cannot.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1cda473dadc56234490012ec6c5679625cdfe565" target='_blank'>Nonlinear Data-Driven Approximation of the Koopman Operator</a></td>
-          <td>
-            Dan Wilson
-          </td>
-          <td>2022-10-10</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>19</td>
-        </tr>
-    
-        <tr id="Koopman operators are infinite‐dimensional operators that globally linearize nonlinear dynamical systems, making their spectral information valuable for understanding dynamics. However, Koopman operators can have continuous spectra and infinite‐dimensional invariant subspaces, making computing their spectral information a considerable challenge. This paper describes data‐driven algorithms with rigorous convergence guarantees for computing spectral information of Koopman operators from trajectory data. We introduce residual dynamic mode decomposition (ResDMD), which provides the first scheme for computing the spectra and pseudospectra of general Koopman operators from snapshot data without spectral pollution. Using the resolvent operator and ResDMD, we compute smoothed approximations of spectral measures associated with general measure‐preserving dynamical systems. We prove explicit convergence theorems for our algorithms (including for general systems that are not measure‐preserving), which can achieve high‐order convergence even for chaotic systems when computing the density of the continuous spectrum and the discrete spectrum. Since our algorithms have error control, ResDMD allows aposteri verification of spectral quantities, Koopman mode decompositions, and learned dictionaries. We demonstrate our algorithms on the tent map, circle rotations, Gauss iterated map, nonlinear pendulum, double pendulum, and Lorenz system. Finally, we provide kernelized variants of our algorithms for dynamical systems with a high‐dimensional state space. This allows us to compute the spectral measure associated with the dynamics of a protein molecule with a 20,046‐dimensional state space and compute nonlinear Koopman modes with error bounds for turbulent flow past aerofoils with Reynolds number >105 that has a 295,122‐dimensional state space.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1aede45bbc0a7936bcd91fd55a33ddecb2b400a6" target='_blank'>Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems</a></td>
-          <td>
-            Matthew J. Colbrook, Alex Townsend
-          </td>
-          <td>2021-11-29</td>
-          <td>Communications on Pure and Applied Mathematics</td>
-          <td>42</td>
-          <td>28</td>
-        </tr>
-    
-        <tr id="Introduction The end of the 20th century and the beginning of the 21st century has seen a revolutionary increase in the availability of data. Indeed, we are in the middle of the sensing revolution, where sensing is used in the broadest meaning of data acquisition. Most of this data goes unprocessed, unanalyzed, and, consequently, unused. This causes missed opportunities, in domains of vast societal importance—">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/90edc9f58779b5a32848edd2f5a8175642351b48" target='_blank'>Koopman Operator, Geometry, and Learning of Dynamical Systems</a></td>
-          <td>
-            I. Mezić
-          </td>
-          <td>2021-08-01</td>
-          <td>Notices of the American Mathematical Society</td>
-          <td>32</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of the time evolution of observable quantities. Recent methods have aimed to approximate Koopman operators while preserving key structures. However, approximating Koopman operators typically requires a dictionary of observables to capture the system's behavior in a finite-dimensional subspace. The selection of these functions is often heuristic, may result in the loss of spectral information, and can severely complicate structure preservation. This paper introduces Multiplicative Dynamic Mode Decomposition (MultDMD), which enforces the multiplicative structure inherent in the Koopman operator within its finite-dimensional approximation. Leveraging this multiplicative property, we guide the selection of observables and define a constrained optimization problem for the matrix approximation, which can be efficiently solved. MultDMD presents a structured approach to finite-dimensional approximations and can more accurately reflect the spectral properties of the Koopman operator. We elaborate on the theoretical framework of MultDMD, detailing its formulation, optimization strategy, and convergence properties. The efficacy of MultDMD is demonstrated through several examples, including the nonlinear pendulum, the Lorenz system, and fluid dynamics data, where we demonstrate its remarkable robustness to noise.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0cc59f7258cc0c3e219e7edb0f6cbaf13b67c680" target='_blank'>Multiplicative Dynamic Mode Decomposition</a></td>
-          <td>
-            Nicolas Boull'e, Matthew J. Colbrook
-          </td>
-          <td>2024-05-08</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>16</td>
-        </tr>
-    
-        <tr id="We consider the application of Koopman theory to nonlinear partial differential equations and data-driven spatio-temporal systems. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear dynamics. If such observables can be found, then the dynamic mode decomposition (DMD) algorithm can be enacted to compute a finite-dimensional approximation of the Koopman operator, including its eigenfunctions, eigenvalues, and Koopman modes. We demonstrate simple rules of thumb for selecting a parsimonious set of observables that can greatly improve the approximation of the Koopman operator. Further, we show that the clear goal in selecting observables is to place the DMD eigenvalues on the imaginary axis, thus giving an objective function for observable selection. Judiciously chosen observables lead to physically interpretable spatio-temporal features of the complex system under consideration and provide a connection to manifold learning methods. Our method provides a valuable intermediate, yet interpretable, approximation to the Koopman operator that lies between the DMD method and the computationally intensive extended DMD (EDMD). We demonstrate the impact of observable selection, including kernel methods, and construction of the Koopman operator on several canonical nonlinear PDEs: Burgers’ equation, the nonlinear Schrödinger equation, the cubic-quintic Ginzburg-Landau equation, and a reaction-diffusion system. These examples serve to highlight the most pressing and critical challenge of Koopman theory: a principled way to select appropriate observables.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1ce0ee1c0205e37c20daf33a5ad6eed187107614" target='_blank'>Applied Koopman Theory for Partial Differential Equations and Data-Driven Modeling of Spatio-Temporal Systems</a></td>
-          <td>
-            J. Kutz, J. Proctor, S. Brunton
-          </td>
-          <td>2018-12-02</td>
-          <td>Complex.</td>
-          <td>63</td>
-          <td>63</td>
-        </tr>
-    
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-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <i class="footer">This page was last updated on 2024-07-22 06:06:59 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Systems biology informed neural networks (SBINN) predict response and novel combinations for PD-1 checkpoint blockade</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68d54a4ef82873fd3a0e857ad2c136d65fa17db8" target='_blank'>Systems biology informed neural networks (SBINN) predict response and novel combinations for PD-1 checkpoint blockade</a></td>
-          <td>
-            M. Przedborski, Munisha Smalley, S. Thiyagarajan, A. Goldman, M. Kohandel
-          </td>
-          <td>2021-07-15</td>
-          <td>Communications Biology</td>
-          <td>9</td>
-          <td>28</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f4624f66c438a80c62525b6af71f20d1edb159bd" target='_blank'>Integrating Systems Biology and an Ex Vivo Human Tumor Model Elucidates PD-1 Blockade Response Dynamics</a></td>
-          <td>
-            Munisha Smalley, Munisha Smalley, M. Przedborski, S. Thiyagarajan, Moriah Pellowe, A. Verma, N. Brijwani, Debika Datta, Misti Jain, Basavaraja U. Shanthappa, Vidushi Kapoor, K. Gopinath, D. C. Doval, K. Sabitha, G. Taroncher-Oldenburg, B. Majumder, P. Majumder, M. Kohandel, Aaron Goldman, Aaron Goldman
-          </td>
-          <td>2020-06-01</td>
-          <td>iScience</td>
-          <td>6</td>
-          <td>73</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/acdf4e69bc25f2c08197466cbe432159a3f675d2" target='_blank'>Network-based machine learning approach to predict immunotherapy response in cancer patients</a></td>
-          <td>
-            JungHo Kong, Doyeon Ha, Juhun Lee, Inhae Kim, Minhyuk Park, S. Im, Kunyoo Shin, Sanguk Kim
-          </td>
-          <td>2022-06-28</td>
-          <td>Nature Communications</td>
-          <td>65</td>
-          <td>45</td>
-        </tr>
-    
-        <tr id="3136 Background: Tremendous progress towards understanding the molecular underpinnings of cancer has ushered in an era of precision medicine, where actionable biomarkers inform rational design of novel drugs, repurposing of existing medications or new combination therapies, agnostic of tumor type. However less than 20% of cancer patients match to therapies using existing predictive biomarkers. There is therefore an acute need for new methods to expand the population of patients who could benefit from existing drugs and improve patient selection and design of clinical trials evaluating new or repurposed drugs. Methods: We developed systems biology-informed AI methods trained on vast multi-omics and multi-modal datasets from DepMap, TCGA and other publicly available sources, to uncover latent vulnerabilities existing in tumors. These vulnerabilities map to pharmacological sensitivities and can be assigned to individual patients using clinically available molecular data. To evaluate our model, we focused on predicting sensitivities to a third-generation tyrosine kinase inhibitor (TKI), which we assessed in non-small cell lung cancer (NSCLC) cell lines, patient derived xenografts (PDXs) and a clinicogenomics cohort from AACR Project GENIE (n=2004 patients, n=273 patients treated with TKI of interest). Where applicable, whole exome data used as input for validation model predictions were filtered to ~300 genes included on commercial NGS panels to reflect data available in RWD cohorts. Results: Our model accurately predicts response to the TKI across diverse cancer cell lines with high accuracy (r2= 0.768; rho= 0.83; mean absolute error = 0.065). Using NSCLC cancer cell lines and PDX model systems heterogeneous for this TKI’s current FDA molecular label (but within the scope of the drug’s current cancer indication), we were able to further validate our model’s predictions, show they were not dependent on obvious molecular confounders, and demonstrate a potential label expansion opportunity for this drug beyond the current narrow molecular label. While all NSCLC patients from AACR Project GENIE treated with this TKI were “on label”, NSCLC patients our model predicted to be sensitive to the TKI had a 4-month increased median PFS compared to patients predicted to be less sensitive (Log-rank test p-value< 0.05; HR= 1.64; 1.23-2.22, 95% CI). The PFS partition was not due to obvious clinical confounders such as stage (p= 0.91), age (p=0.86), sex (p=0.63), smoking status (p=0.57) or on-target mutations (p=0.70). Biological networks associated with each prediction provide rich context and highlight a putative rational drug combination strategy for this drug. Conclusions: We have developed an ML model that uses clinically obtainable NGS data to accurately predict increased sensitivity to a third-generation TKI validated in NSCLC cell lines, PDX models and a RWD patient cohort.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b4346310495ab63af1d7f88c90bf128d0bd32a82" target='_blank'>Use of a systems-biology informed machine learning model to predict drug response using clinically available NGS data.</a></td>
-          <td>
-            Maayan Baron, Andrey Chursov, Brandon Funkhouser, Jacob Kaffey, S. Sushanth Kumar, G. Komatsoulis, Felicia Kuperwaser, M. Ramchandran, J. Sherman, E. Vucic
-          </td>
-          <td>2023-06-01</td>
-          <td>Journal of Clinical Oncology</td>
-          <td>0</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="Cancer cells can leverage several cell-intrinsic and -extrinsic mechanisms to escape immune system recognition. The inherent complexity of the tumor microenvironment, with its multicellular and dynamic nature, poses great challenges for the extraction of biomarkers of immune response and immunotherapy efficacy. Here, we use RNA-seq data combined with different sources of prior-knowledge to derive system-based signatures of the tumor microenvironment, quantifying immune-cell composition and intra- and inter-cellular communications. We applied multi-task learning to these signatures to predict different hallmarks of immune responses and derive cancer-type-specific models based on interpretable systems biomarkers. By applying our models to independent RNA-seq data from cancer patients treated with PD-1 inhibitors, we demonstrated that our method to Estimate Systems Immune Response (EaSIeR) accurately predicts therapeutic outcome. We anticipate that EaSIeR will be a valuable tool to provide a holistic description of immune responses in complex and dynamic systems such as tumors using available RNA-seq data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6c2aaa9d42938b19deef4e268b53afddc2ccc6e8" target='_blank'>Predictive systems biomarkers of response to immune checkpoint inhibitors</a></td>
-          <td>
-            Óscar Lapuente-Santana, Maisa van Genderen, P. Hilbers, F. Finotello, Federica Eduati
-          </td>
-          <td>2021-02-07</td>
-          <td>bioRxiv</td>
-          <td>0</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="Immunotherapy and immune checkpoint blocking antibodies such as anti-PD-1 are approved and significantly improve the survival of advanced non-small cell lung cancer (NSCLC) patients, but there has been little success in identifying biomarkers capable of separating the responders from non-responders before the onset of the therapy. In this study, we developed a quantitative system pharmacology (QSP) model to represent the anti-tumor immune response in human NSCLC that integrated our knowledge of tumor growth, antigen processing and presentation, T cell activation and distribution, antibody pharmacokinetics, and immune checkpoint dynamics. The model was calibrated with the available data and was used to identify potential biomarkers as well as patient-specific response based on the patient parameters. The model predicted that in addition to tumor mutational burden (TMB), a known biomarker for anti-PD-1 therapy in NSCLC, the number of effector T cells and regulatory T cells in the tumor and blood is a predictor of the responders. Furthermore, the model simulated a set of 12 patients with known TMB and MHC/antigen-binding affinity from a recent clinical trial (ClinicalTrials.gov number, NCT02259621) on neoadjuvant nivolumab therapy in resectable lung cancer and predicted an augmented durable response in patients with adjuvant nivolumab treatment in addition to the clinical trial protocol of neoadjuvant nivolumab treatment followed by resection. Overall, the model provides a valuable framework to model tumor immunity and response to immune checkpoint blockers to enhance biomarker discovery and performing virtual clinical trials to aid in design and interpretation of the current trials with fewer patients.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e6107c61042002f08fd5b87757a1769200845b10" target='_blank'>A Computational Model of Neoadjuvant PD-1 Inhibition in Non-Small Cell Lung Cancer</a></td>
-          <td>
-            M. Jafarnejad, Chang Gong, E. Gabrielson, I. Bartelink, P. Vicini, B. Wang, R. Narwal, L. Roskos, A. Popel
-          </td>
-          <td>2019-06-24</td>
-          <td>The AAPS Journal</td>
-          <td>50</td>
-          <td>69</td>
-        </tr>
-    
-        <tr id="We present a study where predictive mechanistic modeling is used in combination with deep learning methods to predict individual patient survival probabilities under immune checkpoint inhibitor (ICI) therapy. This hybrid approach enables prediction based on both measures that are calculable from mechanistic models (but may not be directly measurable in the clinic) and easily measurable quantities or characteristics (that are not always readily incorporated into predictive mechanistic models). The mechanistic model we have applied here can predict tumor response from CT or MRI imaging based on key mechanisms underlying checkpoint inhibitor therapy, and in the present work, its parameters were combined with readily-available clinical measures from 93 patients into a hybrid training set for a deep learning time-to-event predictive model. Analysis revealed that training an artificial neural network with both mechanistic modeling-derived and clinical measures achieved higher per-patient predictive accuracy based on event-time concordance, Brier score, and negative binomial log-likelihood-based criteria than when only mechanistic model-derived values or only clinical data were used. Feature importance analysis revealed that both clinical and model-derived parameters play prominent roles in neural network decision making, and in increasing prediction accuracy, further supporting the advantage of our hybrid approach. We anticipate that many existing mechanistic models may be hybridized with deep learning methods in a similar manner to improve predictive accuracy through addition of additional data that may not be readily implemented in mechanistic descriptions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d7b3da8173ee0e944bcc41b5f5c4c90ff6088d34" target='_blank'>Hybridizing mechanistic mathematical modeling with deep learning methods to predict individual cancer patient survival after immune checkpoint inhibitor therapy</a></td>
-          <td>
-            J. D. Butner, P. Dogra, Caroline Chung, Eugene J Koay, James Welsh, David Hong, Vittorio Cristini, Zhihui Wang
-          </td>
-          <td>2024-03-29</td>
-          <td>Research Square</td>
-          <td>0</td>
-          <td>16</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/73679d28d06ad0d4ebed1bb9857e3cbc975de458" target='_blank'>Biology-aware mutation-based deep learning for outcome prediction of cancer immunotherapy with immune checkpoint inhibitors</a></td>
-          <td>
-            Junyan Liu, Md Tauhidul Islam, Shengtian Sang, Liang Qiu, Lei Xing
-          </td>
-          <td>2023-11-06</td>
-          <td>NPJ Precision Oncology</td>
-          <td>0</td>
-          <td>16</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/44c74be92bfee5ad8a4f41543b36dd3d2c83e2bf" target='_blank'>Interpretable predictions of cellular behavior</a></td>
-          <td>
-            Ananya Rastogi
-          </td>
-          <td>2021-03-01</td>
-          <td>Nature Computational Science</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Abstract Understanding the intricate interactions of cancer cells with the tumor microenvironment (TME) is a pre-requisite for the optimization of immunotherapy. Mechanistic models such as quantitative systems pharmacology (QSP) provide insights into the TME dynamics and predict the efficacy of immunotherapy in virtual patient populations/digital twins but require vast amounts of multimodal data for parameterization. Large-scale datasets characterizing the TME are available due to recent advances in bioinformatics for multi-omics data. Here, we discuss the perspectives of leveraging omics-derived bioinformatics estimates to inform QSP models and circumvent the challenges of model calibration and validation in immuno-oncology.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/771e6ee84353828e640c230c07c64013c8803ab5" target='_blank'>Leveraging multi-omics data to empower quantitative systems pharmacology in immuno-oncology</a></td>
-          <td>
-            Theinmozhi Arulraj, Hanwen Wang, Alberto Ippolito, Shuming Zhang, E. Fertig, Aleksander S. Popel
-          </td>
-          <td>2024-03-27</td>
-          <td>Briefings in Bioinformatics</td>
-          <td>1</td>
-          <td>43</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/6adeda1af8abc6bc3c17c0b39f635a845476cd9f.md b/docs/recommendations/6adeda1af8abc6bc3c17c0b39f635a845476cd9f.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:07:13 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Deep learning for universal linear embeddings of nonlinear dynamics</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where the dynamics of the underlying phenomenon can be described by a linear operator, based on the Koopman operator theory. However, despite being able to provide reliable long-term predictions for some dynamical systems in ideal situations, the methods proposed so far have limitations, such as requiring to discretize intrinsically continuous dynamical systems, leading to data loss, especially when handling incomplete or sparsely sampled data. Here, we propose a new deep Koopman framework that represents dynamics in an intrinsically continuous way, leading to better performance on limited training data, as exemplified on several datasets arising from dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5605d94c26994720fa032f1e9ff32423d9dcf51d" target='_blank'>Leveraging Neural Koopman Operators to Learn Continuous Representations of Dynamical Systems from Scarce Data</a></td>
-          <td>
-            Anthony Frion, Lucas Drumetz, M. Mura, G. Tochon, Abdeldjalil Aissa El Bey
-          </td>
-          <td>2023-03-13</td>
-          <td>ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</td>
-          <td>4</td>
-          <td>34</td>
-        </tr>
-    
-        <tr id="The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches that formulate models in operator theoretic or probabilistic frameworks. Koopman spectral theory has emerged as a dominant perspective over the past decade, in which nonlinear dynamics are represented in terms of an infinite-dimensional linear operator acting on the space of all possible measurement functions of the system. This linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. However, obtaining finite-dimensional coordinate systems and embeddings in which the dynamics appear approximately linear remains a central open challenge. The success of Koopman analysis is due primarily to three key factors: 1) there exists rigorous theory connecting it to classical geometric approaches for dynamical systems, 2) the approach is formulated in terms of measurements, making it ideal for leveraging big-data and machine learning techniques, and 3) simple, yet powerful numerical algorithms, such as the dynamic mode decomposition (DMD), have been developed and extended to reduce Koopman theory to practice in real-world applications. In this review, we provide an overview of modern Koopman operator theory, describing recent theoretical and algorithmic developments and highlighting these methods with a diverse range of applications. We also discuss key advances and challenges in the rapidly growing field of machine learning that are likely to drive future developments and significantly transform the theoretical landscape of dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68b6ca45a588d538b36335b23f6969c960cf2e6e" target='_blank'>Modern Koopman Theory for Dynamical Systems</a></td>
-          <td>
-            S. Brunton, M. Budišić, E. Kaiser, J. Kutz
-          </td>
-          <td>2021-02-24</td>
-          <td>SIAM Rev.</td>
-          <td>273</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers a framework for global linearization for nonlinear systems, thereby allowing the usage of linear tools for design studies. In this work, we focus on the identification of global linearized embeddings for canonical nonlinear Hamiltonian systems through a symplectic transformation. While this task is often challenging, we leverage the power of deep learning to discover the desired embeddings. Furthermore, to overcome the shortcomings of Koopman operators for systems with continuous spectra, we apply the lifting principle and learn global cubicized embeddings. Additionally, a key emphasis is paid to enforce the bounded stability for the dynamics of the discovered embeddings. We demonstrate the capabilities of deep learning in acquiring compact symplectic coordinate transformation and the corresponding simple dynamical models, fostering data-driven learning of nonlinear canonical Hamiltonian systems, even those with continuous spectra.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/89d480a9bf884e736c0779a23e8e67f81c484b8e" target='_blank'>Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamics</a></td>
-          <td>
-            P. Goyal, Süleyman Yıldız, P. Benner
-          </td>
-          <td>2023-08-26</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>53</td>
-        </tr>
-    
-        <tr id="Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through the Koopman operator(KO) analysis. However, computing Koopman eigenpairs for high-dimensional observable data can be inefficient. This paper proposes using deep autoencoders(AE), a type of deep learning technique, to perform nonlinear geometric transformations on raw data before computing Koopman eigenvectors. The encoded data produced by the deep AE is diffeomorphic to a manifold of the dynamical system and has a significantly lower dimension than the raw data. To handle high-dimensional time series data, Takens' time delay embedding is presented as a preprocessing technique. The paper concludes by presenting examples of these techniques in action.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bb005a9027b08e1d2b513a9c23001bbc4c28c352" target='_blank'>Autoencoding for the 'Good Dictionary' of eigen pairs of the Koopman Operator</a></td>
-          <td>
-            Neranjaka Jayarathne, E. Bollt
-          </td>
-          <td>2023-06-08</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/000794cdc9985ec8e3008d8f4e61c56e1dc96820" target='_blank'>Deep learning for Koopman Operator Optimal Control.</a></td>
-          <td>
-            Mostafa Al‐Gabalawy
-          </td>
-          <td>2021-01-06</td>
-          <td>ISA transactions</td>
-          <td>13</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="The engineering design process often relies on mathematical modeling that can describe the underlying dynamic behavior. In this work, we present a data-driven methodology for modeling the dynamics of nonlinear systems. To simplify this task, we aim to identify a coordinate transformation that allows us to represent the dynamics of nonlinear systems using a common, simple model structure. The advantage of a common simple model is that customized design tools developed for it can be applied to study a large variety of nonlinear systems. The simplest common model -- one can think of -- is linear, but linear systems often fall short in accurately capturing the complex dynamics of nonlinear systems. In this work, we propose using quadratic systems as the common structure, inspired by the lifting principle. According to this principle, smooth nonlinear systems can be expressed as quadratic systems in suitable coordinates without approximation errors. However, finding these coordinates solely from data is challenging. Here, we leverage deep learning to identify such lifted coordinates using only data, enabling a quadratic dynamical system to describe the system's dynamics. Additionally, we discuss the asymptotic stability of these quadratic dynamical systems. We illustrate the approach using data collected from various numerical examples, demonstrating its superior performance with the existing well-known techniques.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b7dc380fa94c29c88c415c89f8170c0d653e7ca5" target='_blank'>Generalized Quadratic-Embeddings for Nonlinear Dynamics using Deep Learning</a></td>
-          <td>
-            P. Goyal, P. Benner
-          </td>
-          <td>2022-11-01</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>53</td>
-        </tr>
-    
-        <tr id="This letter presents a Koopman lifting linearization method that is applicable to nonlinear dynamical systems having both stable and unstable regions. It is known that Dynamic Mode Decomposition (DMD) and its extended methods are often unable to model unstable systems accurately and reliably. Here we solve the problem through merging three methodologies: decomposition of a lifted linear system into stable and unstable modes, deep learning of a dictionary of observable functions in the separated subspaces, and a new formula for obtaining the Koopman operator, called Direct Encoding. Two sets of effective observable functions are obtained through neural net training where the training data are separated into stable and unstable trajectories. The resultant learned observables are used for lifting the state space, and a linear state transition matrix is constructed using Direct Encoding where inner products of the learned observables are computed. The proposed method shows a dramatic improvement over existing DMD and data-driven methods. Furthermore, a method is developed for determining the boundaries between stable and unstable regions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eba28c4d66f0e67ded357875e2d04a95a5adeb39" target='_blank'>Learned Lifted Linearization Applied to Unstable Dynamic Systems Enabled by Koopman Direct Encoding</a></td>
-          <td>
-            Jerry Ng, H. Asada
-          </td>
-          <td>2022-10-24</td>
-          <td>IEEE Control Systems Letters</td>
-          <td>1</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode decomposition; this requires a combinatorially large basis set to adequately describe many nonlinear systems of interest, e.g. cyber-physical infrastructure systems, biological networks, social systems, and fluid dynamics. Often the dictionaries generated for these problems are manually curated, requiring domain-specific knowledge and painstaking tuning. In this paper we introduce a computational framework for learning Koopman operators of nonlinear dynamical systems using deep learning. We show that this novel method automatically selects efficient deep dictionaries, requiring much lower dimensional dictionaries while outperforming state-of-the-art methods. We benchmark this method on partially observed nonlinear systems, including the glycolytic oscillator and show it is able to predict on test data quantitatively 100 steps into the future, using only a single timepoint as an initial condition, and quantitative oscillatory behavior 400 steps into the future.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a02e0608b79a4b3670324839160073a8f49d77f9" target='_blank'>Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems</a></td>
-          <td>
-            Enoch Yeung, Soumya Kundu, Nathan Oken Hodas
-          </td>
-          <td>2017-08-22</td>
-          <td>2019 American Control Conference (ACC)</td>
-          <td>326</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="We present DLKoopman -- a software package for Koopman theory that uses deep learning to learn an encoding of a nonlinear dynamical system into a linear space, while simultaneously learning the linear dynamics. While several previous efforts have either restricted the ability to learn encodings, or been bespoke efforts designed for specific systems, DLKoopman is a generalized tool that can be applied to data-driven learning and optimization of any dynamical system. It can either be trained on data from individual states (snapshots) of a system and used to predict its unknown states, or trained on data from trajectories of a system and used to predict unknown trajectories for new initial states. DLKoopman is available on the Python Package Index (PyPI) as 'dlkoopman', and includes extensive documentation and tutorials. Additional contributions of the package include a novel metric called Average Normalized Absolute Error for evaluating performance, and a ready-to-use hyperparameter search module for improving performance.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9e4566a8c46f18398a26546ebc874d6f571c55a4" target='_blank'>DLKoopman: A deep learning software package for Koopman theory</a></td>
-          <td>
-            Sourya Dey, Eric K. Davis
-          </td>
-          <td>2022-11-15</td>
-          <td>ArXiv, DBLP</td>
-          <td>2</td>
-          <td>6</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/6bd28606fbae3449f831248804264c9885e992f9.md b/docs/recommendations/6bd28606fbae3449f831248804264c9885e992f9.md
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-    Recommendations for the article <i>CellBox: Interpretable Machine Learning for Perturbation Biology with Application to the Design of Cancer Combination Therapy.</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
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-    
-        <tr id="Systematic perturbation of cells followed by comprehensive measurements of molecular and phenotypic responses provides an informative data resource for constructing computational models of cell biology. Models that generalize well beyond training data can be used to identify combinatorial perturbations of potential therapeutic interest. Major challenges for machine learning on large biological datasets are to find global optima in an enormously complex multi-dimensional solution space and to mechanistically interpret the solutions. To address these challenges, we introduce a hybrid approach that combines explicit mathematical models of dynamic cell biological processes with a machine learning framework, implemented in Tensorflow. We tested the modelling framework on a perturbation-response dataset for a melanoma cell line after drug treatments. The models can be efficiently trained to accurately describe cellular behavior, as tested by cross-validation. Even though completely data-driven and independent of prior knowledge, the resulting de novo network models recapitulate known interactions. The main predictive application is the identification of combinatorial candidates for cancer therapy. The approach is readily applicable to a wide range of kinetic models of cell biology.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/250017f99bdff84eb0a2ac65698224b4abe7c8a4" target='_blank'>Interpretable Machine Learning for Perturbation Biology</a></td>
-          <td>
-            Bo Yuan, Ciyue Shen, Augustin Luna, Anil Korkut, D. Marks, John Ingraham, C. Sander
-          </td>
-          <td>2019-08-28</td>
-          <td>bioRxiv</td>
-          <td>6</td>
-          <td>153</td>
-        </tr>
-    
-        <tr id="Systematic perturbation of cells followed by comprehensive measurements of molecular and phenotypic responses provides an informative data resource for constructing computational models of cell biology. Models that generalize well beyond training data can be used to identify combinatorial perturbations of potential therapeutic interest. Major challenges for machine learning on large biological datasets are to find global optima in an enormously complex multi-dimensional solution space and to mechanistically interpret the solutions. To address these challenges, we introduce a hybrid approach that combines explicit mathematical models of dynamic cell biological processes with a machine learning framework, implemented in Tensorflow. We tested the modeling framework on a perturbation-response dataset for a melanoma cell line after drug treatments. The models can be efficiently trained to accurately describe cellular behavior, as tested by cross-validation. Even though completely data-driven and independent of prior knowledge, the resulting de novo network models recapitulate known interactions. The main predictive application of our work is the identification of combinatorial candidates for cancer therapy. This approach is readily applicable to a wide range of kinetic models of cell biology. Citation Format: Judy Shen, Bo Yuan, Augustin Luna, Anil Korkut, Debora Marks, John Ingraham, Chris Sander. Interpretable machine learning for perturbation biology [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 2102.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e6f21c31f5c969c279bb555f1dff954d04e64763" target='_blank'>Abstract 2102: Interpretable machine learning for perturbation biology</a></td>
-          <td>
-            Judy Shen, Bo Yuan, Augustin Luna, Anil Korkut, D. Marks, John Ingraham, C. Sander
-          </td>
-          <td>2020-08-13</td>
-          <td>Clinical Research (Excluding Clinical Trials)</td>
-          <td>0</td>
-          <td>153</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/44c74be92bfee5ad8a4f41543b36dd3d2c83e2bf" target='_blank'>Interpretable predictions of cellular behavior</a></td>
-          <td>
-            Ananya Rastogi
-          </td>
-          <td>2021-03-01</td>
-          <td>Nature Computational Science</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="We present a powerful experimental-computational technology for inferring network models that predict the response of cells to perturbations, and that may be useful in the design of combinatorial therapy against cancer. The experiments are systematic series of perturbations of cancer cell lines by targeted drugs, singly or in combination. The response to perturbation is quantified in terms of relative changes in the measured levels of proteins, phospho-proteins and cellular phenotypes such as viability. Computational network models are derived de novo, i.e., without prior knowledge of signaling pathways, and are based on simple non-linear differential equations. The prohibitively large solution space of all possible network models is explored efficiently using a probabilistic algorithm, Belief Propagation (BP), which is three orders of magnitude faster than standard Monte Carlo methods. Explicit executable models are derived for a set of perturbation experiments in SKMEL-133 melanoma cell lines, which are resistant to the therapeutically important inhibitor of RAF kinase. The resulting network models reproduce and extend known pathway biology. They empower potential discoveries of new molecular interactions and predict efficacious novel drug perturbations, such as the inhibition of PLK1, which is verified experimentally. This technology is suitable for application to larger systems in diverse areas of molecular biology.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1e881a1d1a8c8f35ba366d63693c2ac0094344e4" target='_blank'>Perturbation Biology: Inferring Signaling Networks in Cellular Systems</a></td>
-          <td>
-            Evan J. Molinelli, Anil Korkut, Weiqing Wang, Martin L. Miller, N. Gauthier, Xiaohong Jing, Poorvi Kaushik, Qin He, Gordon Mills, D. Solit, C. Pratilas, M. Weigt, A. Braunstein, A. Pagnani, R. Zecchina, C. Sander
-          </td>
-          <td>2013-08-23</td>
-          <td>PLoS Computational Biology</td>
-          <td>130</td>
-          <td>153</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/489d291fe97c3be2453f795365b1fe447d6e0896" target='_blank'>A gray box framework that optimizes a white box logical model using a black box optimizer for simulating cellular responses to perturbations</a></td>
-          <td>
-            Yunseong Kim, Y. Han, Corbin Hopper, Jonghoon Lee, J. Joo, Jeong-Ryeol Gong, Chun-Kyung Lee, Seong-Hoon Jang, Junsoo Kang, Taeyoung Kim, Kwang-Hyun Cho
-          </td>
-          <td>2024-05-01</td>
-          <td>Cell Reports Methods</td>
-          <td>0</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="Data-driven mathematical modeling of biological systems has enormous potential to understand and predict the interplay between molecular and phenotypic response to perturbation, and provides a rational approach to the nomination of therapies in complex diseases such as cancer. Melanoma is a particularly debilitating disease for which most therapies eventually fail as resistance to chemotherapy and targeted drugs develop. We have previously applied an iterative experimental-computational modeling approach, termed perturbation biology, to predict and test effective drug combinations in melanoma cell lines [1]. In this work, we extend our analysis framework to derive models of temporally-acquired perturbation data that do not require prior knowledge and explicit specification of the targets of individual drugs. Specifically, we characterize the response of the melanoma cell line A2058 to 54 cancer drug combinations at 8 logarithmically spaced time points from 10 minutes to 67 hours. At each time point, 124 antibodies of proteins and phospho-proteins with broad coverage of cancer-related pathways and two phenotypes (cell number and apoptosis) were measured. These data are used to infer interactions in ordinary differential equation-based models that capture temporal aspects of the drug perturbation data. This network representation of drug–protein, protein–protein, and protein–phenotype interactions can be used to identify new logical (not necessarily direct biochemical) interactions. The agreement between the predicted phenotypic response and corresponding data for unseen drug perturbations has a Pearson’s correlation coefficient of 0.79. We further use model predictions to nominate effective combination therapies and perform experimental validation of the highest ranked combinations. This new data-driven modeling framework is a step forward in perturbation biology as it incorporates the temporal aspect of data. This work therefore opens the door to a new understanding of dynamic drug responses at a molecular level.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/14c762a67f5a9622f2d23ad99cb08992af10b2d5" target='_blank'>Perturbation biology links temporal protein changes to drug responses in a melanoma cell line</a></td>
-          <td>
-            Elin Nyman, R. Stein, Xiaohong Jing, Weiqing Wang, Benjamin Marks, I. Zervantonakis, Anil Korkut, N. Gauthier, C. Sander
-          </td>
-          <td>2019-03-06</td>
-          <td>PLoS Computational Biology</td>
-          <td>12</td>
-          <td>153</td>
-        </tr>
-    
-        <tr id="In cell line perturbation experiments, a collection of cells is perturbed with external agents (e.g. drugs) and responses such as protein expression measured. Due to cost constraints, only a small fraction of all possible perturbations can be tested in vitro. This has led to the development of computational (in silico) models which can predict cellular responses to perturbations. Perturbations with clinically interesting predicted responses can be prioritized for in vitro testing. In this work, we compare causal and non-causal regression models for perturbation response prediction in a Melanoma cancer cell line. The current best performing method on this data set is Cellbox which models how proteins causally effect each other using a system of ordinary differential equations (ODEs). We derive a closed form solution to the Cellbox system of ODEs in the linear case. These analytic results facilitate comparison of Cellbox to regression approaches. We show that causal models such as Cellbox, while requiring more assumptions, enable extrapolation in ways that non-causal regression models cannot. For example, causal models can predict responses for never before tested drugs. We illustrate these strengths and weaknesses in simulations. In an application to the Melanoma cell line data, we find that regression models outperform the Cellbox causal model.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fbff9ee6f0bdabf0ef4cd37032398f2655399604" target='_blank'>Causal Models, Prediction, and Extrapolation in Cell Line Perturbation Experiments</a></td>
-          <td>
-            J. Long, Yumeng Yang, K. Do
-          </td>
-          <td>2022-07-20</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Phenotype-based screening has attracted much attention for identifying cell-active compounds. Transcriptional and proteomic profiles of cell population or single cells are informative phenotypic measures of cellular responses to perturbations. In this paper, we proposed a deep learning framework based on encoder-decoder architecture that maps the initial cellular states to a latent space, in which we assume the effects of drug perturbation on cellular states follow linear additivity. Next, we introduced the cycle consistency constraints to enforce that initial cellular state subjected to drug perturbations would produce the perturbed cellular responses, and, conversely, removal of drug perturbation from the perturbed cellular states would restore the initial cellular states. The cycle consistency constraints and linear modeling in latent space enable to learn interpretable and transferable drug perturbation representations, so that our model can predict cellular response to unseen drugs. We validated our model on three different types of datasets, including bulk transcriptional responses, bulk proteomic responses, and single-cell transcriptional responses to drug perturbations. The experimental results show that our model achieves better performance than existing state-of-the-art methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/219ca99cb481dd119358086b5ced78904cf72071" target='_blank'>Interpretable Modeling of Single-cell perturbation Responses to Novel Drugs Using Cycle Consistence Learning</a></td>
-          <td>
-            Wei Huang, Aichun Zhu, Hui Liu
-          </td>
-          <td>2023-11-17</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="Abstract Summary Phenotype-based drug screening emerges as a powerful approach for identifying compounds that actively interact with cells. Transcriptional and proteomic profiling of cell lines and individual cells provide insights into the cellular state alterations that occur at the molecular level in response to external perturbations, such as drugs or genetic manipulations. In this paper, we propose cycleCDR, a novel deep learning framework to predict cellular response to external perturbations. We leverage the autoencoder to map the unperturbed cellular states to a latent space, in which we postulate the effects of drug perturbations on cellular states follow a linear additive model. Next, we introduce the cycle consistency constraints to ensure that unperturbed cellular state subjected to drug perturbation in the latent space would produces the perturbed cellular state through the decoder. Conversely, removal of perturbations from the perturbed cellular states can restore the unperturbed cellular state. The cycle consistency constraints and linear modeling in the latent space enable to learn transferable representations of external perturbations, so that our model can generalize well to unseen drugs during training stage. We validate our model on four different types of datasets, including bulk transcriptional responses, bulk proteomic responses, and single-cell transcriptional responses to drug/gene perturbations. The experimental results demonstrate that our model consistently outperforms existing state-of-the-art methods, indicating our method is highly versatile and applicable to a wide range of scenarios. Availability and implementation The source code is available at: https://github.com/hliulab/cycleCDR.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f1c2b23f3deb29435692d8627c8b4e0b406ec968" target='_blank'>Predicting single-cell cellular responses to perturbations using cycle consistency learning</a></td>
-          <td>
-            Wei Huang, Hui Liu
-          </td>
-          <td>2024-06-28</td>
-          <td>Bioinformatics</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="MOTIVATION
-Predicting trajectories of signaling networks under complex perturbations is one of the most valuable, but challenging, tasks in systems biology. Signaling networks are involved in most of the biological pathways, and modeling their dynamics has wide applications including drug design and treatment outcome prediction.
-
-
-RESULTS
-In this paper, we report a novel model for predicting the cell type-specific time course response of signaling proteins under unseen perturbations. This algorithm achieved the top performance in the 2013 8th Dialogue for Reverse Engineering Assessments and Methods (DREAM 8) subchallenge: time course prediction in breast cancer cell lines. We formulate the trajectory prediction problem into a standard regularization problem; the solution becomes solving this discrete ill-posed problem. This algorithm includes three steps: denoising, estimating regression coefficients and modeling trajectories under unseen perturbations. We further validated the accuracy of this method against simulation and experimental data. Furthermore, this method reduces computational time by magnitudes compared to state-of-the-art methods, allowing genome-wide modeling of signaling pathways and time course trajectories to be carried out in a practical time.
-
-
-AVAILABILITY AND IMPLEMENTATION
-Source code is available at http://guanlab.ccmb.med.umich.edu/DREAM/code.html and as supplementary file online.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/39f3131ed92cb56b1c5af701ea805e6fd9bbe339" target='_blank'>Predicting dynamic signaling network response under unseen perturbations</a></td>
-          <td>
-            Fan Zhu, Y. Guan
-          </td>
-          <td>2014-10-01</td>
-          <td>Bioinformatics</td>
-          <td>15</td>
-          <td>38</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Learning Discrepancy Models From Experimental Data</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
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-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4cb7ffb5dfa4330c7fcc70afce6f8129c1699c42" target='_blank'>Sparse identification of Lagrangian for nonlinear dynamical systems via proximal gradient method</a></td>
-          <td>
-            Adam Purnomo, M. Hayashibe
-          </td>
-          <td>2022-09-04</td>
-          <td>Scientific Reports</td>
-          <td>2</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="Data-driven modeling frameworks that adopt sparse regression techniques, such as sparse identification of nonlinear dynamics (SINDy) and its modifications, are developed to resolve difficulties in extracting underlying dynamics from experimental data. In contrast to neural-network-based methods, these methods are designed to obtain white-box analytical models. In this work, we incorporate the concept of SINDy and knowledge in the field of classical mechanics to identify interpretable and sparse expressions of total energy and the Lagrangian that shelters the hidden dynamics. Moreover, our method (hereafter referred as Lagrangian-SINDy) is developed to use knowledge of simple systems that form the system being analyzed to ensure the likelihood of correct results and to improve the learning pace. Lagrangian-SINDy is highly accurate in discovering interpretable dynamics via energy-related physical quantities. Its performance is validated with three popular multi-DOF nonlinear dynamical systems, namely the spherical pendulum, double pendulum and cart-pendulum system. Comparisons with other SINDy-based methods are made and Lagrangian-SINDy is found to provide the most compact analytical models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7d7e107bcb40ed9596642ff12cc60f33f3eb47e2" target='_blank'>Discovering Interpretable Dynamics by Sparsity Promotion on Energy and the Lagrangian</a></td>
-          <td>
-            H. Chu, M. Hayashibe
-          </td>
-          <td>2020-01-31</td>
-          <td>IEEE Robotics and Automation Letters</td>
-          <td>23</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/99877062e70fae24c531d58aa880fa443ec10c9b" target='_blank'>SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study</a></td>
-          <td>
-            Aurelio Raffa Ugolini, Valentina Breschi, Andrea Manzoni, M. Tanelli
-          </td>
-          <td>2024-03-01</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="In this thesis, we draw inspiration from both classical system identification and modern machine learning in order to solve estimation problems for real-world, physical systems. The main approach to estimation and learning adopted is optimization based. Concepts such as regularization will be utilized for encoding of prior knowledge and basis-function expansions will be used to add nonlinear modeling power while keeping data requirements practical. The thesis covers a wide range of applications, many inspired by applications within robotics, but also extending outside this already wide field. Usage of the proposed methods and algorithms are in many cases illustrated in the real-world applications that motivated the research. Topics covered include dynamics modeling and estimation, model-based reinforcement learning, spectral estimation, friction modeling and state estimation and calibration in robotic machining. In the work on modeling and identification of dynamics, we develop regularization strategies that allow us to incorporate prior domain knowledge into flexible, overparameterized models. We make use of classical control theory to gain insight into training and regularization while using flexible tools from modern deep learning. A particular focus of the work is to allow use of modern methods in scenarios where gathering data is associated with a high cost. In the robotics-inspired parts of the thesis, we develop methods that are practically motivated and ensure that they are implementable also outside the research setting. We demonstrate this by performing experiments in realistic settings and providing open-source implementations of all proposed methods and algorithms.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8eeb63862b519544040b709740df7d93773a7d84" target='_blank'>Machine Learning and System Identification for Estimation in Physical Systems</a></td>
-          <td>
-            Fredrik Bagge Carlson
-          </td>
-          <td>2018-12-20</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>8</td>
-        </tr>
-    
-        <tr id="In control design most control strategies are model-based and require accurate models to be applied successfully. Due to simplifications and the model-reality-gap physics-derived models frequently exhibit deviations from real-world-systems. Likewise, purely data-driven methods often do not generalise well enough and may violate physical laws. Recently Physics-Guided Neural Networks (PGNN) and physics-inspired loss functions separately have shown promising results to conquer these drawbacks. In this contribution we extend existing methods towards the identification of non-autonomous systems and propose a combined approach PGNN-L, which uses a PGNN and a physics-inspired loss term (-L) to successfully identify the system's dynamics, while maintaining the consistency with physical laws. The proposed method is demonstrated on two real-world nonlinear systems and outperforms existing techniques regarding complexity and reliability.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/63d38b16f00d3103741b6dc3c4361488f48eaeed" target='_blank'>Composed Physics- and Data-driven System Identification for Non-autonomous Systems in Control Engineering</a></td>
-          <td>
-            Ricarda-Samantha Götte, Julia Timmermann
-          </td>
-          <td>2021-12-15</td>
-          <td>2022 3rd International Conference on Artificial Intelligence, Robotics and Control (AIRC)</td>
-          <td>3</td>
-          <td>5</td>
-        </tr>
-    
-        <tr id="Data-driven discovery of dynamics via machine learning is pushing the frontiers of modelling and control efforts, providing a tremendous opportunity to extend the reach of model predictive control (MPC). However, many leading methods in machine learning, such as neural networks (NN), require large volumes of training data, may not be interpretable, do not easily include known constraints and symmetries, and may not generalize beyond the attractor where models are trained. These factors limit their use for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics. In this work, we extend the recent sparse identification of nonlinear dynamics (SINDY) modelling procedure to include the effects of actuation and demonstrate the ability of these models to enhance the performance of MPC, based on limited, noisy data. SINDY models are parsimonious, identifying the fewest terms in the model needed to explain the data, making them interpretable and generalizable. We show that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than NN models, making it viable for online training and execution in response to rapid system changes. SINDY-MPC also shows improved performance over linear data-driven models, although linear models may provide a stopgap until enough data is available for SINDY. SINDY-MPC is demonstrated on a variety of dynamical systems with different challenges, including the chaotic Lorenz system, a simple model for flight control of an F8 aircraft, and an HIV model incorporating drug treatment.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b2eb064f432557c59ce99834d7dc7817e4687271" target='_blank'>Sparse identification of nonlinear dynamics for model predictive control in the low-data limit</a></td>
-          <td>
-            E. Kaiser, J. Kutz, S. Brunton
-          </td>
-          <td>2017-11-15</td>
-          <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>425</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/acd85b948087067938680356a0cb7597de12a25d" target='_blank'>Data-based modeling and control of nonlinear process systems using sparse identification: An overview of recent results</a></td>
-          <td>
-            Fahim Abdullah, P. Christofides
-          </td>
-          <td>2023-03-01</td>
-          <td>Comput. Chem. Eng.</td>
-          <td>12</td>
-          <td>75</td>
-        </tr>
-    
-        <tr id="Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov–Zhabotinsky (BZ) reaction.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4971f9abd024e40fbbdff2e9492745b68a6bca01" target='_blank'>SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics</a></td>
-          <td>
-            Kadierdan Kaheman, J. Kutz, S. Brunton
-          </td>
-          <td>2020-04-05</td>
-          <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>190</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide finite sample error bounds of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems, such as upper bounds on noise levels and model difference, is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f22b5a826ef61edb741f547b6e73999476cd695d" target='_blank'>Learning Dynamical Systems by Leveraging Data from Similar Systems</a></td>
-          <td>
-            Lei Xin, Lintao Ye, G. Chiu, S. Sundaram
-          </td>
-          <td>2023-02-08</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>36</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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diff --git a/docs/recommendations/80744010d90c8ede052c7ac6ba8c38c9de959c6e.md b/docs/recommendations/80744010d90c8ede052c7ac6ba8c38c9de959c6e.md
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator.</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
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-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
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-  <tbody>
-    
-        <tr id="The Koopman operator provides a powerful framework for data-driven analysis of dynamical systems. In the last few years, a wealth of numerical methods providing finite-dimensional approximations of the operator have been proposed [e.g., extended dynamic mode decomposition (EDMD) and its variants]. While convergence results for EDMD require an infinite number of dictionary elements, recent studies have shown that only a few dictionary elements can yield an efficient approximation of the Koopman operator, provided that they are well-chosen through a proper training process. However, this training process typically relies on nonlinear optimization techniques. In this paper, we propose two novel methods based on a reservoir computer to train the dictionary. These methods rely solely on linear convex optimization. We illustrate the efficiency of the method with several numerical examples in the context of data reconstruction, prediction, and computation of the Koopman operator spectrum. These results pave the way for the use of the reservoir computer in the Koopman operator framework.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d99279af5ea33ac16ec90a1d2480089d0af44faa" target='_blank'>Two methods to approximate the Koopman operator with a reservoir computer.</a></td>
-          <td>
-            Marvyn Gulina, A. Mauroy
-          </td>
-          <td>2020-08-24</td>
-          <td>Chaos</td>
-          <td>9</td>
-          <td>15</td>
-        </tr>
-    
-        <tr id="Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with the nonlinear phenomena, have been rapidly developing by incorporating machine learning methods. Neural ordinary differential equations (NODEs), which are a neural network equipped with a continuum of layers, and have high parameter and memory efficiencies, have been proposed. In this paper, we propose an algorithm to perform EDMD using NODEs. NODEs are used to find a parameter-efficient dictionary which provides a good finite-dimensional approximation of the Koopman operator. We show the superiority of the parameter efficiency of the proposed method through numerical experiments.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0ca5b03a2a5f4b635ebfd442eab174fe73aa034e" target='_blank'>Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations</a></td>
-          <td>
-            H. Terao, Sho Shirasaka, Hideyuki Suzuki
-          </td>
-          <td>2021-10-01</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>26</td>
-        </tr>
-    
-        <tr id="Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of the time evolution of observable quantities. Recent methods have aimed to approximate Koopman operators while preserving key structures. However, approximating Koopman operators typically requires a dictionary of observables to capture the system's behavior in a finite-dimensional subspace. The selection of these functions is often heuristic, may result in the loss of spectral information, and can severely complicate structure preservation. This paper introduces Multiplicative Dynamic Mode Decomposition (MultDMD), which enforces the multiplicative structure inherent in the Koopman operator within its finite-dimensional approximation. Leveraging this multiplicative property, we guide the selection of observables and define a constrained optimization problem for the matrix approximation, which can be efficiently solved. MultDMD presents a structured approach to finite-dimensional approximations and can more accurately reflect the spectral properties of the Koopman operator. We elaborate on the theoretical framework of MultDMD, detailing its formulation, optimization strategy, and convergence properties. The efficacy of MultDMD is demonstrated through several examples, including the nonlinear pendulum, the Lorenz system, and fluid dynamics data, where we demonstrate its remarkable robustness to noise.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0cc59f7258cc0c3e219e7edb0f6cbaf13b67c680" target='_blank'>Multiplicative Dynamic Mode Decomposition</a></td>
-          <td>
-            Nicolas Boull'e, Matthew J. Colbrook
-          </td>
-          <td>2024-05-08</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>16</td>
-        </tr>
-    
-        <tr id="Data-driven approximations of the Koopman operator are promising for predicting the time evolution of systems characterized by complex dynamics. Among these methods, the approach known as extended dynamic mode decomposition with dictionary learning (EDMD-DL) has garnered significant attention. Here, we present a modification of EDMD-DL that concurrently determines both the dictionary of observables and the corresponding approximation of the Koopman operator. This innovation leverages automatic differentiation to facilitate gradient descent computations through the pseudoinverse. We also address the performance of several alternative methodologies. We assess a "pure" Koopman approach, which involves the direct time-integration of a linear, high-dimensional system governing the dynamics within the space of observables. Additionally, we explore a modified approach where the system alternates between spaces of states and observables at each time step-this approach no longer satisfies the linearity of the true Koopman operator representation. For further comparisons, we also apply a state-space approach (neural ordinary differential equations). We consider systems encompassing two- and three-dimensional ordinary differential equation systems featuring steady, oscillatory, and chaotic attractors, as well as partial differential equations exhibiting increasingly complex and intricate behaviors. Our framework significantly outperforms EDMD-DL. Furthermore, the state-space approach offers superior performance compared to the "pure" Koopman approach where the entire time evolution occurs in the space of observables. When the temporal evolution of the Koopman approach alternates between states and observables at each time step, however, its predictions become comparable to those of the state-space approach.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1598a1165ae2a7fa531ffc54c5a0cd3a8158b6e4" target='_blank'>Enhancing Predictive Capabilities in Data-Driven Dynamical Modeling with Automatic Differentiation: Koopman and Neural ODE Approaches</a></td>
-          <td>
-            Ricardo Constante-Amores, Alec J. Linot, Michael D. Graham
-          </td>
-          <td>2023-10-10</td>
-          <td>Chaos</td>
-          <td>2</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0142e817afd03e2c5d2180e2919239a73782a6a0" target='_blank'>Extended Dynamic Mode Decomposition with Invertible Dictionary Learning</a></td>
-          <td>
-            Yuhong Jin, Lei Hou, Shun Zhong
-          </td>
-          <td>2024-02-01</td>
-          <td>Neural networks : the official journal of the International Neural Network Society</td>
-          <td>1</td>
-          <td>5</td>
-        </tr>
-    
-        <tr id="PyKoopman is a Python package for the data-driven approximation of the Koopman operator associated with a dynamical system. The Koopman operator is a principled linear embedding of nonlinear dynamics and facilitates the prediction, estimation, and control of strongly nonlinear dynamics using linear systems theory. In particular, PyKoopman provides tools for data-driven system identification for unforced and actuated systems that build on the equation-free dynamic mode decomposition (DMD) and its variants. In this work, we provide a brief description of the mathematical underpinnings of the Koopman operator, an overview and demonstration of the features implemented in PyKoopman (with code examples), practical advice for users, and a list of potential extensions to PyKoopman. Software is available at http://github.com/dynamicslab/pykoopman">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5a220582e1ff56332a3800470ffdc25f663f9030" target='_blank'>PyKoopman: A Python Package for Data-Driven Approximation of the Koopman Operator</a></td>
-          <td>
-            Shaowu Pan, E. Kaiser, Brian M. de Silva, J. Kutz, S. Brunton
-          </td>
-          <td>2023-06-22</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4815aedae0a93d8e313e2f9c3e0f266d7132161e" target='_blank'>Generalizing Dynamic Mode Decomposition: Balancing Accuracy and Expressiveness in Koopman Approximations</a></td>
-          <td>
-            Masih Haseli, Jorge Cort'es
-          </td>
-          <td>2021-08-08</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often need to prepare nonlinear observables manually according to the underlying dynamics, which is not always possible since we may not have any a priori knowledge about them. In this paper, we propose a fully data-driven method for Koopman spectral analysis based on the principle of learning Koopman invariant subspaces from observed data. To this end, we propose minimization of the residual sum of squares of linear least-squares regression to estimate a set of functions that transforms data into a form in which the linear regression fits well. We introduce an implementation with neural networks and evaluate performance empirically using nonlinear dynamical systems and applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/49ee811e5c7af5980d3dfe791f6b18e0080ad566" target='_blank'>Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition</a></td>
-          <td>
-            Naoya Takeishi, Y. Kawahara, T. Yairi
-          </td>
-          <td>2017-10-12</td>
-          <td>ArXiv</td>
-          <td>326</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . A widely used algorithm, is Extended Dynamic Mode Decomposition , where the dictionary functions are drawn from a fixed, homogeneous class of functions. Recently, deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We discover a novel class of dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. We discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as deepDMD. This mixed dictionary does so with an order of magnitude reduction in parameters, while maintaining geometric interpretability. Our results provide a hypothesis to explain the success of deep neural networks in learning numerical approximations to Koopman operators.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6eadb57b4978af7337a7ee5fdaf36a0e60505dbe" target='_blank'>Heterogeneous mixtures of dictionary functions to approximate subspace invariance in Koopman operators</a></td>
-          <td>
-            Charles A. Johnson, Shara Balakrishnan, Enoch Yeung
-          </td>
-          <td>2022-06-27</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary. In a widely used algorithm, Extended Dynamic Mode Decomposition, the dictionary functions are drawn from a fixed class of functions. Recently, deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Our results provide a hypothesis to explain the success of deep neural networks in learning numerical approximations to Koopman operators. Part 2 of this paper will extend this explanation by demonstrating the subspace invariant of heterogeneous dictionaries and presenting a head-to-head numerical comparison of deepDMD and low-parameter heterogeneous dictionary learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a3bc5cdd4c960594fe0690a326e49070938c893a" target='_blank'>Learning Invariant Subspaces of Koopman Operators-Part 1: A Methodology for Demonstrating a Dictionary's Approximate Subspace Invariance</a></td>
-          <td>
-            Charles A. Johnson, Shara Balakrishnan, Enoch Yeung
-          </td>
-          <td>2022-12-14</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>17</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
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-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We introduce the framework of continuous-depth graph neural networks (GNNs). Neural graph differential equations (Neural GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN layers, blending discrete topological structures and differential equations. The proposed framework is shown to be compatible with static GNN models and is extended to dynamic and stochastic settings through hybrid dynamical system theory. Here, Neural GDEs improve performance by exploiting the underlying dynamics geometry, further introducing the ability to accommodate irregularly sampled data. Results prove the effectiveness of the proposed models across applications, such as traffic forecasting or prediction in genetic regulatory networks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/460307e2b0582aae32a9b3c95579c55672c1d1e0" target='_blank'>Continuous-Depth Neural Models for Dynamic Graph Prediction</a></td>
-          <td>
-            Michael Poli, Stefano Massaroli, Clayton M. Rabideau, Junyoung Park, A. Yamashita, H. Asama, Jinkyoo Park
-          </td>
-          <td>2021-06-22</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>39</td>
-        </tr>
-    
-        <tr id="Modeling continuous-time dynamics constitutes a foundational challenge, and uncovering inter-component correlations within complex systems holds promise for enhancing the efficacy of dynamic modeling. The prevailing approach of integrating graph neural networks with ordinary differential equations has demonstrated promising performance. However, they disregard the crucial signed information potential on graphs, impeding their capacity to accurately capture real-world phenomena and leading to subpar outcomes. In response, we introduce a novel approach: a signed graph neural ordinary differential equation, adeptly addressing the limitations of miscapturing signed information. Our proposed solution boasts both flexibility and efficiency. To substantiate its effectiveness, we seamlessly integrate our devised strategies into three preeminent graph-based dynamic modeling frameworks: graph neural ordinary differential equations, graph neural controlled differential equations, and graph recurrent neural networks. Rigorous assessments encompass three intricate dynamic scenarios from physics and biology, as well as scrutiny across four authentic real-world traffic datasets. Remarkably outperforming the trio of baselines, empirical results underscore the substantial performance enhancements facilitated by our proposed approach. Our code can be found at https://github.com/beautyonce/SGODE.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/45ece02ea82f79c4c678c8de8e95cd0dfbe5a37d" target='_blank'>Signed Graph Neural Ordinary Differential Equation for Modeling Continuous-time Dynamics</a></td>
-          <td>
-            Lanlan Chen, K. Wu, Jian Lou, Jing Liu
-          </td>
-          <td>2023-12-18</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="Learning continuous-time dynamics on complex networks is crucial for understanding, predicting, and controlling complex systems in science and engineering. However, this task is very challenging due to the combinatorial complexities in the structures of high dimensional systems, their elusive continuous-time nonlinear dynamics, and their structural-dynamic dependencies. To address these challenges, we propose to combine Ordinary Differential Equation Systems (ODEs) and Graph Neural Networks (GNNs) to learn continuous-time dynamics on complex networks in a data-driven manner. We model differential equation systems by GNNs. Instead of mapping through a discrete number of neural layers in the forward process, we integrate GNN layers over continuous time numerically, leading to capturing continuous-time dynamics on graphs. Our model can be interpreted as a Continuous-time GNN model or a Graph Neural ODEs model. Our model can be utilized for continuous-time network dynamics prediction, structured sequence prediction (a regularly-sampled case), and node semi-supervised classification tasks (a one-snapshot case) in a unified framework. We validate our model by extensive experiments in the above three scenarios. The promising experimental results demonstrate our model's capability of jointly capturing the structure and dynamics of complex systems in a unified framework.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c2c27c1001b7cb320bf80ef3c71c4cf87b852334" target='_blank'>Neural Dynamics on Complex Networks</a></td>
-          <td>
-            Chengxi Zang, Fei Wang
-          </td>
-          <td>2019-08-18</td>
-          <td>Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining</td>
-          <td>45</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="In this paper, we extend the idea of continuous-depth models to pseudo graphs and present pseudo graph ordinary differential equations (PGODE), which are inspired by the neural ordinary differential equation (NODE) for data in the Euclidean domain. All existing graph networks have discrete depth. A pseudo graph neural network (PGNN) is used to parameterize the derivative of hidden node states, and the output states are the solution to this ordinary differential equation (ODE). A memory-efficient framework with precise gradient estimates is then proposed for free-form ODEs. We also introduce the framework of continuous–depth pseudo graph neural networks (PGNNs) on ODE by blending discrete structures and differential equations">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d187ea847836a8c7d4ee0ea72dfae3ae5431a260" target='_blank'>Pseudo-Graph Neural Networks On Ordinary Differential Equations</a></td>
-          <td>
-            Vembu B, Loghambal S
-          </td>
-          <td>2022-03-22</td>
-          <td>Journal of Computational Mathematica</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="This paper focuses on representation learning for dynamic graphs with temporal interactions. A fundamental issue is that both the graph structure and the nodes own their own dynamics, and their blending induces intractable complexity in the temporal evolution over graphs. Drawing inspiration from the recent process of physical dynamic models in deep neural networks, we propose Graph Neural Controlled Differential Equation (GN-CDE) model, a generic differential model for dynamic graphs that characterise the continuously dynamic evolution of node embedding trajectories with a neural network parameterised vector field and the derivatives of interactions w.r.t. time. Our framework exhibits several desirable characteristics, including the ability to express dynamics on evolving graphs without integration by segments, the capability to calibrate trajectories with subsequent data, and robustness to missing observations. Empirical evaluation on a range of dynamic graph representation learning tasks demonstrates the superiority of our proposed approach compared to the baselines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/58a2baecdc4e4b3f16d1899c0f1080cefe73013a" target='_blank'>Learning Dynamic Graph Embeddings with Neural Controlled Differential Equations</a></td>
-          <td>
-            Tiexin Qin, Benjamin Walker, Terry Lyons, Hongfei Yan, Hao Li
-          </td>
-          <td>2023-02-22</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>48</td>
-        </tr>
-    
-        <tr id="We propose Graph-Coupled Oscillator Networks (GraphCON), a novel framework for deep learning on graphs. It is based on discretizations of a second-order system of ordinary differential equations (ODEs), which model a network of nonlinear controlled and damped oscillators, coupled via the adjacency structure of the underlying graph. The flexibility of our framework permits any basic GNN layer (e.g. convolutional or attentional) as the coupling function, from which a multi-layer deep neural network is built up via the dynamics of the proposed ODEs. We relate the oversmoothing problem, commonly encountered in GNNs, to the stability of steady states of the underlying ODE and show that zero-Dirichlet energy steady states are not stable for our proposed ODEs. This demonstrates that the proposed framework mitigates the oversmoothing problem. Moreover, we prove that GraphCON mitigates the exploding and vanishing gradients problem to facilitate training of deep multi-layer GNNs. Finally, we show that our approach offers competitive performance with respect to the state-of-the-art on a variety of graph-based learning tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a50a2a191c98dfe045ac2139495ee80ff1338e47" target='_blank'>Graph-Coupled Oscillator Networks</a></td>
-          <td>
-            T. Konstantin Rusch, B. Chamberlain, J. Rowbottom, S. Mishra, M. Bronstein
-          </td>
-          <td>2022-02-04</td>
-          <td>ArXiv, DBLP</td>
-          <td>72</td>
-          <td>76</td>
-        </tr>
-    
-        <tr id="We introduce the FRactional-Order graph Neural Dynamical network (FROND), a new continuous graph neural network (GNN) framework. Unlike traditional continuous GNNs that rely on integer-order differential equations, FROND employs the Caputo fractional derivative to leverage the non-local properties of fractional calculus. This approach enables the capture of long-term dependencies in feature updates, moving beyond the Markovian update mechanisms in conventional integer-order models and offering enhanced capabilities in graph representation learning. We offer an interpretation of the node feature updating process in FROND from a non-Markovian random walk perspective when the feature updating is particularly governed by a diffusion process. We demonstrate analytically that oversmoothing can be mitigated in this setting. Experimentally, we validate the FROND framework by comparing the fractional adaptations of various established integer-order continuous GNNs, demonstrating their consistently improved performance and underscoring the framework's potential as an effective extension to enhance traditional continuous GNNs. The code is available at \url{https://github.com/zknus/ICLR2024-FROND}.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/900fc1f1d2b9ceeacbc92d74491b0a19c823af20" target='_blank'>Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND</a></td>
-          <td>
-            Qiyu Kang, Kai Zhao, Qinxu Ding, Feng Ji, Xuhao Li, Wenfei Liang, Yang Song, Wee Peng Tay
-          </td>
-          <td>2024-04-26</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="Graph Neural Networks (GNNs) have established themselves as the preferred methodology in a multitude of domains, ranging from computer vision to computational biology, especially in contexts where data inherently conform to graph structures. While many existing methods have endeavored to model GNNs using various techniques, a prevalent challenge they grapple with is the issue of over-smoothing. This paper presents new Graph Neural Network models that incorporate two first-order Partial Differential Equations (PDEs). These models do not increase complexity but effectively mitigate the over-smoothing problem. Our experimental findings highlight the capacity of our new PDE model to achieve comparable results with higher-order PDE models and fix the over-smoothing problem up to 64 layers. These results underscore the adaptability and versatility of GNNs, indicating that unconventional approaches can yield outcomes on par with established techniques.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/893093c71f2ae257120ae6789b3f86dc0dfeeaa1" target='_blank'>First-order PDES for Graph Neural Networks: Advection And Burgers Equation Models</a></td>
-          <td>
-            Yifan Qu, O. Krzysik, H. Sterck, Omer Ege Kara
-          </td>
-          <td>2024-04-03</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>25</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We propose a probabilistic model discovery method for identifying ordinary differential equations governing the dynamics of observed multivariate data. Our method is based on the sparse identification of nonlinear dynamics (SINDy) framework, where models are expressed as sparse linear combinations of pre-specified candidate functions. Promoting parsimony through sparsity leads to interpretable models that generalize to unknown data. Instead of targeting point estimates of the SINDy coefficients, we estimate these coefficients via sparse Bayesian inference. The resulting method, uncertainty quantification SINDy (UQ-SINDy), quantifies not only the uncertainty in the values of the SINDy coefficients due to observation errors and limited data, but also the probability of inclusion of each candidate function in the linear combination. UQ-SINDy promotes robustness against observation noise and limited data, interpretability (in terms of model selection and inclusion probabilities) and generalization capacity for out-of-sample forecast. Sparse inference for UQ-SINDy employs Markov chain Monte Carlo, and we explore two sparsifying priors: the spike and slab prior, and the regularized horseshoe prior. UQ-SINDy is shown to discover accurate models in the presence of noise and with orders-of-magnitude less data than current model discovery methods, thus providing a transformative method for real-world applications which have limited data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f49be6cd88ca6021319adb76dbb76616457e04c0" target='_blank'>Sparsifying priors for Bayesian uncertainty quantification in model discovery</a></td>
-          <td>
-            Seth M. Hirsh, D. Barajas-Solano, J. Kutz
-          </td>
-          <td>2021-07-05</td>
-          <td>Royal Society Open Science</td>
-          <td>52</td>
-          <td>31</td>
-        </tr>
-    
-        <tr id="Sparse model identification enables nonlinear dynamical system discovery from data. However, the control of false discoveries for sparse model identification is challenging, especially in the low-data and high-noise limit. In this paper, we perform a theoretical study on ensemble sparse model discovery, which shows empirical success in terms of accuracy and robustness to noise. In particular, we analyse the bootstrapping-based sequential thresholding least-squares estimator. We show that this bootstrapping-based ensembling technique can perform a provably correct variable selection procedure with an exponential convergence rate of the error rate. In addition, we show that the ensemble sparse model discovery method can perform computationally efficient uncertainty estimation, compared to expensive Bayesian uncertainty quantification methods via MCMC. We demonstrate the convergence properties and connection to uncertainty quantification in various numerical studies on synthetic sparse linear regression and sparse model discovery. The experiments on sparse linear regression support that the bootstrapping-based sequential thresholding least-squares method has better performance for sparse variable selection compared to LASSO, thresholding least-squares, and bootstrapping-based LASSO. In the sparse model discovery experiment, we show that the bootstrapping-based sequential thresholding least-squares method can provide valid uncertainty quantification, converging to a delta measure centered around the true value with increased sample sizes. Finally, we highlight the improved robustness to hyperparameter selection under shifting noise and sparsity levels of the bootstrapping-based sequential thresholding least-squares method compared to other sparse regression methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/87b249ffe98481e48db131fa5a95e654aa53c97b" target='_blank'>Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery</a></td>
-          <td>
-            Liyao (Mars) Gao, Urban Fasel, S. Brunton, J. Kutz
-          </td>
-          <td>2023-01-30</td>
-          <td>ArXiv</td>
-          <td>11</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1f18c5206491626d36c2271aaf491dbc945f6247" target='_blank'>Automatically discovering ordinary differential equations from data with sparse regression</a></td>
-          <td>
-            Kevin Egan, Weizhen Li, Rui Carvalho
-          </td>
-          <td>2024-01-09</td>
-          <td>Communications Physics</td>
-          <td>7</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov–Zhabotinsky (BZ) reaction.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4971f9abd024e40fbbdff2e9492745b68a6bca01" target='_blank'>SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics</a></td>
-          <td>
-            Kadierdan Kaheman, J. Kutz, S. Brunton
-          </td>
-          <td>2020-04-05</td>
-          <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>190</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as Lynx-Hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9a7c2ef233e227fb29637216a52b334c9eca288f" target='_blank'>Rapid Bayesian identification of sparse nonlinear dynamics from scarce and noisy data</a></td>
-          <td>
-            Lloyd Fung, Urban Fasel, M. Juniper
-          </td>
-          <td>2024-02-23</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="Significance Understanding dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled technology, including aircraft, combustion engines, satellites, and electrical power. This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. There are many critical data-driven problems, such as understanding cognition from neural recordings, inferring climate patterns, determining stability of financial markets, predicting and suppressing the spread of disease, and controlling turbulence for greener transportation and energy. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an important role in these efforts. Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5d150cec2775f9bc863760448f14104cc8f42368" target='_blank'>Discovering governing equations from data by sparse identification of nonlinear dynamical systems</a></td>
-          <td>
-            S. Brunton, J. Proctor, J. Kutz
-          </td>
-          <td>2015-09-11</td>
-          <td>Proceedings of the National Academy of Sciences</td>
-          <td>3168</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that can act as a basis for the system. In this paper, we demonstrate on real world data how the Augmented SINDy algorithm outperforms SINDy in the presence of system variable uncertainty. We then show SINDy can be further augmented to perform robustly when both kinds of uncertainty are present.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/658fb61bfa8d1910205e13b6a853cfab2be5d1bd" target='_blank'>Sparse identification of nonlinear dynamics in the presence of library and system uncertainty</a></td>
-          <td>
-            Andrew O'Brien
-          </td>
-          <td>2024-01-23</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="We consider the data-driven discovery of governing equations from time-series data in the limit of high noise. The algorithms developed describe an extensive toolkit of methods for circumventing the deleterious effects of noise in the context of the <italic>sparse identification of nonlinear dynamics</italic> (SINDy) framework. We offer two primary contributions, both focused on noisy data acquired from a system <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol x} = { \boldsymbol f} ({ \boldsymbol x})$ </tex-math></inline-formula>. First, we propose, for use in high-noise settings, an extensive toolkit of critically enabling extensions for the SINDy regression method, to progressively cull functionals from an over-complete library and yield a set of sparse equations that regress to the derivate <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol {x}}$ </tex-math></inline-formula>. This toolkit includes: (regression step) weight timepoints based on estimated noise, use ensembles to estimate coefficients, and regress using FFTs; (culling step) leverage linear dependence of functionals, and restore and protect culled functionals based on Figures of Merit (FoMs). In a novel Assessment step, we define FoMs that compare model predictions to the original time-series (i.e., <inline-formula> <tex-math notation="LaTeX">${ \boldsymbol x}(t)$ </tex-math></inline-formula> rather than <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol {x}}(t)$ </tex-math></inline-formula>). These innovations can extract sparse governing equations and coefficients from high-noise time-series data (e.g., 300% added noise). For example, it discovers the correct sparse libraries in the Lorenz system, with median coefficient estimate errors equal to 1%−3% (for 50% noise), 6%−8% (for 100% noise), and 23%−25% (for 300% noise). The enabling modules in the toolkit are combined into a single method, but the individual modules can be tactically applied in other equation discovery methods (SINDy or not) to improve results on high-noise data. Second, we propose a technique, applicable to any model discovery method based on <inline-formula> <tex-math notation="LaTeX">$\dot { \boldsymbol x} = { \boldsymbol f} ({ \boldsymbol x})$ </tex-math></inline-formula>, to assess the accuracy of a discovered model in the context of non-unique solutions due to noisy data. Currently, this non-uniqueness can obscure a discovered model’s accuracy and thus a discovery method’s effectiveness. We describe a technique that uses linear dependencies among functionals to transform a discovered model into an equivalent form that is closest to the <italic>true</italic> model, enabling more accurate assessment of a discovered model’s correctness.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a9803137946f0dc8997f23de925d5aec6e92dfb9" target='_blank'>A Toolkit for Data-Driven Discovery of Governing Equations in High-Noise Regimes</a></td>
-          <td>
-            Charles B. Delahunt, J. Kutz
-          </td>
-          <td>2021-11-08</td>
-          <td>IEEE Access</td>
-          <td>16</td>
-          <td>31</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
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-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/893768d957f8a46f0ba5bab11e5f2e2698ef1409.md b/docs/recommendations/893768d957f8a46f0ba5bab11e5f2e2698ef1409.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:07:16 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Parsimony as the ultimate regularizer for physics-informed machine learning</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Machine learning (ML) is redefining what is possible in data-intensive fields of science and engineering. However, applying ML to problems in the physical sciences comes with a unique set of challenges: scientists want physically interpretable models that can (i) generalize to predict previously unobserved behaviors, (ii) provide effective forecasting predictions (extrapolation), and (iii) be certifiable. Autonomous systems will necessarily interact with changing and uncertain environments, motivating the need for models that can accurately extrapolate based on physical principles (e.g. Newton’s universal second law for classical mechanics, $F=ma$ ). Standard ML approaches have shown impressive performance for predicting dynamics in an interpolatory regime, but the resulting models often lack interpretability and fail to generalize. We build on a sparse regression framework that discovers governing dynamical systems models from data, selecting relevant terms in the dynamics from a library of possible functions. Our critically enabling innovation introduces a relaxed version of a sparse optimization framework that allows the use of non-convex sparsity promoting regularization functions and addresses three open challenges in scientific problems and data sets: (i) robust handling of outliers and corrupt data within noisy sensor measurements, (ii) parametric dependencies in candidate library functions, and (iii) the imposition of physical constraints. By explicitly addressing these open challenges, the integrated and unified algorithm developed provides a significant advancement over current state-of-the-art sparse model discovery methods. We show that the approach discovers parsimonious dynamical models on several example systems. This flexible approach can be tailored to the unique challenges associated with a wide range of applications and data sets, providing a powerful ML-based framework for learning governing models for physical systems from data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7a752ef2c71afa4566dd038b63929e75e41ab32f" target='_blank'>A Unified Sparse Optimization Framework to Learn Parsimonious Physics-Informed Models From Data</a></td>
-          <td>
-            Kathleen P. Champion, P. Zheng, A. Aravkin, S. Brunton, J. Kutz
-          </td>
-          <td>2019-06-25</td>
-          <td>IEEE Access</td>
-          <td>94</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are first-principled, explainable, and sample-efficient. However, they often rely on strong modeling assumptions and expensive numerical integration, requiring significant computational resources and domain expertise. While deep learning (DL) provides efficient alternatives for modeling complex dynamics, they require a large amount of labeled training data. Furthermore, its predictions may disobey the governing physical laws and are difficult to interpret. Physics-guided DL aims to integrate first-principled physical knowledge into data-driven methods. It has the best of both worlds and is well equipped to better solve scientific problems. Recently, this field has gained great progress and has drawn considerable interest across discipline Here, we introduce the framework of physics-guided DL with a special emphasis on learning dynamical systems. We describe the learning pipeline and categorize state-of-the-art methods under this framework. We also offer our perspectives on the open challenges and emerging opportunities.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/60d721e89c2f9c549241a4982b77f9c752b34460" target='_blank'>Learning dynamical systems from data: An introduction to physics-guided deep learning</a></td>
-          <td>
-            Rose Yu, Rui Wang
-          </td>
-          <td>2024-06-24</td>
-          <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>1</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning-specifically deep learning-techniques have shown their capabilities in approximating dynamics from data, but a shortcoming of traditional deep learning is that there is little insight into the underlying mapping beyond its numerical output for a given input. This limits their utility in analysis beyond simple prediction. Simultaneously, a number of strategies exist which identify models based on a fixed dictionary of basis functions, but most either require some intuition or insight about the system, or are susceptible to overfitting or a lack of parsimony. Here, we present a novel approach that combines the flexibility and accuracy of deep learning approaches with the utility of symbolic solutions: a deep neural network that generates a symbolic expression for the governing equations. We first describe the architecture for our model and then show the accuracy of our algorithm across a range of classical dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eddffa1f2cf18c7ca4edbdaf01fd805f415aa4b8" target='_blank'>Symbolic regression via neural networks.</a></td>
-          <td>
-            N. Boddupalli, T. Matchen, J. Moehlis
-          </td>
-          <td>2023-08-01</td>
-          <td>Chaos</td>
-          <td>2</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This review will examine several promising avenues of PDE research that are being advanced by machine learning, including: 1) the discovery of new governing PDEs and coarse-grained approximations for complex natural and engineered systems, 2) learning effective coordinate systems and reduced-order models to make PDEs more amenable to analysis, and 3) representing solution operators and improving traditional numerical algorithms. In each of these fields, we summarize key advances, ongoing challenges, and opportunities for further development.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/036441fb7af2f04ef5ee8def7e8e0461fb9fdc66" target='_blank'>Machine Learning for Partial Differential Equations</a></td>
-          <td>
-            S. Brunton, J. Kutz
-          </td>
-          <td>2023-03-30</td>
-          <td>ArXiv</td>
-          <td>14</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation is usually computationally intensive, requiring significant computational resources and expertise, and many real-world systems do not have fully-known governing laws. While deep learning (DL) provides novel alternatives for efficiently recognizing complex patterns and emulating nonlinear dynamics, its predictions do not necessarily obey the governing laws of physical systems, nor do they generalize well across different systems. Thus, the study of physics-guided DL emerged and has gained great progress. Physics-guided DL aims to take the best from both physics-based modeling and state-of-the-art DL models to better solve scientific problems. In this paper, we provide a structured overview of existing methodologies of integrating prior physical knowledge or physics-based modeling into DL, with a special emphasis on learning dynamical systems. We also discuss the fundamental challenges and emerging opportunities in the area.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7ac3e74f927b01f2b54661b09d9014a4e3a77bf8" target='_blank'>Physics-Guided Deep Learning for Dynamical Systems: A survey</a></td>
-          <td>
-            Rui Wang
-          </td>
-          <td>2021-07-02</td>
-          <td>ArXiv</td>
-          <td>46</td>
-          <td>10</td>
-        </tr>
-    
-        <tr id="Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here consider aspects of these models relevant for their application in science and engineering. Scientific predictions generally require structured uncertainty estimates. As a first contribution, we show that basic and lightweight Bayesian deep learning techniques like the Laplace approximation can be applied to neural ODEs to yield structured and meaningful uncertainty quantification. But, in the scientific domain, available information often goes beyond raw trajectories, and also includes mechanistic knowledge, e.g., in the form of conservation laws. We explore how mechanistic knowledge and uncertainty quantification interact on two recently proposed neural ODE frameworks - symplectic neural ODEs and physical models augmented with neural ODEs. In particular, uncertainty reflects the effect of mechanistic information more directly than the predictive power of the trained model could. And vice versa, structure can improve the extrapolation abilities of neural ODEs, a fact that can be best assessed in practice through uncertainty estimates. Our experimental analysis demonstrates the effectiveness of the Laplace approach on both low dimensional ODE problems and a high dimensional partial differential equation.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bd5a854fe7f97a373a15ebf31264bb795adae877" target='_blank'>Uncertainty and Structure in Neural Ordinary Differential Equations</a></td>
-          <td>
-            Katharina Ott, Michael Tiemann, Philipp Hennig
-          </td>
-          <td>2023-05-22</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e596988b1df3a0bc78bf72c0bfdb21c85eaab6c9" target='_blank'>Physics-informed learning of governing equations from scarce data</a></td>
-          <td>
-            Zhao Chen, Yang Liu, Hao Sun
-          </td>
-          <td>2020-05-05</td>
-          <td>Nature Communications</td>
-          <td>232</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. Recent advances in sparse identification show encouraging success in distilling closed-form governing equations from data for a wide range of nonlinear dynamical systems. However, the fundamental bottleneck of this approach lies in the robustness and scalability with respect to data scarcity and noise. This work introduces a novel physics-informed deep learning framework to discover governing partial differential equations (PDEs) from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this approach seamlessly integrates the strengths of deep neural networks for rich representation learning, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the PDEs. The efficacy and robustness of this method are demonstrated on discovering a variety of PDE systems with different levels of data scarcity and noise. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e2acd4a2bc6af5deb02f542846766868e3f1b180" target='_blank'>Deep learning of physical laws from scarce data</a></td>
-          <td>
-            Zhao Chen, Yang Liu, Hao Sun
-          </td>
-          <td>2020-05-05</td>
-          <td>ArXiv</td>
-          <td>19</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="Physics-Informed Machine Learning (PIML) has gained momentum in the last 5 years with scientists and researchers aiming to utilize the benefits afforded by advances in machine learning, particularly in deep learning. With large scientific data sets with rich spatio-temporal data and high-performance computing providing large amounts of data to be inferred and interpreted, the task of PIML is to ensure that these predictions, categorizations, and inferences are enforced by, and conform to the limits imposed by physical laws. In this work a new approach to utilizing PIML is discussed that deals with the use of physics-based loss functions. While typical usage of physical equations in the loss function requires complex layers of derivatives and other functions to ensure that the known governing equation is satisfied, here we show that a similar level of enforcement can be found by implementing more simpler loss functions on specific kinds of output data. The generalizability that this approach affords is shown using examples of simple mechanical models that can be thought of as sufficiently simplified surrogate models for a wide class of problems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/28d4ee0a9db172bd2c67b3e617d4ce465c3ba46e" target='_blank'>Applying physics-based loss functions to neural networks for improved generalizability in mechanics problems</a></td>
-          <td>
-            Samuel J. Raymond, David B. Camarillo
-          </td>
-          <td>2021-04-30</td>
-          <td>ArXiv</td>
-          <td>10</td>
-          <td>30</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1a2c2bd1496da55a109939766c3ff8512b4a6851" target='_blank'>Physical laws meet machine intelligence: current developments and future directions</a></td>
-          <td>
-            T. Muther, A. K. Dahaghi, F. I. Syed, Vuong Van Pham
-          </td>
-          <td>2022-12-05</td>
-          <td>Artificial Intelligence Review</td>
-          <td>17</td>
-          <td>16</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
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-    Recommendations for the article <i>Physical Design using Differentiable Learned Simulators</i>
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-  <tbody>
-    
-        <tr id="We present a novel framework to explore neural control and design of complex fluidic systems with dynamic solid boundaries. Our system features a fast differentiable Navier-Stokes solver with solid-fluid interface handling, a low-dimensional differentiable parametric geometry representation, a control-shape co-design algorithm, and gym-like simulation environments to facilitate various fluidic control design applications. Additionally, we present a benchmark of design, control, and learning tasks on high-fidelity, high-resolution dynamic fluid environments that pose challenges for existing differentiable fluid simulators. These tasks include designing the control of artificial hearts, identifying robotic end-effector shapes, and controlling a fluid gate. By seamlessly incorporating our differentiable fluid simulator into a learning framework, we demonstrate successful design, control, and learning results that surpass gradient-free solutions in these benchmark tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/527f3a03a03d3573ea5d162c03cf4e251f6fb9bd" target='_blank'>Neural Fluidic System Design and Control with Differentiable Simulation</a></td>
-          <td>
-            Yifei Li, Yuchen Sun, Pingchuan Ma, Eftychios Sifakis, Tao Du, Bo Zhu, Wojciech Matusik
-          </td>
-          <td>2024-05-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>33</td>
-        </tr>
-    
-        <tr id="We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned interactions as edges. Compared to modeling global dynamics, GNS enables learning local interaction laws through edge messages, improving its generalization to new environments. GNS achieves over 165x speedup for granular flow prediction compared to parallel CPU numerical simulations. We propose a novel hybrid GNS/Material Point Method (MPM) to accelerate forward simulations by minimizing error on a pure surrogate model by interleaving MPM in GNS rollouts to satisfy conservation laws and minimize errors achieving 24x speedup compared to pure numerical simulations. The differentiable GNS enables solving inverse problems through automatic differentiation, identifying material parameters that result in target runout distances. We demonstrate the ability of GNS to solve inverse problems by iteratively updating the friction angle (a material property) by computing the gradient of a loss function based on the final and target runouts, thereby identifying the friction angle that best matches the observed runout. The physics-embedded and differentiable simulators open an exciting new paradigm for AI-accelerated design, control, and optimization.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/dd68409179b26b5a21c360142f5a834fa28dcaf6" target='_blank'>Accelerating Particle and Fluid Simulations with Differentiable Graph Networks for Solving Forward and Inverse Problems</a></td>
-          <td>
-            Krishna Kumar, Yonjin Choi
-          </td>
-          <td>2023-09-23</td>
-          <td>Proceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis</td>
-          <td>3</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Humans manipulate various kinds of fluids in their everyday life: creating latte art, scooping floating objects from water, rolling an ice cream cone, etc. Using robots to augment or replace human labors in these daily settings remain as a challenging task due to the multifaceted complexities of fluids. Previous research in robotic fluid manipulation mostly consider fluids governed by an ideal, Newtonian model in simple task settings (e.g., pouring). However, the vast majority of real-world fluid systems manifest their complexities in terms of the fluid's complex material behaviors and multi-component interactions, both of which were well beyond the scope of the current literature. To evaluate robot learning algorithms on understanding and interacting with such complex fluid systems, a comprehensive virtual platform with versatile simulation capabilities and well-established tasks is needed. In this work, we introduce FluidLab, a simulation environment with a diverse set of manipulation tasks involving complex fluid dynamics. These tasks address interactions between solid and fluid as well as among multiple fluids. At the heart of our platform is a fully differentiable physics simulator, FluidEngine, providing GPU-accelerated simulations and gradient calculations for various material types and their couplings. We identify several challenges for fluid manipulation learning by evaluating a set of reinforcement learning and trajectory optimization methods on our platform. To address these challenges, we propose several domain-specific optimization schemes coupled with differentiable physics, which are empirically shown to be effective in tackling optimization problems featured by fluid system's non-convex and non-smooth properties. Furthermore, we demonstrate reasonable sim-to-real transfer by deploying optimized trajectories in real-world settings.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/73003cb9f5c1b30cd495f31f70323b1b17b24ff3" target='_blank'>FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulation</a></td>
-          <td>
-            Zhou Xian, Bo Zhu, Zhenjia Xu, H. Tung, A. Torralba, Katerina Fragkiadaki, Chuang Gan
-          </td>
-          <td>2023-03-04</td>
-          <td>ArXiv</td>
-          <td>32</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="Differentiable physics enables efficient gradient-based optimizations of neural network (NN) controllers. However, existing work typically only delivers NN controllers with limited capability and generalizability. We present a practical learning framework that outputs unified NN controllers capable of tasks with significantly improved complexity and diversity. To systematically improve training robustness and efficiency, we investigated a suite of improvements over the baseline approach, including periodic activation functions, and tailored loss functions. In addition, we find our adoption of batching and an Adam optimizer effective in training complex locomotion tasks. We evaluate our framework on differentiable mass-spring and material point method (MPM) simulations, with challenging locomotion tasks and multiple robot designs. Experiments show that our learning framework, based on differentiable physics, delivers better results than reinforcement learning and converges much faster. We demonstrate that users can interactively control soft robot locomotion and switch among multiple goals with specified velocity, height, and direction instructions using a unified NN controller trained in our system. Code is available at https://github.com/erizmr/Complex-locomotion-skill-learning-via-differentiable-physics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7b520ede894490bd202f6606cfb2fcfc8b9ae9fa" target='_blank'>Complex Locomotion Skill Learning via Differentiable Physics</a></td>
-          <td>
-            Yu Fang, Jiancheng Liu, Mingrui Zhang, Jiasheng Zhang, Y. Ma, Minchen Li, Yuanming Hu, Chenfanfu Jiang, Tiantian Liu
-          </td>
-          <td>2022-06-06</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="The manifold hypothesis forms a pillar of many modern machine learning techniques. Within the context of design, it proposes that valid designs reside on low dimensional manifolds in the high dimensional design spaces. Our previous research—BézierGAN—suggests learning the low dimensional parameterization of valid airfoil designs can indeed accelerate aerodynamic optimizations. However, it incurs problems such as misalignment, long training time, and the trouble of finding the latent dimensionality. In this work we present the optimal-transport-based sibling of BézierGAN that surpass its predecessor in terms of both manifold approximating precision and learning speed, and provide methodology that helps determine the intrinsic dimension of the design manifold beforehand.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a3d57a0669fdee17dce11f890b69a802a6519612" target='_blank'>Learning Airfoil Manifolds with Optimal Transport</a></td>
-          <td>
-            Qiuyi Chen, Phillip E. Pope, M. Fuge
-          </td>
-          <td>2022-01-03</td>
-          <td>AIAA SCITECH 2022 Forum</td>
-          <td>4</td>
-          <td>20</td>
-        </tr>
-    
-        <tr id="Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ebfcbc508023b3033aa421ce7d2344a52de696f6" target='_blank'>Compositional Generative Inverse Design</a></td>
-          <td>
-            Tailin Wu, Takashi Maruyama, Long Wei, Tao Zhang, Yilun Du, Gianluca Iaccarino, J. Leskovec
-          </td>
-          <td>2024-01-24</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>134</td>
-        </tr>
-    
-        <tr id="Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for physical systems with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. Finally, we demonstrate that our method also performs well when taking discontinuous effects into account such as collisions between individual rods. A video showing dynamic results of our graph learning assisted simulations of elastic rods can be found on the project website available at this http URL .">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0bf48ff5241fcf7116db676d87d98188dfcac175" target='_blank'>Accurately Solving Physical Systems with Graph Learning</a></td>
-          <td>
-            Han Shao, Tassilo Kugelstadt, Wojciech Palubicki, Jan Bender, S. Pirk, D. Michels
-          </td>
-          <td>2020-06-06</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>27</td>
-        </tr>
-    
-        <tr id="We introduce an efficient differentiable fluid simulator that can be integrated with deep neural networks as a part of layers for learning dynamics and solving control problems. It offers the capability to handle one-way coupling of fluids with rigid objects using a variational principle that naturally enforces necessary boundary conditions at the fluid-solid interface with sub-grid details. This simulator utilizes the adjoint method to efficiently compute the gradient for multiple time steps of fluid simulation with user defined objective functions. We demonstrate the effectiveness of our method for solving inverse and control problems on fluids with one-way coupled solids. Our method outperforms the previous gradient computations, state-of-the-art derivative-free optimization, and model-free reinforcement learning techniques by at least one order of magnitude.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ccbaf40ac70e0c1812910048816b0dcd3332cd97" target='_blank'>Differentiable Fluids with Solid Coupling for Learning and Control</a></td>
-          <td>
-            Tetsuya Takahashi, Junbang Liang, Yi-Ling Qiao, M. Lin
-          </td>
-          <td>2021-05-18</td>
-          <td>DBLP</td>
-          <td>26</td>
-          <td>78</td>
-        </tr>
-    
-        <tr id="
- Humans as designers have quite versatile problem-solving strategies. Computer agents on the other hand can access large-scale computational resources to solve certain design problems. Hence, if agents can learn from human behavior, a synergetic human-agent problem-solving team can be created. This paper presents an approach to extract human design strategies and implicit rules, purely from historical human data, and use that for design generation. A two-step framework that learns to imitate human design strategies from observation is proposed and implemented. This framework makes use of deep learning constructs to learn to generate designs without any explicit information about objective and performance metrics. The framework is designed to interact with the problem through a visual interface as humans did when solving the problem. It is trained to imitate a set of human designers by observing their design state sequences without inducing problem-specific modeling bias or extra information about the problem. Furthermore, an end-to-end agent is developed that uses this deep learning framework as its core in conjunction with image processing to map pixel-to-design moves as a mechanism to generate designs. Finally, the designs generated by a computational team of these agents are then compared with actual human data for teams solving a truss design problem. Results demonstrate that these agents are able to create feasible and efficient truss designs without guidance, showing that this methodology allows agents to learn effective design strategies.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cbcefe2282397911b17949f535438314a97ec1b8" target='_blank'>Learning to design from humans: Imitating human designers through deep learning</a></td>
-          <td>
-            Ayush Raina, Christopher McComb, J. Cagan
-          </td>
-          <td>2019-07-26</td>
-          <td>ArXiv</td>
-          <td>57</td>
-          <td>50</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <i class="footer">This page was last updated on 2024-07-22 06:05:56 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>GRAND: Graph Neural Diffusion</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Graph neural networks (GNNs) are widely used in domains like social networks and biological systems. However, the locality assumption of GNNs, which limits information exchange to neighboring nodes, hampers their ability to capture long-range dependencies and global patterns in graphs. To address this, we propose a new inductive bias based on variational analysis, drawing inspiration from the Brachistochrone problem. Our framework establishes a mapping between discrete GNN models and continuous diffusion functionals. This enables the design of application-specific objective functions in the continuous domain and the construction of discrete deep models with mathematical guarantees. To tackle over-smoothing in GNNs, we analyze the existing layer-by-layer graph embedding models and identify that they are equivalent to l2-norm integral functionals of graph gradients, which cause over-smoothing. Similar to edge-preserving filters in image denoising, we introduce total variation (TV) to align the graph diffusion pattern with global community topologies. Additionally, we devise a selective mechanism to address the trade-off between model depth and over-smoothing, which can be easily integrated into existing GNNs. Furthermore, we propose a novel generative adversarial network (GAN) that predicts spreading flows in graphs through a neural transport equation. To mitigate vanishing flows, we customize the objective function to minimize transportation within each community while maximizing inter-community flows. Our GNN models achieve state-of-the-art (SOTA) performance on popular graph learning benchmarks such as Cora, Citeseer, and Pubmed.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/827643cf750b714a74ed70ac949178b7de5a30a9" target='_blank'>Re-Think and Re-Design Graph Neural Networks in Spaces of Continuous Graph Diffusion Functionals</a></td>
-          <td>
-            Tingting Dan, Jiaqi Ding, Ziquan Wei, S. Kovalsky, Minjeong Kim, Won Hwa Kim, Guorong Wu
-          </td>
-          <td>2023-07-01</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>39</td>
-        </tr>
-    
-        <tr id="Graph neural networks (GNNs) have achieved remarkable success in numerous domains. Nevertheless, many popular GNNs are known to suffer from over-smoothing. This phenomenon causes node features to become indistinguishable and hurts the classification accuracy as layer depth increases, which limits their effectiveness at capturing complex and long range graph interactions. We propose the Deep Graph Neural Diffusion (DeepGRAND), a continuous-depth graph neural network that is based on the diffusion process on graphs that theoretically alleviates the over-smoothing issue. DeepGRand pertubes the learnable graph diffusivity and re-scales the underlying diffusion equation by a data-dependent term. We empirically show that DeepGRAND mitigates the accuracy drop-off caused by over-smoothing and surpasses the best accuracy achieved by popular GNNs on various graph deep learning benchmarks. We further demonstrate the advantage of DeepGRAND over many existing graph neural networks in the low label rate regimes.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8bf72c3f66f86b56130bdeb3e7a59d8785a9081c" target='_blank'>DeepGRAND: Deep Graph Neural Diffusion</a></td>
-          <td>
-            Khang Nguyen, Hieu Nong, Khuong Nguyen, Tan M. Nguyen, Vinh Nguyen
-          </td>
-          <td>2023-10-29</td>
-          <td>2023 57th Asilomar Conference on Signals, Systems, and Computers</td>
-          <td>1</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to ensure efficient and accurate long-distance communication between nodes, as deep convolutional networks are prone to oversmoothing. In this paper, we present a novel method based on time derivative graph diffusion (TIDE) to overcome these structural limitations of the message-passing framework. Our approach allows for optimizing the spatial extent of diffusion across various tasks and network channels, thus enabling medium and long-distance communication efficiently. Furthermore, we show that our architecture design also enables local message-passing and thus inherits from the capabilities of local message-passing approaches. We show that on both widely used graph benchmarks and synthetic mesh and graph datasets, the proposed framework outperforms state-of-the-art methods by a significant margin">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/96d2ac139c1d305d597fb6533db893f2231fecc6" target='_blank'>TIDE: Time Derivative Diffusion for Deep Learning on Graphs</a></td>
-          <td>
-            Maximilian Krahn, M. Behmanesh, M. Ovsjanikov
-          </td>
-          <td>2022-12-05</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>43</td>
-        </tr>
-    
-        <tr id="Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural networks (GNNs), such as the problems of over-smoothing and bottlenecks, has been investigated but not their robustness to adversarial attacks. In this work, we explore the robustness properties of graph neural PDEs. We empirically demonstrate that graph neural PDEs are intrinsically more robust against topology perturbation as compared to other GNNs. We provide insights into this phenomenon by exploiting the stability of the heat semigroup under graph topology perturbations. We discuss various graph diffusion operators and relate them to existing graph neural PDEs. Furthermore, we propose a general graph neural PDE framework based on which a new class of robust GNNs can be defined. We verify that the new model achieves comparable state-of-the-art performance on several benchmark datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/489da8995c34704bb285d902d73c938c7bc4dd4e" target='_blank'>On the Robustness of Graph Neural Diffusion to Topology Perturbations</a></td>
-          <td>
-            Yang Song, Qiyu Kang, Sijie Wang, Zhao Kai, Wee Peng Tay
-          </td>
-          <td>2022-09-16</td>
-          <td>ArXiv</td>
-          <td>23</td>
-          <td>30</td>
-        </tr>
-    
-        <tr id="Graph neural networks (GNNs) have shown state-of-the-art performances in various applications. However, GNNs often struggle to capture long-range dependencies in graphs due to oversmoothing. In this paper, we generalize the concept of oversmoothing from undirected to directed graphs. To this aim, we extend the notion of Dirichlet energy by considering a directed symmetrically normalized Laplacian. As vanilla graph convolutional networks are prone to oversmooth, we adopt a neural graph ODE framework. Specifically, we propose fractional graph Laplacian neural ODEs, which describe non-local dynamics. We prove that our approach allows propagating information between distant nodes while maintaining a low probability of long-distance jumps. Moreover, we show that our method is more flexible with respect to the convergence of the graph's Dirichlet energy, thereby mitigating oversmoothing. We conduct extensive experiments on synthetic and real-world graphs, both directed and undirected, demonstrating our method's versatility across diverse graph homophily levels. Our code is available at https://github.com/RPaolino/fLode .">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2f2d4ce7ca8ed125e3ee5ecd97bd638eabadd2e1" target='_blank'>A Fractional Graph Laplacian Approach to Oversmoothing</a></td>
-          <td>
-            Sohir Maskey, Raffaele Paolino, Aras Bacho, Gitta Kutyniok
-          </td>
-          <td>2023-05-22</td>
-          <td>ArXiv</td>
-          <td>18</td>
-          <td>52</td>
-        </tr>
-    
-        <tr id="We propose a novel class of graph neural networks based on the discretised Beltrami flow, a non-Euclidean diffusion PDE. In our model, node features are supplemented with positional encodings derived from the graph topology and jointly evolved by the Beltrami flow, producing simultaneously continuous feature learning and topology evolution. The resulting model generalises many popular graph neural networks and achieves state-of-the-art results on several benchmarks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/af84c6db6b5c41ca628867ff4a27566e9ca3c69e" target='_blank'>Beltrami Flow and Neural Diffusion on Graphs</a></td>
-          <td>
-            B. Chamberlain, J. Rowbottom, D. Eynard, Francesco Di Giovanni, Xiaowen Dong, M. Bronstein
-          </td>
-          <td>2021-10-18</td>
-          <td>ArXiv</td>
-          <td>65</td>
-          <td>76</td>
-        </tr>
-    
-        <tr id="Implicit Graph Neural Networks (GNNs) have achieved significant success in addressing graph learning problems recently. However, poorly designed implicit GNN layers may have limited adaptability to learn graph metrics, experience over-smoothing issues, or exhibit suboptimal convergence and generalization properties, potentially hindering their practical performance. To tackle these issues, we introduce a geometric framework for designing implicit graph diffusion layers based on a parameterized graph Laplacian operator. Our framework allows learning the metrics of vertex and edge spaces, as well as the graph diffusion strength from data. We show how implicit GNN layers can be viewed as the fixed-point equation of a Dirichlet energy minimization problem and give conditions under which it may suffer from over-smoothing during training (OST) and inference (OSI). We further propose a new implicit GNN model to avoid OST and OSI. We establish that with an appropriately chosen hyperparameter greater than the largest eigenvalue of the parameterized graph Laplacian, DIGNN guarantees a unique equilibrium, quick convergence, and strong generalization bounds. Our models demonstrate better performance than most implicit and explicit GNN baselines on benchmark datasets for both node and graph classification tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8f1257580125857cf8e162546a962459d9d1bc7e" target='_blank'>Implicit Graph Neural Diffusion Networks: Convergence, Generalization, and Over-Smoothing</a></td>
-          <td>
-            Guoji Fu, Mohammed Haroon Dupty, Yanfei Dong, Lee Wee Sun
-          </td>
-          <td>2023-08-07</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="Graph Neural Networks (GNNs) have received much attention in the graph deep learning domain. However, recent research empirically and theoretically shows that deep GNNs suffer from over-fitting and over-smoothing problems. The usual solutions either cannot solve extensive runtime of deep GNNs or restrict graph convolution in the same feature space. We propose the Adaptive Graph Diffusion Networks (AGDNs) which perform multi-layer generalized graph diffusion in different feature spaces with moderate complexity and runtime. Standard graph diffusion methods combine large and dense powers of the transition matrix with predefined weighting coefficients. Instead, AGDNs combine smaller multi-hop node representations with learnable and generalized weighting coefficients. We propose two scalable mechanisms of weighting coefficients to capture multi-hop information: Hop-wise Attention (HA) and Hop-wise Convolution (HC). We evaluate AGDNs on diverse, challenging Open Graph Benchmark (OGB) datasets with semi-supervised node classification and link prediction tasks. Until the date of submission (Aug 26, 2022), AGDNs achieve top-1 performance on the ogbn-arxiv, ogbn-proteins and ogbl-ddi datasets and top-3 performance on the ogbl-citation2 dataset. On the similar Tesla V100 GPU cards, AGDNs outperform Reversible GNNs (RevGNNs) with 13% complexity and 1% training runtime of RevGNNs on the ogbn-proteins dataset. AGDNs also achieve comparable performance to SEAL with 36% training and 0.2% inference runtime of SEAL on the ogbl-citation2 dataset.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/88b13d0fc75e0ec3cee69258c218dbf737844319" target='_blank'>Adaptive Graph Diffusion Networks</a></td>
-          <td>
-            Chuxiong Sun, Jie Hu, Hongming Gu, Jinpeng Chen, Mingchuan Yang
-          </td>
-          <td>2020-12-30</td>
-          <td>ArXiv</td>
-          <td>9</td>
-          <td>12</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/979c112d5ed2f7653990a3591cdfccfad0dc27fd.md b/docs/recommendations/979c112d5ed2f7653990a3591cdfccfad0dc27fd.md
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Graph network simulators can learn discontinuous, rigid contact dynamics</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Common methods for learning robot dynamics assume motion is continuous, causing unrealistic model predictions for systems undergoing discontinuous impact and stiction behavior. In this work, we resolve this conflict with a smooth, implicit encoding of the structure inherent to contact-induced discontinuities. Our method, ContactNets, learns parameterizations of inter-body signed distance and contact-frame Jacobians, a representation that is compatible with many simulation, control, and planning environments for robotics. We furthermore circumvent the need to differentiate through stiff or non-smooth dynamics with a novel loss function inspired by the principles of complementarity and maximum dissipation. Our method can predict realistic impact, non-penetration, and stiction when trained on 60 seconds of real-world data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/13e0e335c0471e16bb92a283cfc6817f8ceda566" target='_blank'>ContactNets: Learning of Discontinuous Contact Dynamics with Smooth, Implicit Representations</a></td>
-          <td>
-            Samuel Pfrommer, Mathew Halm, Michael Posa
-          </td>
-          <td>2020-09-23</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>66</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="Learning physically structured representa-tions of dynamical systems that include contact between different objects is an important problem for learning-based approaches in robotics. Black-box neural networks can learn to approximately represent discontinuous dynamics, but they typically require large quantities of data and often suffer from patho-logical behaviour when forecasting for longer time horizons. In this work, we use connec-tions between deep neural networks and dif-ferential equations to design a family of deep network architectures for representing contact dynamics between objects. We show that these networks can learn discontinuous contact events in a data-efficient manner from noisy observations in settings that are tra-ditionally difficult for black-box approaches and recent physics inspired neural networks. Our results indicate that an idealised form of touch feedback—which is heavily relied upon by biological systems—is a key component of making this learning problem tractable. Together with the inductive biases introduced through the network architectures, our techniques enable accurate learning of contact dynamics from observations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bd42788e01e9f8c35aa45440cd7edf484fb27528" target='_blank'>Learning Contact Dynamics using Physically Structured Neural Networks</a></td>
-          <td>
-            Andreas Hochlehnert, Alexander Terenin, Steindór Sæmundsson, M. Deisenroth
-          </td>
-          <td>2021-02-22</td>
-          <td>ArXiv</td>
-          <td>14</td>
-          <td>44</td>
-        </tr>
-    
-        <tr id="Frictional contact has been extensively studied as the core underlying behavior of legged locomotion and manipulation, and its nearly-discontinuous nature makes planning and control difficult even when an accurate model of the robot is available. Here, we present empirical evidence that learning an accurate model in the first place can be confounded by contact, as modern deep learning approaches are not designed to capture this non-smoothness. We isolate the effects of contact’s non-smoothness by varying the mechanical stiffness of a compliant contact simulator. Even for a simple system, we find that stiffness alone dramatically degrades training processes, generalization, and data-efficiency. Our results raise serious questions about simulated testing environments which do not accurately reflect the stiffness of rigid robotic hardware. Significant additional investigation will be necessary to fully understand and mitigate these effects, and we suggest several avenues for future study.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bfbd66fc944115ed6c8ca8755db3daec1b7b2621" target='_blank'>Fundamental Challenges in Deep Learning for Stiff Contact Dynamics</a></td>
-          <td>
-            Mihir Parmar, Mathew Halm, Michael Posa
-          </td>
-          <td>2021-03-29</td>
-          <td>2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)</td>
-          <td>30</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or Hamiltonian dynamics into the neural network architecture. These existing approaches are based on differential equations, which do not allow discontinuity in the states and thereby limit the class of systems one can learn. However, in reality, most physical systems, such as legged robots and robotic manipulators, involve contacts and collisions, which introduce discontinuities in the states. In this paper, we introduce a differentiable contact model, which can capture contact mechanics: frictionless/frictional, as well as elastic/inelastic. This model can also accommodate inequality constraints, such as limits on the joint angles. The proposed contact model extends the scope of Lagrangian and Hamiltonian neural networks by allowing simultaneous learning of contact and system properties. We demonstrate this framework on a series of challenging 2D and 3D physical systems with different coefficients of restitution and friction. The learned dynamics can be used as a differentiable physics simulator for downstream gradient-based optimization tasks, such as planning and control.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7e1438c3b39e4a533cd2369fc181c65800979b5a" target='_blank'>Extending Lagrangian and Hamiltonian Neural Networks with Differentiable Contact Models</a></td>
-          <td>
-            Yaofeng Desmond Zhong, Biswadip Dey, Amit Chakraborty
-          </td>
-          <td>2021-02-12</td>
-          <td>ArXiv, DBLP</td>
-          <td>29</td>
-          <td>16</td>
-        </tr>
-    
-        <tr id="Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6c7dbbb11ba59c09bf73869f9fa5f73fd5d17e72" target='_blank'>Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer</a></td>
-          <td>
-            Youn-Yeol Yu, Jeongwhan Choi, Woojin Cho, Kookjin Lee, Nayong Kim, Kiseok Chang, ChangSeung Woo, Ilho Kim, Seok-Woo Lee, Joon Young Yang, S. Yoon, Noseong Park
-          </td>
-          <td>2023-12-19</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>8</td>
-        </tr>
-    
-        <tr id="Robotic manipulation can greatly benefit from the data efficiency, robustness, and predictability of model-based methods if robots can quickly generate models of novel objects they encounter. This is especially difficult when effects like complex joint friction lack clear first-principles models and are usually ignored by physics simulators. Further, numerically-stiff contact dynamics can make common model-building approaches struggle. We propose a method to simultaneously learn contact and continuous dynamics of a novel, possibly multi-link object by observing its motion through contact-rich trajectories. We formulate a system identification process with a loss that infers unmeasured contact forces, penalizing their violation of physical constraints and laws of motion given current model parameters. Our loss is unlike prediction-based losses used in differentiable simulation. Using a new dataset of real articulated object trajectories and an existing cube toss dataset, our method outperforms differentiable simulation and end-to-end alternatives with more data efficiency. See our project page for code, datasets, and media: https://sites.google.com/view/continuous-contact-nets/home">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/128550ef51c2044306d3f4a4aa9adca661837e5d" target='_blank'>Simultaneous Learning of Contact and Continuous Dynamics</a></td>
-          <td>
-            Bibit Bianchini, Mathew Halm, Michael Posa
-          </td>
-          <td>2023-10-18</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. However, they still encounter several challenges: 1) Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization and should be incorporated into the model design. Existing simulators either consider insufficient symmetry, or enforce excessive equivariance in practice when symmetry is partially broken by gravity. 2) Objects in the physical world possess diverse shapes, sizes, and properties, which should be appropriately processed by the model. To tackle these difficulties, we propose a novel backbone, Subequivariant Graph Neural Network, which 1) relaxes equivariance to subequivariance by considering external fields like gravity, where the universal approximation ability holds theoretically; 2) introduces a new subequivariant object-aware message passing for learning physical interactions between multiple objects of various shapes in the particle-based representation; 3) operates in a hierarchical fashion, allowing for modeling long-range and complex interactions. Our model achieves on average over 3% enhancement in contact prediction accuracy across 8 scenarios on Physion and 2X lower rollout MSE on RigidFall compared with state-of-the-art GNN simulators, while exhibiting strong generalization and data efficiency.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/91090894c7fda3a19000f7224349e9168f9d7d42" target='_blank'>Learning Physical Dynamics with Subequivariant Graph Neural Networks</a></td>
-          <td>
-            Jiaqi Han, Wenbing Huang, Hengbo Ma, Jiachen Li, J. Tenenbaum, Chuang Gan
-          </td>
-          <td>2022-10-13</td>
-          <td>ArXiv</td>
-          <td>21</td>
-          <td>124</td>
-        </tr>
-    
-        <tr id="Simulating rigid collisions among arbitrary shapes is notoriously difficult due to complex geometry and the strong non-linearity of the interactions. While graph neural network (GNN)-based models are effective at learning to simulate complex physical dynamics, such as fluids, cloth and articulated bodies, they have been less effective and efficient on rigid-body physics, except with very simple shapes. Existing methods that model collisions through the meshes' nodes are often inaccurate because they struggle when collisions occur on faces far from nodes. Alternative approaches that represent the geometry densely with many particles are prohibitively expensive for complex shapes. Here we introduce the Face Interaction Graph Network (FIGNet) which extends beyond GNN-based methods, and computes interactions between mesh faces, rather than nodes. Compared to learned node- and particle-based methods, FIGNet is around 4x more accurate in simulating complex shape interactions, while also 8x more computationally efficient on sparse, rigid meshes. Moreover, FIGNet can learn frictional dynamics directly from real-world data, and can be more accurate than analytical solvers given modest amounts of training data. FIGNet represents a key step forward in one of the few remaining physical domains which have seen little competition from learned simulators, and offers allied fields such as robotics, graphics and mechanical design a new tool for simulation and model-based planning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d6fdd8fc0c5fc052d040687e72638fb4297661cc" target='_blank'>Learning rigid dynamics with face interaction graph networks</a></td>
-          <td>
-            Kelsey R. Allen, Yulia Rubanova, Tatiana Lopez-Guevara, William F. Whitney, Alvaro Sanchez-Gonzalez, P. Battaglia, T. Pfaff
-          </td>
-          <td>2022-12-07</td>
-          <td>ArXiv</td>
-          <td>22</td>
-          <td>46</td>
-        </tr>
-    
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-        <th>Abstract</th>
-        <th>Title</th>
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-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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-  <tbody>
-    
-        <tr id="Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine learning approaches have demonstrated their ability to accelerate spatio-temporal predictions, although, with only moderate accuracy in comparison. Here we introduce MultiScaleGNN, a novel multi-scale graph neural network model for learning to infer unsteady continuum mechanics. MultiScaleGNN represents the physical domain as an unstructured set of nodes, and it constructs one or more graphs, each of them encoding different scales of spatial resolution. Successive learnt message passing between these graphs improves the ability of GNNs to capture and forecast the system state in problems encompassing a range of length scales. Using graph representations, MultiScaleGNN can impose periodic boundary conditions as an inductive bias on the edges in the graphs, and achieve independence to the nodes' positions. We demonstrate this method on advection problems and incompressible fluid dynamics. Our results show that the proposed model can generalise from uniform advection fields to high-gradient fields on complex domains at test time and infer long-term Navier-Stokes solutions within a range of Reynolds numbers. Simulations obtained with MultiScaleGNN are between two and four orders of magnitude faster than the ones on which it was trained.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bc9df947dee9aa269ef9d5fcd06980598293aea5" target='_blank'>Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks</a></td>
-          <td>
-            Mario Lino, C. Cantwell, A. Bharath, Stathi Fotiadis
-          </td>
-          <td>2021-06-09</td>
-          <td>ArXiv</td>
-          <td>37</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote physical faithfulness, but hardware limitations have precluded their application to large computational domains. We show that it is \textit{possible} to train a class of GNN surrogates on 3D meshes. We scale MeshGraphNets (MGN), a subclass of GNNs for mesh-based physics modeling, via our domain decomposition approach to facilitate training that is mathematically equivalent to training on the whole domain under certain conditions. With this, we were able to train MGN on meshes with \textit{millions} of nodes to generate computational fluid dynamics (CFD) simulations. Furthermore, we show how to enhance MGN via higher-order numerical integration, which can reduce MGN's error and training time. We validated our methods on an accompanying dataset of 3D $\text{CO}_2$-capture CFD simulations on a 3.1M-node mesh. This work presents a practical path to scaling MGN for real-world applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e8c880ff190ca6184e2d18f2a87ccb992951e435" target='_blank'>Scientific Computing Algorithms to Learn Enhanced Scalable Surrogates for Mesh Physics</a></td>
-          <td>
-            Brian Bartoldson, Yeping Hu, Amarjeet Saini, Jose Cadena, Yu-Hang Fu, Jie Bao, Zhijie Xu, Brenda Ng, P. Nguyen
-          </td>
-          <td>2023-04-01</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="In recent years, there has been a growing interest in using machine learning to overcome the high cost of numerical simulation, with some learned models achieving impressive speed-ups over classical solvers whilst maintaining accuracy. However, these methods are usually tested at low-resolution settings, and it remains to be seen whether they can scale to the costly high-resolution simulations that we ultimately want to tackle. In this work, we propose two complementary approaches to improve the framework from MeshGraphNets, which demonstrated accurate predictions in a broad range of physical systems. MeshGraphNets relies on a message passing graph neural network to propagate information, and this structure becomes a limiting factor for high-resolution simulations, as equally distant points in space become further apart in graph space. First, we demonstrate that it is possible to learn accurate surrogate dynamics of a high-resolution system on a much coarser mesh, both removing the message passing bottleneck and improving performance; and second, we introduce a hierarchical approach (MultiScale MeshGraphNets) which passes messages on two different resolutions (fine and coarse), significantly improving the accuracy of MeshGraphNets while requiring less computational resources.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b6841ed68e0e6d9cabeb28e9dfca22ffa853f30f" target='_blank'>MultiScale MeshGraphNets</a></td>
-          <td>
-            Meire Fortunato, Tobias Pfaff, Peter Wirnsberger, A. Pritzel, Peter W. Battaglia
-          </td>
-          <td>2022-10-02</td>
-          <td>ArXiv</td>
-          <td>45</td>
-          <td>27</td>
-        </tr>
-    
-        <tr id="Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term "Graph Network-based Simulators" (GNS)---represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c529f5b08675f787cdcc094ee495239592339f82" target='_blank'>Learning to Simulate Complex Physics with Graph Networks</a></td>
-          <td>
-            Alvaro Sanchez-Gonzalez, Jonathan Godwin, T. Pfaff, Rex Ying, J. Leskovec, P. Battaglia
-          </td>
-          <td>2020-02-21</td>
-          <td>ArXiv</td>
-          <td>849</td>
-          <td>134</td>
-        </tr>
-    
-        <tr id="Simulating fluid dynamics is crucial for the design and development process, ranging from simple valves to complex turbomachinery. Accurately solving the underlying physical equations is computationally expensive. Therefore, learning-based solvers that model interactions on meshes have gained interest due to their promising speed-ups. However, it is unknown to what extent these models truly understand the underlying physical principles and can generalize rather than interpolate. Generalization is a key requirement for a general-purpose fluid simulator, which should adapt to different topologies, resolutions, or thermodynamic ranges. We propose SURF, a benchmark designed to test the $\textit{generalization}$ of learned graph-based fluid simulators. SURF comprises individual datasets and provides specific performance and generalization metrics for evaluating and comparing different models. We empirically demonstrate the applicability of SURF by thoroughly investigating the two state-of-the-art graph-based models, yielding new insights into their generalization.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b36fc1fa1cf02a8594911f3e6491deb33637843f" target='_blank'>SURF: A Generalization Benchmark for GNNs Predicting Fluid Dynamics</a></td>
-          <td>
-            Stefan Künzli, Florian Grötschla, Joël Mathys, R. Wattenhofer
-          </td>
-          <td>2023-10-30</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer from over-smoothing for problems involving very fine mesh. In this work, we develop a multiscale mesh-based GNN framework mimicking a conventional iterative multigrid solver, coupled with adaptive mesh refinement (AMR), to mitigate challenges with conventional mesh-based GNNs. We use the framework to accelerate phase field (PF) fracture problems involving coupled partial differential equations with a near-singular operator due to near-zero modulus inside the crack. We define the initial graph representation using all mesh resolution levels. We perform a series of downsampling steps using Transformer MP GNNs to reach the coarsest graph followed by upsampling steps to reach the original graph. We use skip connectors from the generated embedding during coarsening to prevent over-smoothing. We use Transfer Learning (TL) to significantly reduce the size of training datasets needed to simulate different crack configurations and loading conditions. The trained framework showed accelerated simulation times, while maintaining high accuracy for all cases compared to physics-based PF fracture model. Finally, this work provides a new approach to accelerate a variety of mesh-based engineering multiphysics problems">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a5805fc04ef9c6bd5534b36fbc2a6a1838c094d5" target='_blank'>Multiscale graph neural networks with adaptive mesh refinement for accelerating mesh-based simulations</a></td>
-          <td>
-            Roberto Perera, V. Agrawal
-          </td>
-          <td>2024-02-14</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>10</td>
-        </tr>
-    
-        <tr id="Simulating rigid collisions among arbitrary shapes is notoriously difficult due to complex geometry and the strong non-linearity of the interactions. While graph neural network (GNN)-based models are effective at learning to simulate complex physical dynamics, such as fluids, cloth and articulated bodies, they have been less effective and efficient on rigid-body physics, except with very simple shapes. Existing methods that model collisions through the meshes' nodes are often inaccurate because they struggle when collisions occur on faces far from nodes. Alternative approaches that represent the geometry densely with many particles are prohibitively expensive for complex shapes. Here we introduce the Face Interaction Graph Network (FIGNet) which extends beyond GNN-based methods, and computes interactions between mesh faces, rather than nodes. Compared to learned node- and particle-based methods, FIGNet is around 4x more accurate in simulating complex shape interactions, while also 8x more computationally efficient on sparse, rigid meshes. Moreover, FIGNet can learn frictional dynamics directly from real-world data, and can be more accurate than analytical solvers given modest amounts of training data. FIGNet represents a key step forward in one of the few remaining physical domains which have seen little competition from learned simulators, and offers allied fields such as robotics, graphics and mechanical design a new tool for simulation and model-based planning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d6fdd8fc0c5fc052d040687e72638fb4297661cc" target='_blank'>Learning rigid dynamics with face interaction graph networks</a></td>
-          <td>
-            Kelsey R. Allen, Yulia Rubanova, Tatiana Lopez-Guevara, William F. Whitney, Alvaro Sanchez-Gonzalez, P. Battaglia, T. Pfaff
-          </td>
-          <td>2022-12-07</td>
-          <td>ArXiv</td>
-          <td>22</td>
-          <td>46</td>
-        </tr>
-    
-        <tr id="Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Amp\`ere PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page is at https://erizmr.github.io/UM2N/.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/569f07b5381b1df88a804a15614ac2ddef7715f2" target='_blank'>Towards Universal Mesh Movement Networks</a></td>
-          <td>
-            Mingrui Zhang, Chunyang Wang, Stephan Kramer, Joseph G. Wallwork, Siyi Li, Jiancheng Liu, Xiang Chen, M. Piggott
-          </td>
-          <td>2024-06-29</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="Simulating the time evolution of physical systems is pivotal in many scientific and engineering problems. An open challenge in simulating such systems is their multi-resolution dynamics: a small fraction of the system is extremely dynamic, and requires very fine-grained resolution, while a majority of the system is changing slowly and can be modeled by coarser spatial scales. Typical learning-based surrogate models use a uniform spatial scale, which needs to resolve to the finest required scale and can waste a huge compute to achieve required accuracy. In this work, we introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep learning-based surrogate model that jointly learns the evolution model and optimizes appropriate spatial resolutions that devote more compute to the highly dynamic regions. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNN-based actor-critic for learning the policy of spatial refinement and coarsening. We introduce learning techniques that optimizes LAMP with weighted sum of error and computational cost as objective, allowing LAMP to adapt to varying relative importance of error vs. computation tradeoff at inference time. We evaluate our method in a 1D benchmark of nonlinear PDEs and a challenging 2D mesh-based simulation. We demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error: it achieves an average of 33.7% error reduction for 1D nonlinear PDEs, and outperforms MeshGraphNets + classical Adaptive Mesh Refinement (AMR) in 2D mesh-based simulations. Project website with data and code can be found at: http://snap.stanford.edu/lamp.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/75cb343edaaa6a5322588bf6f3ef160742e9fbc0" target='_blank'>Learning Controllable Adaptive Simulation for Multi-resolution Physics</a></td>
-          <td>
-            Tailin Wu, T. Maruyama, Qingqing Zhao, Gordon Wetzstein, J. Leskovec
-          </td>
-          <td>2023-05-01</td>
-          <td>ArXiv</td>
-          <td>12</td>
-          <td>134</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning for widely used dynamic mode decomposition algorithms. While such methods have proven to be remarkably useful in the analysis of time-series data, the resulting linear models must generally be of high order to accurately approximate fundamentally nonlinear behaviors. This issue poses an inherent risk of overfitting to training data thereby limiting predictive capabilities. By contrast, this work explores strategies for nonlinear data-driven estimation of the action of the Koopman operator. General strategies that yield nonlinear models are presented for systems both with and without control. Subsequent projection of the resulting nonlinear equations onto a low-rank basis yields a low order representation for the underlying dynamical system. In both computational and experimental examples considered in this work, linear estimators of the Koopman operator are generally only able to provide short-term predictions for the observable dynamics while comparable nonlinear estimators provide accurate predictions on substantially longer timescales and replicate infinite-time behaviors that linear predictors cannot.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1cda473dadc56234490012ec6c5679625cdfe565" target='_blank'>Nonlinear Data-Driven Approximation of the Koopman Operator</a></td>
-          <td>
-            Dan Wilson
-          </td>
-          <td>2022-10-10</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>19</td>
-        </tr>
-    
-        <tr id="The Koopman operator is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinitedimensional Hilbert space. This operator theoretic point of view lifts the dynamics of a finite-dimensional nonlinear system to an infinite-dimensional function space where the evolution of the original system becomes linear. In this paper, we provide a brief summary of the Koopman operator theorem for nonlinear dynamics modeling and focus on analyzing several data-driven implementations using dynamical mode decomposition (DMD) for autonomous and controlled canonical problems. We apply the extended dynamic mode decomposition (EDMD) to identify the leading Koopman eigenfunctions and approximate a finite-dimensional representation of the discovered linear dynamics. This allows us to apply linear control approaches towards nonlinear systems without linearization approximations around fixed points. We can then examine the fidelity of using a linear controller based on a Koopman operator approximated system on under-actuated systems with basic maneuvers. We demonstrate the effectiveness of this theory through numerical simulation on two classic dynamical systems are used to show DMD methods of evaluating and approximating the Koopman operator and its effectiveness at linearizing these systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1a76367c9b3a27f25890eee333195e3aaf8d6841" target='_blank'>Koopman Operator Theory for Nonlinear Dynamic Modeling using Dynamic Mode Decomposition</a></td>
-          <td>
-            Gregory F. Snyder, Zhuoyuan Song
-          </td>
-          <td>2021-10-16</td>
-          <td>ArXiv</td>
-          <td>8</td>
-          <td>10</td>
-        </tr>
-    
-        <tr id="The field of dynamical systems is being transformed by the mathematical tools and algorithms emerging from modern computing and data science. First-principles derivations and asymptotic reductions are giving way to data-driven approaches that formulate models in operator theoretic or probabilistic frameworks. Koopman spectral theory has emerged as a dominant perspective over the past decade, in which nonlinear dynamics are represented in terms of an infinite-dimensional linear operator acting on the space of all possible measurement functions of the system. This linear representation of nonlinear dynamics has tremendous potential to enable the prediction, estimation, and control of nonlinear systems with standard textbook methods developed for linear systems. However, obtaining finite-dimensional coordinate systems and embeddings in which the dynamics appear approximately linear remains a central open challenge. The success of Koopman analysis is due primarily to three key factors: 1) there exists rigorous theory connecting it to classical geometric approaches for dynamical systems, 2) the approach is formulated in terms of measurements, making it ideal for leveraging big-data and machine learning techniques, and 3) simple, yet powerful numerical algorithms, such as the dynamic mode decomposition (DMD), have been developed and extended to reduce Koopman theory to practice in real-world applications. In this review, we provide an overview of modern Koopman operator theory, describing recent theoretical and algorithmic developments and highlighting these methods with a diverse range of applications. We also discuss key advances and challenges in the rapidly growing field of machine learning that are likely to drive future developments and significantly transform the theoretical landscape of dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68b6ca45a588d538b36335b23f6969c960cf2e6e" target='_blank'>Modern Koopman Theory for Dynamical Systems</a></td>
-          <td>
-            S. Brunton, M. Budišić, E. Kaiser, J. Kutz
-          </td>
-          <td>2021-02-24</td>
-          <td>SIAM Rev.</td>
-          <td>273</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often need to prepare nonlinear observables manually according to the underlying dynamics, which is not always possible since we may not have any a priori knowledge about them. In this paper, we propose a fully data-driven method for Koopman spectral analysis based on the principle of learning Koopman invariant subspaces from observed data. To this end, we propose minimization of the residual sum of squares of linear least-squares regression to estimate a set of functions that transforms data into a form in which the linear regression fits well. We introduce an implementation with neural networks and evaluate performance empirically using nonlinear dynamical systems and applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/49ee811e5c7af5980d3dfe791f6b18e0080ad566" target='_blank'>Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition</a></td>
-          <td>
-            Naoya Takeishi, Y. Kawahara, T. Yairi
-          </td>
-          <td>2017-10-12</td>
-          <td>ArXiv</td>
-          <td>326</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of projected Koopman operators acting on this subspace. We parametrize both the projected Koopman operator family and the dictionary that spans the invariant subspace by neural networks and jointly train them with trajectory data. We show theoretically the validity of our approach, and demonstrate via numerical experiments that it exhibits significant improvements over existing methods in solving prediction problems, especially those with large state or parameter dimensions, and those possessing strongly non-linear dynamics. Moreover, our method enables data-driven solution of optimal control problems involving non-linear dynamics, with interesting implications on controllability.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/37f5dd7a54e2c8a74a5cb30270698a6c98047bba" target='_blank'>Learning Parametric Koopman Decompositions for Prediction and Control</a></td>
-          <td>
-            Yue Guo, Milan Korda, I. Kevrekidis, Qianxiao Li
-          </td>
-          <td>2023-10-02</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>76</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0f4b3d72f08bfadc076617850cc8a5e9395738d6" target='_blank'>Koopman Operator Dynamical Models: Learning, Analysis and Control</a></td>
-          <td>
-            Petar Bevanda, Stefan Sosnowski, S. Hirche
-          </td>
-          <td>2021-02-04</td>
-          <td>ArXiv</td>
-          <td>88</td>
-          <td>47</td>
-        </tr>
-    
-        <tr id="This work presents a data-driven framework for learning eigenfunctions of the Koopman operator geared toward prediction and control. The method relies on the richness of the spectrum of the Koopman operator in the transient, off-attractor, regime to construct a large number of eigenfunctions such that the state (or any other observable quantity of interest) is in the span of these eigenfunctions and hence predictable in a linear fashion. Once a predictor for the uncontrolled part of the system is obtained in this way, the incorporation of control is done through a multi-step prediction error minimization, carried out by a simple linear least-squares regression. The predictor so obtained is in the form of a linear controlled dynamical system and can be readily applied within the Koopman model predictive control framework of [11] to control nonlinear dynamical systems using linear model predictive control tools. The method is entirely data-driven and based purely on convex optimization, with no reliance on neural networks or other non-convex machine learning tools. The novel eigenfunction construction method is also analyzed theoretically, proving rigorously that the family of eigenfunctions obtained is rich enough to span the space of all continuous functions. In addition, the method is extended to construct generalized eigenfunctions that also give rise Koopman invariant subspaces and hence can be used for linear prediction. Detailed numerical examples demonstrate the approach, both for prediction and feedback control.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/97629699ff9e1e67b3f4f21cab64d42f3713bfa0" target='_blank'>Learning Koopman eigenfunctions for prediction and control: the transient case</a></td>
-          <td>
-            Milan Korda, I. Mezić
-          </td>
-          <td>2018-10-20</td>
-          <td>arXiv: Optimization and Control</td>
-          <td>7</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="This article presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to construct a set of eigenfunctions such that the state (or any other observable quantity of interest) is in the span of these eigenfunctions and hence predictable in a linear fashion. The eigenfunction construction is optimization-based with no dictionary selection required. Once a predictor for the uncontrolled part of the system is obtained in this way, the incorporation of control is done through a multistep prediction error minimization, carried out by a simple linear least-squares regression. The predictor so obtained is in the form of a linear controlled dynamical system and can be readily applied within the Koopman model predictive control (MPC) framework of (M. Korda and I. Mezić, 2018) to control nonlinear dynamical systems using linear MPC tools. The method is entirely data-driven and based predominantly on convex optimization. The novel eigenfunction construction method is also analyzed theoretically, proving rigorously that the family of eigenfunctions obtained is rich enough to span the space of all continuous functions. In addition, the method is extended to construct generalized eigenfunctions that also give rise Koopman invariant subspaces and hence can be used for linear prediction. Detailed numerical examples demonstrate the approach, both for prediction and feedback control.**Code for the numerical examples is available from https://homepages.laas.fr/mkorda/Eigfuns.zip.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8f3d28be5557a1c87a80c3242d68bddb331b0cbc" target='_blank'>Optimal Construction of Koopman Eigenfunctions for Prediction and Control</a></td>
-          <td>
-            Milan Korda, I. Mezić
-          </td>
-          <td>2018-10-20</td>
-          <td>IEEE Transactions on Automatic Control</td>
-          <td>103</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="The Koopman operator is an useful analytical tool for studying dynamical systems -- both controlled and uncontrolled. For example, Koopman eigenfunctions can provide non-local stability information about the underlying dynamical system. Koopman representations of nonlinear systems are commonly calculated using machine learning methods, which seek to represent the Koopman eigenfunctions as a linear combinations of nonlinear state measurements. As such, it is important to understand whether, in principle, these eigenfunctions can be successfully obtained using machine learning and what eigenfunctions calculated in this way can tell us about the underlying system. To that end, this paper presents an analysis of continuity, stability and control limitations associated with Koopman eigenfunctions under minimal assumptions and provides a discussion that relates these properties to the ability to calculate Koopman representations with machine learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/719cbf3907aa6d2e8c2c623a9268d9ce86116223" target='_blank'>Learning Bounded Koopman Observables: Results on Stability, Continuity, and Controllability</a></td>
-          <td>
-            Craig Bakker, Thiagarajan Ramachandran, W. S. Rosenthal
-          </td>
-          <td>2020-04-30</td>
-          <td>arXiv: Dynamical Systems</td>
-          <td>3</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="We exploit the key idea that nonlinear system identification is equivalent to linear identification of the so-called Koopman operator. Instead of considering nonlinear system identification in the state space, we obtain a novel linear identification technique by recasting the problem in the infinite-dimensional space of observables. This technique can be described in two main steps. In the first step, similar to a component of the Extended Dynamic Mode Decomposition algorithm, the data are lifted to the infinite-dimensional space and used for linear identification of the Koopman operator. In the second step, the obtained Koopman operator is “projected back” to the finite-dimensional state space, and identified to the nonlinear vector field through a linear least squares problem. The proposed technique is efficient to recover (polynomial) vector fields of different classes of systems, including unstable, chaotic, and open systems. In addition, it is robust to noise, well-suited to model low sampling rate datasets, and able to infer network topology and dynamics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4229412ee666f68522dd72ce5f956311a0de4f59" target='_blank'>Linear identification of nonlinear systems: A lifting technique based on the Koopman operator</a></td>
-          <td>
-            A. Mauroy, Jorge M. Gonçalves
-          </td>
-          <td>2016-05-14</td>
-          <td>2016 IEEE 55th Conference on Decision and Control (CDC)</td>
-          <td>98</td>
-          <td>17</td>
-        </tr>
-    
-  </tbody>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ba76406526d5e39c738813118d5407cc05dfb8c6" target='_blank'>Data-driven sparse identification of nonlinear dynamical systems using linear multistep methods</a></td>
-          <td>
-            Hao-guang Chen
-          </td>
-          <td>2023-01-23</td>
-          <td>Calcolo</td>
-          <td>1</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="Identifying hidden dynamics from observed data is a significant and challenging task in a wide range of applications. Recently, the combination of linear multistep methods (LMMs) and deep learning has been successfully employed to discover dynamics, whereas a complete convergence analysis of this approach is still under development. In this work, we consider the deep network-based LMMs for the discovery of dynamics. We put forward error estimates for these methods using the approximation property of deep networks. It indicates, for certain families of LMMs, that the $\ell^2$ grid error is bounded by the sum of $O(h^p)$ and the network approximation error, where $h$ is the time step size and $p$ is the local truncation error order. Numerical results of several physically relevant examples are provided to demonstrate our theory.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a2d1f9d22766d54b81b390c48413e6a570e47ed1" target='_blank'>The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation</a></td>
-          <td>
-            Q. Du, Yiqi Gu, Haizhao Yang, Chao Zhou
-          </td>
-          <td>2021-03-21</td>
-          <td>ArXiv</td>
-          <td>18</td>
-          <td>68</td>
-        </tr>
-    
-        <tr id="Kolmogorov-Arnold Networks (KANs) as an alternative to Multi-layer perceptrons (MLPs) are a recent development demonstrating strong potential for data-driven modeling. This work applies KANs as the backbone of a Neural Ordinary Differential Equation framework, generalizing their use to the time-dependent and grid-sensitive cases often seen in scientific machine learning applications. The proposed KAN-ODEs retain the flexible dynamical system modeling framework of Neural ODEs while leveraging the many benefits of KANs, including faster neural scaling, stronger interpretability, and lower parameter counts when compared against MLPs. We demonstrate these benefits in three test cases: the Lotka-Volterra predator-prey model, Burgers' equation, and the Fisher-KPP PDE. We showcase the strong performance of parameter-lean KAN-ODE systems generally in reconstructing entire dynamical systems, and also in targeted applications to the inference of a source term in an otherwise known flow field. We additionally demonstrate the interpretability of KAN-ODEs via activation function visualization and symbolic regression of trained results. The successful training of KAN-ODEs and their improved performance when compared to traditional Neural ODEs implies significant potential in leveraging this novel network architecture in myriad scientific machine learning applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/efeeddb4162e3eefbe1d974d6ce7cd1d32498a6b" target='_blank'>KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics</a></td>
-          <td>
-            Benjamin C. Koenig, Suyong Kim, Sili Deng
-          </td>
-          <td>2024-07-05</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of timescales, making numerical integration expensive. In this work, we develop a hierarchy of deep neural network time-steppers to approximate the dynamical system flow map over a range of time-scales. The model is purely data-driven, enabling accurate and efficient numerical integration and forecasting. Similar ideas can be used to couple neural network-based models with classical numerical time-steppers. Our hierarchical time-stepping scheme provides advantages over current time-stepping algorithms, including (i) capturing a range of timescales, (ii) improved accuracy in comparison with leading neural network architectures, (iii) efficiency in long-time forecasting due to explicit training of slow time-scale dynamics, and (iv) a flexible framework that is parallelizable and may be integrated with standard numerical time-stepping algorithms. The method is demonstrated on numerous nonlinear dynamical systems, including the Van der Pol oscillator, the Lorenz system, the Kuramoto–Sivashinsky equation, and fluid flow pass a cylinder; audio and video signals are also explored. On the sequence generation examples, we benchmark our algorithm against state-of-the-art methods, such as LSTM, reservoir computing and clockwork RNN. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6958b9125dfbea51cc33f9432c62e2b0ea2c8e4f" target='_blank'>Hierarchical deep learning of multiscale differential equation time-steppers</a></td>
-          <td>
-            Yuying Liu, N. Kutz, S. Brunton
-          </td>
-          <td>2020-08-22</td>
-          <td>Philosophical transactions. Series A, Mathematical, physical, and engineering sciences</td>
-          <td>60</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="In many cases, the equations that dynamical systems are based on are unknown and hard to model and predict. On the other hand, machine learning algorithms are based on the data of a solution as it evolves and do not need equations. In the era of abundant data, using machine learning technology to discover accurate mathematical models of dynamical systems directly from time series data becomes increasingly important. Recently, a multi-step deep neural networks (multi-step DNN) model without need of direct access to temporal gradients is proposed, which can accurately learn the evolution from a given set of observed data, identify nonlinear dynamical systems, and forecast future states. However, the architecture lacks the capability to capture long term temporal dependencies from dynamical time-series data. In the paper, based on the multi-step time-stepping schemes, we proposed a new CLDNN model which combine convolutional layer, long short-term memory layer and fully connected layer, to address the aforementioned weakness. The effectiveness of our model is tested for several benchmark problems involving the identification and prediction of complex, nonlinear and chaotic dynamics. The experiment results show that the multi-step CLDNN has better identification and prediction performance than the multi-step DNN. The research provides possible corroboration for developing new deep learning based algorithms for nonlinear system identification.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/766d4bcb8f8fbbbb47f89e5276f5ec24c8c0d460" target='_blank'>Data driven nonlinear dynamical systems identification using multi-step CLDNN</a></td>
-          <td>
-            Qi Teng, L. Zhang
-          </td>
-          <td>2019-08-19</td>
-          <td>AIP Advances</td>
-          <td>20</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="Discovering mathematical models that characterize the observed behavior of dynamical systems remains a major challenge, especially for systems in a chaotic regime. The challenge is even greater when the physics underlying such systems is not yet understood, and scientific inquiry must solely rely on empirical data. Driven by the need to fill this gap, we develop a framework that learns mathematical expressions modeling complex dynamical behaviors by identifying differential equations from noisy and sparse observable data. We train a small neural network to learn the dynamics of a system, its rate of change in time, and missing model terms, which are used as input for a symbolic regression algorithm to autonomously distill the explicit mathematical terms. This, in turn, enables us to predict the future evolution of the dynamical behavior. The performance of this framework is validated by recovering the right-hand sides and unknown terms of certain complex, chaotic systems such as the well-known Lorenz system, a six-dimensional hyperchaotic system, and the non-autonomous Sprott chaotic system, and comparing them with their known analytical expressions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f5cccd316e70bd2366e67260e1f691761bd512d3" target='_blank'>AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression</a></td>
-          <td>
-            Mario De Florio, I. Kevrekidis, G. Karniadakis
-          </td>
-          <td>2023-12-21</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based on empirical measurement is an important step in characterizing and predicting these processes. Classifying a system as chaotic usually requires estimating its largest Lyapunov exponent, which quantifies the average rate of convergence or divergence of initially close trajectories in state space, and for which a positive value is generally accepted as an operational definition of chaos. Estimating the largest Lyapunov exponent from observations of a process is especially challenging in systems affected by dynamical noise, which is the case for many models of real-world processes, in particular models of biological systems. We describe a novel method for estimating the largest Lyapunov exponent from data, based on training Deep Learning models on synthetically generated trajectories, and demonstrate that this method yields accurate and noise-robust predictions given relatively short inputs and across a range of different dynamical systems. Our method is unique in that it can analyze tree-shaped data, a ubiquitous topology in biological settings, and specifically in dynamics over lineages of cells or organisms. We also characterize the types of input information extracted by our models for their predictions, allowing for a deeper understanding into the different ways by which chaos can be analyzed in different topologies.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9fb357e57624525f27224822502061cc8fb831e1" target='_blank'>Detecting chaos in lineage-trees: A deep learning approach</a></td>
-          <td>
-            H. Rappeport, Irit Levin Reisman, Naftali Tishby, N. Balaban
-          </td>
-          <td>2021-06-08</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>56</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3b44db6efdb3999b65be446114afb04720e572cc" target='_blank'>Modeling of dynamical systems through deep learning</a></td>
-          <td>
-            P. Rajendra, V. Brahmajirao
-          </td>
-          <td>2020-11-22</td>
-          <td>Biophysical Reviews</td>
-          <td>32</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="The success of the current wave of artificial intelligence can be partly attributed to deep neural networks, which have proven to be very effective in learning complex patterns from large datasets with minimal human intervention. However, it is difficult to train these models on complex dynamical systems from data alone due to their low data efficiency and sensitivity to hyperparameters and initialisation. This work demonstrates that injection of partially known information at an intermediate layer in a DNN can improve model accuracy, reduce model uncertainty, and yield improved convergence during the training. The value of these physics-guided neural networks has been demonstrated by learning the dynamics of a wide variety of nonlinear dynamical systems represented by five well-known equations in nonlinear systems theory: the Lotka-Volterra, Duffing, Van der Pol, Lorenz, and Henon-Heiles systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/518a4b3c36c8a0e651caa603ea10d0875a1fbc27" target='_blank'>Physics guided neural networks for modelling of non-linear dynamics</a></td>
-          <td>
-            Haakon Robinson, Suraj Pawar, A. Rasheed, O. San
-          </td>
-          <td>2022-05-13</td>
-          <td>Neural networks : the official journal of the International Neural Network Society</td>
-          <td>27</td>
-          <td>34</td>
-        </tr>
-    
-        <tr id="Complex systems often show macroscopic coherent behavior due to the interactions of microscopic agents like molecules, cells, or individuals in a population with their environment. However, simulating such systems poses several computational challenges during simulation as the underlying dynamics vary and span wide spatiotemporal scales of interest. To capture the fast-evolving features, finer time steps are required while ensuring that the simulation time is long enough to capture the slow-scale behavior, making the analyses computationally unmanageable. This paper showcases how deep learning techniques can be used to develop a precise time-stepping approach for multiscale systems using the joint discovery of coordinates and flow maps. While the former allows us to represent the multiscale dynamics on a representative basis, the latter enables the iterative time-stepping estimation of the reduced variables. The resulting framework achieves state-of-the-art predictive accuracy while incurring lesser computational costs. We demonstrate this ability of the proposed scheme on the large-scale Fitzhugh Nagumo neuron model and the 1D Kuramoto-Sivashinsky equation in the chaotic regime.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/22e6d5918a51fff97d4344a3b5b353d0a1439708" target='_blank'>Enhancing Computational Efficiency in Multiscale Systems Using Deep Learning of Coordinates and Flow Maps</a></td>
-          <td>
-            Asif Hamid, Danish Rafiq, S. A. Nahvi, M. A. Bazaz
-          </td>
-          <td>2024-04-28</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>11</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
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diff --git a/docs/recommendations/a50a2a191c98dfe045ac2139495ee80ff1338e47.md b/docs/recommendations/a50a2a191c98dfe045ac2139495ee80ff1338e47.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:06:00 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Graph-Coupled Oscillator Networks</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We propose the Kuramoto Graph Neural Network (KuramotoGNN), a novel class of continuous-depth graph neural networks (GNNs) that employs the Kuramoto model to mitigate the over-smoothing phenomenon, in which node features in GNNs become indistinguishable as the number of layers increases. The Kuramoto model captures the synchronization behavior of non-linear coupled oscillators. Under the view of coupled oscillators, we first show the connection between Kuramoto model and basic GNN and then over-smoothing phenomenon in GNNs can be interpreted as phase synchronization in Kuramoto model. The KuramotoGNN replaces this phase synchronization with frequency synchronization to prevent the node features from converging into each other while allowing the system to reach a stable synchronized state. We experimentally verify the advantages of the KuramotoGNN over the baseline GNNs and existing methods in reducing over-smoothing on various graph deep learning benchmark tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4eaf18f05ffc165ce6a0c4c44ac123af52fd523c" target='_blank'>From Coupled Oscillators to Graph Neural Networks: Reducing Over-smoothing via a Kuramoto Model-based Approach</a></td>
-          <td>
-            Tuan Nguyen, Tan M. Nguyen, Hirotada Honda, Takashi Sano, Vinh Nguyen, Shugo Nakamura
-          </td>
-          <td>2023-11-06</td>
-          <td>ArXiv, DBLP</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs). To do so, we present a neural-ODE control (NODEC) framework and find that it can learn feedback control signals that drive graph dynamical systems into desired target states. While we use loss functions that do not constrain the control energy, our results show, in accordance with related work, that NODEC produces low energy control signals. Finally, we evaluate the performance and versatility of NODEC against well-known feedback controllers and deep reinforcement learning. We use NODEC to generate feedback controls for systems of more than one thousand coupled, non-linear ODEs that represent epidemic processes and coupled oscillators.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9c3b4e4df0d27f65b09fcb86bef1a04fc759fa97" target='_blank'>Neural ordinary differential equation control of dynamics on graphs</a></td>
-          <td>
-            Thomas Asikis, L. Böttcher, Nino Antulov-Fantulin
-          </td>
-          <td>2020-06-17</td>
-          <td>Physical Review Research</td>
-          <td>30</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="We introduce the framework of continuous--depth graph neural networks (GNNs). Graph neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN layers, blending discrete topological structures and differential equations. The proposed framework is shown to be compatible with various static and autoregressive GNN models. Results prove general effectiveness of GDEs: in static settings they offer computational advantages by incorporating numerical methods in their forward pass; in dynamic settings, on the other hand, they are shown to improve performance by exploiting the geometry of the underlying dynamics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8540780e6b9422f7a1264edb70f39d3ff79bb8c1" target='_blank'>Graph Neural Ordinary Differential Equations</a></td>
-          <td>
-            Michael Poli, Stefano Massaroli, Junyoung Park, A. Yamashita, H. Asama, Jinkyoo Park
-          </td>
-          <td>2019-11-18</td>
-          <td>ArXiv</td>
-          <td>122</td>
-          <td>39</td>
-        </tr>
-    
-        <tr id="Recent works have shown that physics-inspired architectures allow the training of deep graph neural networks (GNNs) without oversmoothing. The role of these physics is unclear, however, with successful examples of both reversible (e.g., Hamiltonian) and irreversible (e.g., diffusion) phenomena producing comparable results despite diametrically opposed mechanisms, and further complications arising due to empirical departures from mathematical theory. This work presents a series of novel GNN architectures based upon structure-preserving bracket-based dynamical systems, which are provably guaranteed to either conserve energy or generate positive dissipation with increasing depth. It is shown that the theoretically principled framework employed here allows for inherently explainable constructions, which contextualize departures from theory in current architectures and better elucidate the roles of reversibility and irreversibility in network performance.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/71395e0be94802971611ec88130af780d4ba90d0" target='_blank'>Reversible and irreversible bracket-based dynamics for deep graph neural networks</a></td>
-          <td>
-            A. Gruber, Kookjin Lee, N. Trask
-          </td>
-          <td>2023-05-24</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="Continuous graph neural networks (CGNNs) have garnered significant attention due to their ability to generalize existing discrete graph neural networks (GNNs) by introducing continuous dynamics. They typically draw inspiration from diffusion-based methods to introduce a novel propagation scheme, which is analyzed using ordinary differential equations (ODE). However, the implementation of CGNNs requires significant computational power, making them challenging to deploy on battery-powered devices. Inspired by recent spiking neural networks (SNNs), which emulate a biological inference process and provide an energy-efficient neural architecture, we incorporate the SNNs with CGNNs in a unified framework, named Continuous Spiking Graph Neural Networks (COS-GNN). We employ SNNs for graph node representation at each time step, which are further integrated into the ODE process along with time. To enhance information preservation and mitigate information loss in SNNs, we introduce the high-order structure of COS-GNN, which utilizes the second-order ODE for spiking representation and continuous propagation. Moreover, we provide the theoretical proof that COS-GNN effectively mitigates the issues of exploding and vanishing gradients, enabling us to capture long-range dependencies between nodes. Experimental results on graph-based learning tasks demonstrate the effectiveness of the proposed COS-GNN over competitive baselines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cb2a45084f0c7bdc38271e94205603d1237945d8" target='_blank'>Continuous Spiking Graph Neural Networks</a></td>
-          <td>
-            Nan Yin, Mengzhu Wang, Li Shen, Hitesh Laxmichand Patel, Baopu Li, Bin Gu, Huan Xiong
-          </td>
-          <td>2024-04-02</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Graph neural networks are increasingly becoming the go-to approach in various fields such as computer vision, computational biology and chemistry, where data are naturally explained by graphs. However, unlike traditional convolutional neural networks, deep graph networks do not necessarily yield better performance than shallow graph networks. This behavior usually stems from the over-smoothing phenomenon. In this work, we propose a family of architectures to control this behavior by design. Our networks are motivated by numerical methods for solving Partial Differential Equations (PDEs) on manifolds, and as such, their behavior can be explained by similar analysis. Moreover, as we demonstrate using an extensive set of experiments, our PDE-motivated networks can generalize and be effective for various types of problems from different fields. Our architectures obtain better or on par with the current state-of-the-art results for problems that are typically approached using different architectures.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/54ff6c9ad037792e938e05985720d313512539b7" target='_blank'>PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations</a></td>
-          <td>
-            Moshe Eliasof, E. Haber, Eran Treister
-          </td>
-          <td>2021-08-04</td>
-          <td>ArXiv, DBLP</td>
-          <td>97</td>
-          <td>45</td>
-        </tr>
-    
-        <tr id="Graph Neural Networks (GNNs) have established themselves as the preferred methodology in a multitude of domains, ranging from computer vision to computational biology, especially in contexts where data inherently conform to graph structures. While many existing methods have endeavored to model GNNs using various techniques, a prevalent challenge they grapple with is the issue of over-smoothing. This paper presents new Graph Neural Network models that incorporate two first-order Partial Differential Equations (PDEs). These models do not increase complexity but effectively mitigate the over-smoothing problem. Our experimental findings highlight the capacity of our new PDE model to achieve comparable results with higher-order PDE models and fix the over-smoothing problem up to 64 layers. These results underscore the adaptability and versatility of GNNs, indicating that unconventional approaches can yield outcomes on par with established techniques.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/893093c71f2ae257120ae6789b3f86dc0dfeeaa1" target='_blank'>First-order PDES for Graph Neural Networks: Advection And Burgers Equation Models</a></td>
-          <td>
-            Yifan Qu, O. Krzysik, H. Sterck, Omer Ege Kara
-          </td>
-          <td>2024-04-03</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>25</td>
-        </tr>
-    
-        <tr id="Deep Graph Networks (DGNs) currently dominate the research landscape of learning from graphs, due to their efficiency and ability to implement an adaptive message-passing scheme between the nodes. However, DGNs are typically limited in their ability to propagate and preserve long-term dependencies between nodes, i.e., they suffer from the over-squashing phenomena. This reduces their effectiveness, since predictive problems may require to capture interactions at different, and possibly large, radii in order to be effectively solved. In this work, we present Anti-Symmetric Deep Graph Networks (A-DGNs), a framework for stable and non-dissipative DGN design, conceived through the lens of ordinary differential equations. We give theoretical proof that our method is stable and non-dissipative, leading to two key results: long-range information between nodes is preserved, and no gradient vanishing or explosion occurs in training. We empirically validate the proposed approach on several graph benchmarks, showing that A-DGN yields to improved performance and enables to learn effectively even when dozens of layers are used.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e516225868c0247007f917213f5b23434299e5df" target='_blank'>Anti-Symmetric DGN: a stable architecture for Deep Graph Networks</a></td>
-          <td>
-            Alessio Gravina, D. Bacciu, C. Gallicchio
-          </td>
-          <td>2022-10-18</td>
-          <td>ArXiv</td>
-          <td>32</td>
-          <td>26</td>
-        </tr>
-    
-        <tr id="Graph Neural Networks (graph NNs) are a promising deep learning approach for analyzing graph-structured data. However, it is known that they do not improve (or sometimes worsen) their predictive performance as we pile up many layers and add non-lineality. To tackle this problem, we investigate the expressive power of graph NNs via their asymptotic behaviors as the layer size tends to infinity. Our strategy is to generalize the forward propagation of a Graph Convolutional Network (GCN), which is a popular graph NN variant, as a specific dynamical system. In the case of a GCN, we show that when its weights satisfy the conditions determined by the spectra of the (augmented) normalized Laplacian, its output exponentially approaches the set of signals that carry information of the connected components and node degrees only for distinguishing nodes. Our theory enables us to relate the expressive power of GCNs with the topological information of the underlying graphs inherent in the graph spectra. To demonstrate this, we characterize the asymptotic behavior of GCNs on the Erdős -- Renyi graph. We show that when the Erdős -- Renyi graph is sufficiently dense and large, a broad range of GCNs on it suffers from the "information loss" in the limit of infinite layers with high probability. Based on the theory, we provide a principled guideline for weight normalization of graph NNs. We experimentally confirm that the proposed weight scaling enhances the predictive performance of GCNs in real data. Code is available at this https URL.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d06ddfa5377c80657f7085dd0ae6ee90675f6d88" target='_blank'>On Asymptotic Behaviors of Graph CNNs from Dynamical Systems Perspective</a></td>
-          <td>
-            Kenta Oono, Taiji Suzuki
-          </td>
-          <td>2019-05-27</td>
-          <td>ArXiv</td>
-          <td>24</td>
-          <td>40</td>
-        </tr>
-    
-        <tr id="Oversmoothing in Graph Neural Networks (GNNs) refers to the phenomenon where increasing network depth leads to homogeneous node representations. While previous work has established that Graph Convolutional Networks (GCNs) exponentially lose expressive power, it remains controversial whether the graph attention mechanism can mitigate oversmoothing. In this work, we provide a definitive answer to this question through a rigorous mathematical analysis, by viewing attention-based GNNs as nonlinear time-varying dynamical systems and incorporating tools and techniques from the theory of products of inhomogeneous matrices and the joint spectral radius. We establish that, contrary to popular belief, the graph attention mechanism cannot prevent oversmoothing and loses expressive power exponentially. The proposed framework extends the existing results on oversmoothing for symmetric GCNs to a significantly broader class of GNN models, including random walk GCNs, Graph Attention Networks (GATs) and (graph) transformers. In particular, our analysis accounts for asymmetric, state-dependent and time-varying aggregation operators and a wide range of common nonlinear activation functions, such as ReLU, LeakyReLU, GELU and SiLU.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8b9f01585a679dffe92261ecdec56425db9ef97f" target='_blank'>Demystifying Oversmoothing in Attention-Based Graph Neural Networks</a></td>
-          <td>
-            Xinyi Wu, A. Ajorlou, Zihui Wu, A. Jadbabaie
-          </td>
-          <td>2023-05-25</td>
-          <td>ArXiv</td>
-          <td>11</td>
-          <td>64</td>
-        </tr>
-    
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-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/aaf2145f9998f304513c0c9b530ee9f7750c6f55.md b/docs/recommendations/aaf2145f9998f304513c0c9b530ee9f7750c6f55.md
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-    Recommendations for the article <i>Coupled Graph ODE for Learning Interacting System Dynamics</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
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-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
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-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
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-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's constituent parts. In this work, we introduce the neural relational inference (NRI) model: an unsupervised model that learns to infer interactions while simultaneously learning the dynamics purely from observational data. Our model takes the form of a variational auto-encoder, in which the latent code represents the underlying interaction graph and the reconstruction is based on graph neural networks. In experiments on simulated physical systems, we show that our NRI model can accurately recover ground-truth interactions in an unsupervised manner. We further demonstrate that we can find an interpretable structure and predict complex dynamics in real motion capture and sports tracking data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c090e6348ae5ccfd6fc799f0b335ae6f0f4485cf" target='_blank'>Neural Relational Inference for Interacting Systems</a></td>
-          <td>
-            T. Fetaya, E. Wang, K.-C. Welling, M. Zemel, Thomas Kipf, Ethan Fetaya, Kuan-Chieh Jackson Wang, M. Welling, R. Zemel
-          </td>
-          <td>2018-02-13</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>729</td>
-          <td>88</td>
-        </tr>
-    
-  </tbody>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/acc257947545c8daa968138e317e03edc90e79b0.md b/docs/recommendations/acc257947545c8daa968138e317e03edc90e79b0.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:07:03 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We propose a randomized physics-informed neural network (PINN) or rPINN method for uncertainty quantification in inverse partial differential equation (PDE) problems with noisy data. This method is used to quantify uncertainty in the inverse PDE PINN solutions. Recently, the Bayesian PINN (BPINN) method was proposed, where the posterior distribution of the PINN parameters was formulated using the Bayes' theorem and sampled using approximate inference methods such as the Hamiltonian Monte Carlo (HMC) and variational inference (VI) methods. In this work, we demonstrate that HMC fails to converge for non-linear inverse PDE problems. As an alternative to HMC, we sample the distribution by solving the stochastic optimization problem obtained by randomizing the PINN loss function. The effectiveness of the rPINN method is tested for linear and non-linear Poisson equations, and the diffusion equation with a high-dimensional space-dependent diffusion coefficient. The rPINN method provides informative distributions for all considered problems. For the linear Poisson equation, HMC and rPINN produce similar distributions, but rPINN is on average 27 times faster than HMC. For the non-linear Poison and diffusion equations, the HMC method fails to converge because a single HMC chain cannot sample multiple modes of the posterior distribution of the PINN parameters in a reasonable amount of time.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9a72f5071131521363e3f04ad6b40fd9347a43b5" target='_blank'>Randomized Physics-Informed Neural Networks for Bayesian Data Assimilation</a></td>
-          <td>
-            Yifei Zong, D. Barajas-Solano, A. Tartakovsky
-          </td>
-          <td>2024-07-05</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>41</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7493597f70faee03cc4c050ea008e9fb9631aad6" target='_blank'>Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Data</a></td>
-          <td>
-            C. Bonneville, C. Earls
-          </td>
-          <td>2021-08-05</td>
-          <td>ArXiv</td>
-          <td>12</td>
-          <td>21</td>
-        </tr>
-    
-        <tr id="Bayesian Physics Informed Neural Networks (B-PINNs) have gained significant attention for inferring physical parameters and learning the forward solutions for problems based on partial differential equations. However, the overparameterized nature of neural networks poses a computational challenge for high-dimensional posterior inference. Existing inference approaches, such as particle-based or variance inference methods, are either computationally expensive for high-dimensional posterior inference or provide unsatisfactory uncertainty estimates. In this paper, we present a new efficient inference algorithm for B-PINNs that uses Ensemble Kalman Inversion (EKI) for high-dimensional inference tasks. We find that our proposed method can achieve inference results with informative uncertainty estimates comparable to Hamiltonian Monte Carlo (HMC)-based B-PINNs with a much reduced computational cost. These findings suggest that our proposed approach has great potential for uncertainty quantification in physics-informed machine learning for practical applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/493e36052afba2f214d7407a63bddb9b91b79c3b" target='_blank'>Efficient Bayesian Physics Informed Neural Networks for Inverse Problems via Ensemble Kalman Inversion</a></td>
-          <td>
-            Andrew Pensoneault, Xueyu Zhu
-          </td>
-          <td>2023-03-13</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="The accessibility of spatially distributed data, enabled by affordable sensors, field, and numerical experiments, has facilitated the development of data-driven solutions for scientific problems, including climate change, weather prediction, and urban planning. Neural Partial Differential Equations (Neural PDEs), which combine deep learning (DL) techniques with domain expertise (e.g., governing equations) for parameterization, have proven to be effective in capturing valuable correlations within spatiotemporal datasets. However, sparse and noisy measurements coupled with modeling approximation introduce aleatoric and epistemic uncertainties. Therefore, quantifying uncertainties propagated from model inputs to outputs remains a challenge and an essential goal for establishing the trustworthiness of Neural PDEs. This work evaluates various Uncertainty Quantification (UQ) approaches for both Forward and Inverse Problems in scientific applications. Specifically, we investigate the effectiveness of Bayesian methods, such as Hamiltonian Monte Carlo (HMC) and Monte-Carlo Dropout (MCD), and a more conventional approach, Deep Ensembles (DE). To illustrate their performance, we take two canonical PDEs: Burger's equation and the Navier-Stokes equation. Our results indicate that Neural PDEs can effectively reconstruct flow systems and predict the associated unknown parameters. However, it is noteworthy that the results derived from Bayesian methods, based on our observations, tend to display a higher degree of certainty in their predictions as compared to those obtained using the DE. This elevated certainty in predictions suggests that Bayesian techniques might underestimate the true underlying uncertainty, thereby appearing more confident in their predictions than the DE approach.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/324225df6c472ba289161cf56e887dc238c4113a" target='_blank'>Evaluating Uncertainty Quantification approaches for Neural PDEs in scientific applications</a></td>
-          <td>
-            Vardhan Dongre, G. S. Hora
-          </td>
-          <td>2023-11-08</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="We propose a physics-informed machine learning method for uncertainty quantification in high-dimensional inverse problems. In this method, the states and parameters of partial differential equations (PDEs) are approximated with truncated conditional Karhunen-Lo\`eve expansions (CKLEs), which, by construction, match the measurements of the respective variables. The maximum a posteriori (MAP) solution of the inverse problem is formulated as a minimization problem over CKLE coefficients where the loss function is the sum of the norm of PDE residuals and the $\ell_2$ regularization term. This MAP formulation is known as the physics-informed CKLE (PICKLE) method. Uncertainty in the inverse solution is quantified in terms of the posterior distribution of CKLE coefficients, and we sample the posterior by solving a randomized PICKLE minimization problem, formulated by adding zero-mean Gaussian perturbations in the PICKLE loss function. We call the proposed approach the randomized PICKLE (rPICKLE) method. For linear and low-dimensional nonlinear problems (15 CKLE parameters), we show analytically and through comparison with Hamiltonian Monte Carlo (HMC) that the rPICKLE posterior converges to the true posterior given by the Bayes rule. For high-dimensional non-linear problems with 2000 CKLE parameters, we numerically demonstrate that rPICKLE posteriors are highly informative--they provide mean estimates with an accuracy comparable to the estimates given by the MAP solution and the confidence interval that mostly covers the reference solution. We are not able to obtain the HMC posterior to validate rPICKLE's convergence to the true posterior due to the HMC's prohibitive computational cost for the considered high-dimensional problems. Our results demonstrate the advantages of rPICKLE over HMC for approximately sampling high-dimensional posterior distributions subject to physics constraints.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/32a4a1f68e10300155d56575e646783c48d915e9" target='_blank'>Randomized Physics-Informed Machine Learning for Uncertainty Quantification in High-Dimensional Inverse Problems</a></td>
-          <td>
-            Yifei Zong, D. Barajas-Solano, A. Tartakovsky
-          </td>
-          <td>2023-12-11</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>41</td>
-        </tr>
-    
-        <tr id="Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive proposition. In this work, a new physics-constrained neural network (NN) approach is proposed to solve PDEs without labels, with a view to enabling high-throughput solutions in support of design and decision-making. Distinct from existing physics-informed NN approaches, where the strong form or weak form of PDEs are used to construct the loss function, we write the loss function of NNs based on the discretized residual of PDEs through an efficient, convolutional operator-based, and vectorized implementation. We explore an encoder-decoder NN structure for both deterministic and probabilistic models, with Bayesian NNs (BNNs) for the latter, which allow us to quantify both epistemic uncertainty from model parameters and aleatoric uncertainty from noise in the data. For BNNs, the discretized residual is used to construct the likelihood function. In our approach, both deterministic and probabilistic convolutional layers are used to learn the applied boundary conditions (BCs) and to detect the problem domain. As both Dirichlet and Neumann BCs are specified as inputs to NNs, a single NN can solve for similar physics, but with different BCs and on a number of problem domains. The trained surrogate PDE solvers can also make interpolating and extrapolating (to a certain extent) predictions for BCs that they were not exposed to during training. Such surrogate models are of particular importance for problems, where similar types of PDEs need to be repeatedly solved for many times with slight variations. We demonstrate the capability and performance of the proposed framework by applying it to steady-state diffusion, linear elasticity, and nonlinear elasticity.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/76ecfab6c86d2936af3b8017a9c9cc8431e2fd38" target='_blank'>Bayesian neural networks for weak solution of PDEs with uncertainty quantification</a></td>
-          <td>
-            Xiaoxuan Zhang, K. Garikipati
-          </td>
-          <td>2021-01-13</td>
-          <td>ArXiv</td>
-          <td>10</td>
-          <td>32</td>
-        </tr>
-    
-        <tr id="Physics-informed extreme learning machine (PIELM) has recently received significant attention as a rapid version of physics-informed neural network (PINN) for solving partial differential equations (PDEs). The key characteristic is to fix the input layer weights with random values and use Moore-Penrose generalized inverse for the output layer weights. The framework is effective, but it easily suffers from overfitting noisy data and lacks uncertainty quantification for the solution under noise scenarios.To this end, we develop the Bayesian physics-informed extreme learning machine (BPIELM) to solve both forward and inverse linear PDE problems with noisy data in a unified framework. In our framework, a prior probability distribution is introduced in the output layer for extreme learning machine with physic laws and the Bayesian method is used to estimate the posterior of parameters. Besides, for inverse PDE problems, problem parameters considered as new output layer weights are unified in a framework with forward PDE problems. Finally, we demonstrate BPIELM considering both forward problems, including Poisson, advection, and diffusion equations, as well as inverse problems, where unknown problem parameters are estimated. The results show that, compared with PIELM, BPIELM quantifies uncertainty arising from noisy data and provides more accurate predictions. In addition, BPIELM is considerably cheaper than PINN in terms of the computational cost.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ee761f28e0b2f4ab684a69d8562e4a7efe23e315" target='_blank'>Bayesian Physics-Informed Extreme Learning Machine for Forward and Inverse PDE Problems with Noisy Data</a></td>
-          <td>
-            Xu Liu, Wenjuan Yao, Wei Peng, Weien Zhou
-          </td>
-          <td>2022-05-14</td>
-          <td>Neurocomputing</td>
-          <td>10</td>
-          <td>40</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/389a0c21dc435dce516b7a28246f7e236b89b84d" target='_blank'>Learning Functional Priors and Posteriors from Data and Physics</a></td>
-          <td>
-            Xuhui Meng, Liu Yang, Zhiping Mao, J. Ferrandis, G. Karniadakis
-          </td>
-          <td>2021-06-08</td>
-          <td>J. Comput. Phys.</td>
-          <td>45</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a neural network-based surrogate model for the unknown state, PINNs can seamlessly blend measurement data with physical constraints. Here, we extend this framework to PDE-constrained optimal control problems, for which the governing PDE is fully known and the goal is to find a control variable that minimizes a desired cost objective. We provide a set of guidelines for obtaining a good optimal control solution; first by selecting an appropriate PINN architecture and training parameters based on a forward problem, second by choosing the best value for a critical scalar weight in the loss function using a simple but effective two-step line search strategy. We then validate the performance of the PINN framework by comparing it to adjoint-based nonlinear optimal control, which performs gradient descent on the discretized control variable while satisfying the discretized PDE. This comparison is carried out on several distributed control examples based on the Laplace, Burgers, Kuramoto-Sivashinsky, and Navier-Stokes equations. Finally, we discuss the advantages and caveats of using the PINN and adjoint-based approaches for solving optimal control problems constrained by nonlinear PDEs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0638f1dbd048064045296134674beb423a4ade89" target='_blank'>Optimal control of PDEs using physics-informed neural networks</a></td>
-          <td>
-            S. Mowlavi, S. Nabi
-          </td>
-          <td>2021-11-18</td>
-          <td>J. Comput. Phys.</td>
-          <td>50</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a neural network-based surrogate model for the unknown state, PINNs can seamlessly blend measurement data with physical constraints. Here, we extend this framework to PDE-constrained optimal control problems, for which the governing PDE is fully known and the goal is to find a control variable that minimizes a desired cost objective. We provide a set of guidelines for obtaining a good optimal control solution; first by selecting an appropriate PINN architecture and training parameters based on a forward problem, second by choosing the best value for a critical scalar weight in the loss function using a simple but effective two-step line search strategy. We then validate the performance of the PINN framework by comparing it to adjoint-based nonlinear optimal control, which performs gradient descent on the discretized control variable while satisfying the discretized PDE. This comparison is carried out on several distributed control examples based on the Laplace, Burgers, Kuramoto-Sivashinsky, and Navier-Stokes equations. Finally, we discuss the advantages and caveats of using the PINN and adjoint-based approaches for solving optimal control problems constrained by nonlinear PDEs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0638f1dbd048064045296134674beb423a4ade89" target='_blank'>Optimal control of PDEs using physics-informed neural networks</a></td>
-          <td>
-            S. Mowlavi, S. Nabi
-          </td>
-          <td>2021-11-18</td>
-          <td>J. Comput. Phys.</td>
-          <td>50</td>
-          <td>11</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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diff --git a/docs/recommendations/ae42c0cff384495683192b06bd985cdd7a54632a.md b/docs/recommendations/ae42c0cff384495683192b06bd985cdd7a54632a.md
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Interaction Networks for Learning about Objects, Relations and Physics</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Humans have a remarkable capacity to understand the physical dynamics of objects in their environment, flexibly capturing complex structures and interactions at multiple levels of detail. Inspired by this ability, we propose a hierarchical particle-based object representation that covers a wide variety of types of three-dimensional objects, including both arbitrary rigid geometrical shapes and deformable materials. We then describe the Hierarchical Relation Network (HRN), an end-to-end differentiable neural network based on hierarchical graph convolution, that learns to predict physical dynamics in this representation. Compared to other neural network baselines, the HRN accurately handles complex collisions and nonrigid deformations, generating plausible dynamics predictions at long time scales in novel settings, and scaling to large scene configurations. These results demonstrate an architecture with the potential to form the basis of next-generation physics predictors for use in computer vision, robotics, and quantitative cognitive science.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d7c2c9c6900f8b637654d220be481eebf22187b1" target='_blank'>Flexible Neural Representation for Physics Prediction</a></td>
-          <td>
-            Damian Mrowca, Chengxu Zhuang, E. Wang, Nick Haber, Li Fei-Fei, J. Tenenbaum, Daniel Yamins
-          </td>
-          <td>2018-06-01</td>
-          <td>ArXiv</td>
-          <td>226</td>
-          <td>130</td>
-        </tr>
-    
-        <tr id="We present the Neural Physics Engine (NPE), a framework for learning simulators of intuitive physics that naturally generalize across variable object count and different scene configurations. We propose a factorization of a physical scene into composable object-based representations and a neural network architecture whose compositional structure factorizes object dynamics into pairwise interactions. Like a symbolic physics engine, the NPE is endowed with generic notions of objects and their interactions; realized as a neural network, it can be trained via stochastic gradient descent to adapt to specific object properties and dynamics of different worlds. We evaluate the efficacy of our approach on simple rigid body dynamics in two-dimensional worlds. By comparing to less structured architectures, we show that the NPE's compositional representation of the structure in physical interactions improves its ability to predict movement, generalize across variable object count and different scene configurations, and infer latent properties of objects such as mass.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a1786540a4e15f0757e1b84a02f98ed436a969e0" target='_blank'>A Compositional Object-Based Approach to Learning Physical Dynamics</a></td>
-          <td>
-            Michael Chang, T. Ullman, A. Torralba, J. Tenenbaum
-          </td>
-          <td>2016-11-04</td>
-          <td>ArXiv</td>
-          <td>417</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="We introduce an approach for imposing physically motivated inductive biases on graph networks to learn interpretable representations and improved zero-shot generalization. Our experiments show that our graph network models, which implement this inductive bias, can learn message representations equivalent to the true force vector when trained on n-body gravitational and spring-like simulations. We use symbolic regression to fit explicit algebraic equations to our trained model's message function and recover the symbolic form of Newton's law of gravitation without prior knowledge. We also show that our model generalizes better at inference time to systems with more bodies than had been experienced during training. Our approach is extensible, in principle, to any unknown interaction law learned by a graph network, and offers a valuable technique for interpreting and inferring explicit causal theories about the world from implicit knowledge captured by deep learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a6aad9ccdcb7674a3b7ab710f0a80d205834f847" target='_blank'>Learning Symbolic Physics with Graph Networks</a></td>
-          <td>
-            M. Cranmer, Rui Xu, P. Battaglia, S. Ho
-          </td>
-          <td>2019-09-12</td>
-          <td>ArXiv</td>
-          <td>77</td>
-          <td>68</td>
-        </tr>
-    
-        <tr id="Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new class of learnable models--based on graph networks--which implement an inductive bias for object- and relation-centric representations of complex, dynamical systems. Our results show that as a forward model, our approach supports accurate predictions from real and simulated data, and surprisingly strong and efficient generalization, across eight distinct physical systems which we varied parametrically and structurally. We also found that our inference model can perform system identification. Our models are also differentiable, and support online planning via gradient-based trajectory optimization, as well as offline policy optimization. Our framework offers new opportunities for harnessing and exploiting rich knowledge about the world, and takes a key step toward building machines with more human-like representations of the world.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/43879cf527f4918955fd55128baa6745174d8555" target='_blank'>Graph networks as learnable physics engines for inference and control</a></td>
-          <td>
-            Alvaro Sanchez-Gonzalez, N. Heess, J. T. Springenberg, J. Merel, Martin A. Riedmiller, R. Hadsell, P. Battaglia
-          </td>
-          <td>2018-06-04</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>550</td>
-          <td>62</td>
-        </tr>
-    
-        <tr id="Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are challenging to learn due to the presence of nonlinear potentials and a number of interactions that scales quadratically with the number of particles N, as in the case of the N-body problem. In this work we introduce an approach that transforms a fully-connected interaction graph into a hierarchical one which reduces the number of edges to O(N). This results in a linear time and space complexity while the pre-computation of the hierarchical graph requires O(N log (N)) time and O(N) space. Using our approach, we are able to train models on much larger particle counts, even on a single GPU. We evaluate how the phase space position accuracy and energy conservation depend on the number of simulated particles. Our approach retains high accuracy and efficiency even on large-scale gravitational N-body simulations which are impossible to run on a single machine if a fully-connected graph is used. Similar results are also observed when simulating Coulomb interactions. Furthermore, we make several important observations regarding the performance of this new hierarchical model, including: i) its accuracy tends to improve with the number of particles in the simulation and ii) its generalisation to unseen particle counts is also much better than for models that use all O(N^2) interactions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/56f6708f22cbedcc1c600d78408bfbb46669d483" target='_blank'>Scalable Graph Networks for Particle Simulations</a></td>
-          <td>
-            Karolis Martinkus, Aurélien Lucchi, Nathanael Perraudin
-          </td>
-          <td>2020-10-14</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>10</td>
-          <td>39</td>
-        </tr>
-    
-        <tr id="We introduce the Continuum Physical Dataset (ContPhy), a novel benchmark for assessing machine physical commonsense. ContPhy complements existing physical reasoning benchmarks by encompassing the inference of diverse physical properties, such as mass and density, across various scenarios and predicting corresponding dynamics. We evaluated a range of AI models and found that they still struggle to achieve satisfactory performance on ContPhy, which shows that the current AI models still lack physical commonsense for the continuum, especially soft-bodies, and illustrates the value of the proposed dataset. We also introduce an oracle model (ContPRO) that marries the particle-based physical dynamic models with the recent large language models, which enjoy the advantages of both models, precise dynamic predictions, and interpretable reasoning. ContPhy aims to spur progress in perception and reasoning within diverse physical settings, narrowing the divide between human and machine intelligence in understanding the physical world. Project page: https://physical-reasoning-project.github.io.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/637b28b5c8283b2118b7bc0aabae6f4795bbee67" target='_blank'>ContPhy: Continuum Physical Concept Learning and Reasoning from Videos</a></td>
-          <td>
-            Zhicheng Zheng, Xin Yan, Zhenfang Chen, Jingzhou Wang, Qin Zhi Eddie Lim, J. B. Tenenbaum, Chuang Gan
-          </td>
-          <td>2024-02-09</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>17</td>
-        </tr>
-    
-        <tr id="Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term "Graph Network-based Simulators" (GNS)---represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c529f5b08675f787cdcc094ee495239592339f82" target='_blank'>Learning to Simulate Complex Physics with Graph Networks</a></td>
-          <td>
-            Alvaro Sanchez-Gonzalez, Jonathan Godwin, T. Pfaff, Rex Ying, J. Leskovec, P. Battaglia
-          </td>
-          <td>2020-02-21</td>
-          <td>ArXiv</td>
-          <td>849</td>
-          <td>134</td>
-        </tr>
-    
-        <tr id="Despite the success of neural networks at solving concrete physics problems, their use as a general-purpose tool for scientific discovery is still in its infancy. Here, we approach this problem by modeling a neural network architecture after the human physical reasoning process, which has similarities to representation learning. This allows us to make progress towards the long-term goal of machine-assisted scientific discovery from experimental data without making prior assumptions about the system. We apply this method to toy examples and show that the network finds the physically relevant parameters, exploits conservation laws to make predictions, and can help to gain conceptual insights, e.g., Copernicus' conclusion that the solar system is heliocentric.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7b2e20a3cdf96fc0bcddf6bd6576e5d5e09f17ec" target='_blank'>Discovering physical concepts with neural networks</a></td>
-          <td>
-            Raban Iten, Tony Metger, H. Wilming, L. D. Rio, R. Renner
-          </td>
-          <td>2018-07-27</td>
-          <td>Physical review letters</td>
-          <td>355</td>
-          <td>69</td>
-        </tr>
-    
-        <tr id="Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d7952de05e25e90a08b79431116ca6d2ec85e710" target='_blank'>Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems</a></td>
-          <td>
-            A. Thangamuthu, Gunjan Kumar, S. Bishnoi, Ravinder Bhattoo, N. Krishnan, Sayan Ranu
-          </td>
-          <td>2022-11-10</td>
-          <td>ArXiv</td>
-          <td>12</td>
-          <td>21</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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diff --git a/docs/recommendations/af84c6db6b5c41ca628867ff4a27566e9ca3c69e.md b/docs/recommendations/af84c6db6b5c41ca628867ff4a27566e9ca3c69e.md
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-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE. In our model, the layer structure and topology correspond to the discretisation choices of temporal and spatial operators. Our approach allows a principled development of a broad new class of GNNs that are able to address the common plights of graph learning models such as depth, oversmoothing, and bottlenecks. Key to the success of our models are stability with respect to perturbations in the data and this is addressed for both implicit and explicit discretisation schemes. We develop linear and nonlinear versions of GRAND, which achieve competitive results on many standard graph benchmarks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/95eee51c1cb1771e96cd182f47c90a7877461530" target='_blank'>GRAND: Graph Neural Diffusion</a></td>
-          <td>
-            B. Chamberlain, J. Rowbottom, Maria I. Gorinova, Stefan Webb, Emanuele Rossi, M. Bronstein
-          </td>
-          <td>2021-06-21</td>
-          <td>ArXiv</td>
-          <td>199</td>
-          <td>76</td>
-        </tr>
-    
-        <tr id="We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and graph connectivity patterns. Second, we model a tangent multilayer perceptron by transferring ideas from the vector neuron framework to our general setting. Both layers are equivariant with respect to node permutations and isometries of the feature manifold. These properties have been shown to lead to a beneficial inductive bias in many deep learning tasks. Numerical examples on synthetic data as well as on triangle meshes of the right hippocampus to classify Alzheimer's disease demonstrate the very good performance of our layers.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ed6e3428dea2bd0623d3f875deb7385f0b5f49d6" target='_blank'>Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs</a></td>
-          <td>
-            M. Hanik, Gabriele Steidl, C. V. Tycowicz
-          </td>
-          <td>2024-01-25</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>13</td>
-        </tr>
-    
-        <tr id="Information over-squashing is a phenomenon of inefficient information propagation between distant nodes on networks. It is an important problem that is known to significantly impact the training of graph neural networks (GNNs), as the receptive field of a node grows exponentially. To mitigate this problem, a preprocessing procedure known as rewiring is often applied to the input network. In this paper, we investigate the use of discrete analogues of classical geometric notions of curvature to model information flow on networks and rewire them. We show that these classical notions achieve state-of-the-art performance in GNN training accuracy on a variety of real-world network datasets. Moreover, compared to the current state-of-the-art, these classical notions exhibit a clear advantage in computational runtime by several orders of magnitude.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f299132e9393e19a909a7f2aa89075f2261bcd84" target='_blank'>Rewiring Networks for Graph Neural Network Training Using Discrete Geometry</a></td>
-          <td>
-            Jakub Bober, Anthea Monod, Emil Saucan, K. Webster
-          </td>
-          <td>2022-07-16</td>
-          <td>ArXiv</td>
-          <td>10</td>
-          <td>19</td>
-        </tr>
-    
-        <tr id="Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural networks (GNNs), such as the problems of over-smoothing and bottlenecks, has been investigated but not their robustness to adversarial attacks. In this work, we explore the robustness properties of graph neural PDEs. We empirically demonstrate that graph neural PDEs are intrinsically more robust against topology perturbation as compared to other GNNs. We provide insights into this phenomenon by exploiting the stability of the heat semigroup under graph topology perturbations. We discuss various graph diffusion operators and relate them to existing graph neural PDEs. Furthermore, we propose a general graph neural PDE framework based on which a new class of robust GNNs can be defined. We verify that the new model achieves comparable state-of-the-art performance on several benchmark datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/489da8995c34704bb285d902d73c938c7bc4dd4e" target='_blank'>On the Robustness of Graph Neural Diffusion to Topology Perturbations</a></td>
-          <td>
-            Yang Song, Qiyu Kang, Sijie Wang, Zhao Kai, Wee Peng Tay
-          </td>
-          <td>2022-09-16</td>
-          <td>ArXiv</td>
-          <td>23</td>
-          <td>30</td>
-        </tr>
-    
-        <tr id="A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to ensure efficient and accurate long-distance communication between nodes, as deep convolutional networks are prone to oversmoothing. In this paper, we present a novel method based on time derivative graph diffusion (TIDE) to overcome these structural limitations of the message-passing framework. Our approach allows for optimizing the spatial extent of diffusion across various tasks and network channels, thus enabling medium and long-distance communication efficiently. Furthermore, we show that our architecture design also enables local message-passing and thus inherits from the capabilities of local message-passing approaches. We show that on both widely used graph benchmarks and synthetic mesh and graph datasets, the proposed framework outperforms state-of-the-art methods by a significant margin">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/96d2ac139c1d305d597fb6533db893f2231fecc6" target='_blank'>TIDE: Time Derivative Diffusion for Deep Learning on Graphs</a></td>
-          <td>
-            Maximilian Krahn, M. Behmanesh, M. Ovsjanikov
-          </td>
-          <td>2022-12-05</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>43</td>
-        </tr>
-    
-        <tr id="This paper builds on the connection between graph neural networks and traditional dynamical systems. We propose continuous graph neural networks (CGNN), which generalise existing graph neural networks with discrete dynamics in that they can be viewed as a specific discretisation scheme. The key idea is how to characterise the continuous dynamics of node representations, i.e. the derivatives of node representations, w.r.t. time. Inspired by existing diffusion-based methods on graphs (e.g. PageRank and epidemic models on social networks), we define the derivatives as a combination of the current node representations, the representations of neighbors, and the initial values of the nodes. We propose and analyse two possible dynamics on graphs---including each dimension of node representations (a.k.a. the feature channel) change independently or interact with each other---both with theoretical justification. The proposed continuous graph neural networks are robust to over-smoothing and hence allow us to build deeper networks, which in turn are able to capture the long-range dependencies between nodes. Experimental results on the task of node classification demonstrate the effectiveness of our proposed approach over competitive baselines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/903d62dccc969f5e6642d89fc746b94de7e8c1af" target='_blank'>Continuous Graph Neural Networks</a></td>
-          <td>
-            Louis-Pascal Xhonneux, Meng Qu, Jian Tang
-          </td>
-          <td>2019-12-02</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>120</td>
-          <td>40</td>
-        </tr>
-    
-        <tr id="Neural message passing is a basic feature extraction unit for graph-structured data considering neighboring node features in network propagation from one layer to the next. We model such process by an interacting particle system with attractive and repulsive forces and the Allen-Cahn force arising in the modeling of phase transition. The dynamics of the system is a reaction-diffusion process which can separate particles without blowing up. This induces an Allen-Cahn message passing (ACMP) for graph neural networks where the numerical iteration for the particle system solution constitutes the message passing propagation. ACMP which has a simple implementation with a neural ODE solver can propel the network depth up to one hundred of layers with theoretically proven strictly positive lower bound of the Dirichlet energy. It thus provides a deep model of GNNs circumventing the common GNN problem of oversmoothing. GNNs with ACMP achieve state of the art performance for real-world node classification tasks on both homophilic and heterophilic datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fea03f338db94581753f9588bd07937996aee63d" target='_blank'>ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks</a></td>
-          <td>
-            Yuelin Wang, Kai Yi, Xinliang Liu, Yu Guang Wang, Shi Jin
-          </td>
-          <td>2022-06-11</td>
-          <td>ArXiv, DBLP</td>
-          <td>24</td>
-          <td>15</td>
-        </tr>
-    
-        <tr id="Graph neural networks (GNNs) are widely used in domains like social networks and biological systems. However, the locality assumption of GNNs, which limits information exchange to neighboring nodes, hampers their ability to capture long-range dependencies and global patterns in graphs. To address this, we propose a new inductive bias based on variational analysis, drawing inspiration from the Brachistochrone problem. Our framework establishes a mapping between discrete GNN models and continuous diffusion functionals. This enables the design of application-specific objective functions in the continuous domain and the construction of discrete deep models with mathematical guarantees. To tackle over-smoothing in GNNs, we analyze the existing layer-by-layer graph embedding models and identify that they are equivalent to l2-norm integral functionals of graph gradients, which cause over-smoothing. Similar to edge-preserving filters in image denoising, we introduce total variation (TV) to align the graph diffusion pattern with global community topologies. Additionally, we devise a selective mechanism to address the trade-off between model depth and over-smoothing, which can be easily integrated into existing GNNs. Furthermore, we propose a novel generative adversarial network (GAN) that predicts spreading flows in graphs through a neural transport equation. To mitigate vanishing flows, we customize the objective function to minimize transportation within each community while maximizing inter-community flows. Our GNN models achieve state-of-the-art (SOTA) performance on popular graph learning benchmarks such as Cora, Citeseer, and Pubmed.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/827643cf750b714a74ed70ac949178b7de5a30a9" target='_blank'>Re-Think and Re-Design Graph Neural Networks in Spaces of Continuous Graph Diffusion Functionals</a></td>
-          <td>
-            Tingting Dan, Jiaqi Ding, Ziquan Wei, S. Kovalsky, Minjeong Kim, Won Hwa Kim, Guorong Wu
-          </td>
-          <td>2023-07-01</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>39</td>
-        </tr>
-    
-        <tr id="While Hyperbolic Graph Neural Network (HGNN) has recently emerged as a powerful tool dealing with hierarchical graph data, the limitations of scalability and efficiency hinder itself from generalizing to deep models. In this paper, by envisioning depth as a continuous-time embedding evolution, we decouple the HGNN and reframe the information propagation as a partial differential equation, letting node-wise attention undertake the role of diffusivity within the Hyperbolic Neural PDE (HPDE). By introducing theoretical principles \textit{e.g.,} field and flow, gradient, divergence, and diffusivity on a non-Euclidean manifold for HPDE integration, we discuss both implicit and explicit discretization schemes to formulate numerical HPDE solvers. Further, we propose the Hyperbolic Graph Diffusion Equation (HGDE) -- a flexible vector flow function that can be integrated to obtain expressive hyperbolic node embeddings. By analyzing potential energy decay of embeddings, we demonstrate that HGDE is capable of modeling both low- and high-order proximity with the benefit of local-global diffusivity functions. Experiments on node classification and link prediction and image-text classification tasks verify the superiority of the proposed method, which consistently outperforms various competitive models by a significant margin.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d4909dc88aef0484f13041239c784ab5413b8e83" target='_blank'>Continuous Geometry-Aware Graph Diffusion via Hyperbolic Neural PDE</a></td>
-          <td>
-            Jiaxu Liu, Xinping Yi, Sihao Wu, Xiangyu Yin, Tianle Zhang, Xiaowei Huang, Shi Jin
-          </td>
-          <td>2024-06-03</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>2</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Sparse identification of nonlinear dynamics for model predictive control in the low-data limit</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based optimization technique that enables the control of such nonlinear systems with constraints. However, modern systems often lack computationally tractable models, motivating the use of system identification techniques to learn accurate and efficient models for real-time control. In this tutorial article, we review emerging data-driven methods for model discovery and how they are used for nonlinear MPC. In particular, we focus on the sparse identification of nonlinear dynamics (SINDy) algorithm and show how it may be used with MPC on an infectious disease control example. We compare the performance against MPC based on a linear dynamic mode decomposition (DMD) model. Code is provided to run the tutorial examples and may be modified to extend this data-driven control framework to arbitrary nonlinear systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/700552dde778bd1f6b76f7237e9b561597b859ba" target='_blank'>SINDy with Control: A Tutorial</a></td>
-          <td>
-            Urban Fasel, E. Kaiser, J. Kutz, Bingni W. Brunton, S. Brunton
-          </td>
-          <td>2021-08-30</td>
-          <td>2021 60th IEEE Conference on Decision and Control (CDC)</td>
-          <td>45</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/99877062e70fae24c531d58aa880fa443ec10c9b" target='_blank'>SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study</a></td>
-          <td>
-            Aurelio Raffa Ugolini, Valentina Breschi, Andrea Manzoni, M. Tanelli
-          </td>
-          <td>2024-03-01</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Data-driven modeling frameworks that adopt sparse regression techniques, such as sparse identification of nonlinear dynamics (SINDy) and its modifications, are developed to resolve difficulties in extracting underlying dynamics from experimental data. In contrast to neural-network-based methods, these methods are designed to obtain white-box analytical models. In this work, we incorporate the concept of SINDy and knowledge in the field of classical mechanics to identify interpretable and sparse expressions of total energy and the Lagrangian that shelters the hidden dynamics. Moreover, our method (hereafter referred as Lagrangian-SINDy) is developed to use knowledge of simple systems that form the system being analyzed to ensure the likelihood of correct results and to improve the learning pace. Lagrangian-SINDy is highly accurate in discovering interpretable dynamics via energy-related physical quantities. Its performance is validated with three popular multi-DOF nonlinear dynamical systems, namely the spherical pendulum, double pendulum and cart-pendulum system. Comparisons with other SINDy-based methods are made and Lagrangian-SINDy is found to provide the most compact analytical models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7d7e107bcb40ed9596642ff12cc60f33f3eb47e2" target='_blank'>Discovering Interpretable Dynamics by Sparsity Promotion on Energy and the Lagrangian</a></td>
-          <td>
-            H. Chu, M. Hayashibe
-          </td>
-          <td>2020-01-31</td>
-          <td>IEEE Robotics and Automation Letters</td>
-          <td>23</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov–Zhabotinsky (BZ) reaction.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4971f9abd024e40fbbdff2e9492745b68a6bca01" target='_blank'>SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics</a></td>
-          <td>
-            Kadierdan Kaheman, J. Kutz, S. Brunton
-          </td>
-          <td>2020-04-05</td>
-          <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>190</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that violate basic physical laws. This work proposes a novel method for the Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI). SINDy-SI is an iterative method that uses Sum-of-Squares (SOS) programming to learn optimally fitted models while guaranteeing that the learned model satisfies side information, such as symmetry's and physical laws. Guided by the principle of Occam's razor, that the simplest or most regularized best fitted model is typically the superior choice, during each iteration SINDy-SI prunes the basis functions associated with small coefficients, yielding a sparse dynamical model upon termination. Through several numerical experiments we will show how the combination of side information constraints and sparse polynomial representation cultivates dynamical models that obey known physical laws while displaying impressive generalized performance beyond the training set.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/13a6b8f2d60ef8006dfe6e6bed42df96f773a323" target='_blank'>Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI)</a></td>
-          <td>
-            Gabriel F. Machado, Morgan Jones
-          </td>
-          <td>2023-10-06</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized systems, SINDy requires data from transient trajectories for various parameter values over the range of interest, which are typically difficult to acquire experimentally. In this work, we extend SINDy to be able to leverage data on fixed points and/or limit cycles to reduce the number of transient trajectories needed for successful system identification. To achieve this, we incorporate the data on these attractors at various parameter values as constraints in the optimization problem. First, we show that enforcing these as hard constraints leads to an ill-conditioned regression problem due to the large number of constraints. Instead, we implement soft constraints by modifying the cost function to be minimized. This leads to the formulation of a multi-objective sparse regression problem where we simultaneously seek to minimize the error of the fit to the transients trajectories and to the data on attractors, while penalizing the number of terms in the model. Our extension, demonstrated on several numerical examples, is more robust to noisy measurements and requires substantially less training data than the original SINDy method to correctly identify a parameterized dynamical system.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0c03c126b4d641a81099470f03a7d5215a2a6820" target='_blank'>Multi-objective SINDy for parameterized model discovery from single transient trajectory data</a></td>
-          <td>
-            Javier A. Lemus, Benjamin Herrmann
-          </td>
-          <td>2024-05-14</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="Significance Understanding dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled technology, including aircraft, combustion engines, satellites, and electrical power. This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. There are many critical data-driven problems, such as understanding cognition from neural recordings, inferring climate patterns, determining stability of financial markets, predicting and suppressing the spread of disease, and controlling turbulence for greener transportation and energy. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an important role in these efforts. Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5d150cec2775f9bc863760448f14104cc8f42368" target='_blank'>Discovering governing equations from data by sparse identification of nonlinear dynamical systems</a></td>
-          <td>
-            S. Brunton, J. Proctor, J. Kutz
-          </td>
-          <td>2015-09-11</td>
-          <td>Proceedings of the National Academy of Sciences</td>
-          <td>3168</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/433ba35ced5d3f47fa2688c81a60363a74193449" target='_blank'>PySINDy: A comprehensive Python package for robust sparse system identification</a></td>
-          <td>
-            A. Kaptanoglu, Brian M. de Silva, Urban Fasel, Kadierdan Kaheman, Jared L. Callaham, Charles B. Delahunt, Kathleen P. Champion, Jean-Christophe Loiseau, J. Kutz, S. Brunton
-          </td>
-          <td>2021-11-12</td>
-          <td>J. Open Source Softw.</td>
-          <td>109</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="We develop a principled mathematical framework for controlling nonlinear, networked dynamical systems. Our method integrates dimensionality reduction, bifurcation theory, and emerging model discovery tools to find low-dimensional subspaces where feed-forward control can be used to manipulate a system to a desired outcome. The method leverages the fact that many high-dimensional networked systems have many fixed points, allowing for the computation of control signals that will move the system between any pair of fixed points. The sparse identification of nonlinear dynamics (SINDy) algorithm is used to fit a nonlinear dynamical system to the evolution on the dominant, low-rank subspace. This then allows us to use bifurcation theory to find collections of constant control signals that will produce the desired objective path for a prescribed outcome. Specifically, we can destabilize a given fixed point while making the target fixed point an attractor. The discovered control signals can be easily projected back to the original high-dimensional state and control space. We illustrate our nonlinear control procedure on established bistable, low-dimensional biological systems, showing how control signals are found that generate switches between the fixed points. We then demonstrate our control procedure for high-dimensional systems on random high-dimensional networks and Hopfield memory networks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4b849d45b437a09d1ea5321a304c5bc411bf3de4" target='_blank'>Nonlinear Control of Networked Dynamical Systems</a></td>
-          <td>
-            Megan Morrison, Nathan Kutz
-          </td>
-          <td>2020-06-09</td>
-          <td>IEEE Transactions on Network Science and Engineering</td>
-          <td>10</td>
-          <td>5</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/899995e30820d657b2e2feb791025cd6b2027e22" target='_blank'>Discovering sparse interpretable dynamics from partial observations</a></td>
-          <td>
-            Peter Y. Lu, Joan Ariño Bernad, M. Soljačić
-          </td>
-          <td>2021-07-22</td>
-          <td>Communications Physics</td>
-          <td>17</td>
-          <td>94</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Dissecting Neural ODEs</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Residual neural networks are state-of-the-art deep learning models. Their continuous-depth analog, neural ordinary differential equations (ODEs), are also widely used. Despite their success, the link between the discrete and continuous models still lacks a solid mathematical foundation. In this article, we take a step in this direction by establishing an implicit regularization of deep residual networks towards neural ODEs, for nonlinear networks trained with gradient flow. We prove that if the network is initialized as a discretization of a neural ODE, then such a discretization holds throughout training. Our results are valid for a finite training time, and also as the training time tends to infinity provided that the network satisfies a Polyak-Lojasiewicz condition. Importantly, this condition holds for a family of residual networks where the residuals are two-layer perceptrons with an overparameterization in width that is only linear, and implies the convergence of gradient flow to a global minimum. Numerical experiments illustrate our results.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5975aca3c006549e7fa57f050854ceb5474c61e0" target='_blank'>Implicit regularization of deep residual networks towards neural ODEs</a></td>
-          <td>
-            P. Marion, Yu-Han Wu, Michael E. Sander, G'erard Biau
-          </td>
-          <td>2023-09-03</td>
-          <td>ArXiv</td>
-          <td>10</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="This short, self-contained article seeks to introduce and survey continuous-time deep learning approaches that are based on neural ordinary differential equations (neural ODEs). It primarily targets readers familiar with ordinary and partial differential equations and their analysis who are curious to see their role in machine learning. Using three examples from machine learning and applied mathematics, we will see how neural ODEs can provide new insights into deep learning and a foundation for more efficient algorithms.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3579984410df7b486c162597584cc5179b9d3343" target='_blank'>Differential Equations for Continuous-Time Deep Learning</a></td>
-          <td>
-            Lars Ruthotto
-          </td>
-          <td>2024-01-08</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of recently introduced Recurrent Equilibrium Networks (RENs). We show how to endow our proposed NodeRENs with contractivity and dissipativity - crucial properties for robust learning and control. Most importantly, as for RENs, we derive parametrizations of contractive and dissipative NodeRENs which are unconstrained, hence enabling their learning for a large number of parameters. We validate the properties of NodeRENs, including the possibility of handling irregularly sampled data, in a case study in nonlinear system identification.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b40b7a44f7e4c1752ab4ed3d492869f5f9a91d02" target='_blank'>Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equations</a></td>
-          <td>
-            D. Martinelli, C. Galimberti, I. Manchester, Luca Furieri, Giancarlo Ferrari-Trecate
-          </td>
-          <td>2023-04-06</td>
-          <td>2023 62nd IEEE Conference on Decision and Control (CDC)</td>
-          <td>9</td>
-          <td>31</td>
-        </tr>
-    
-        <tr id="We show that Neural Ordinary Differential Equations (ODEs) learn representations that preserve the topology of the input space and prove that this implies the existence of functions Neural ODEs cannot represent. To address these limitations, we introduce Augmented Neural ODEs which, in addition to being more expressive models, are empirically more stable, generalize better and have a lower computational cost than Neural ODEs.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/31156009c49a88b5f0fb37437512eec570310d24" target='_blank'>Augmented Neural ODEs</a></td>
-          <td>
-            Emilien Dupont, A. Doucet, Y. Teh
-          </td>
-          <td>2019-04-02</td>
-          <td>ArXiv</td>
-          <td>535</td>
-          <td>81</td>
-        </tr>
-    
-        <tr id="To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View DNN as ODE discretization; (2) View the training of DNN as solving an optimal control problem. The former connection motivates people either to design neural architectures based on ODE discretization schemes or to replace DNN by a continuous model characterized by ODEs. Several works demonstrated distinct advantages of using a continuous model instead of traditional DNN in some specific applications. The latter connection is inspiring. Based on Pontryagin's maximum principle, which is popular in the optimal control literature, some developed new optimization methods for training neural networks and some developed algorithms to train the infinite-deep continuous model with low memory-cost. This paper is organized as follows: In Section 2, the relation between neural architecture and ODE discretization is introduced. Some architectures are not motivated by ODE, but they are later found to be associated with some specific discretization schemes. Some architectures are designed based on ODE discretization and expected to achieve some special properties. Section 3 formulates the optimization problem where a traditional neural network is replaced by a continuous model (ODE). The formulated optimization problem is an optimal control problem. Therefore, two different types of controls will also be discussed in this section. In Section 4, we will discuss how we can utilize the optimization methods that are popular in optimal control literature to help the training of machine learning problems. Finally, two applications of using a continuous model will be shown in Section 5 and 6 to demonstrate some of its advantages over traditional neural networks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/edb4f7042f4754db42dd2373ed9f77c841306376" target='_blank'>Review: Ordinary Differential Equations For Deep Learning</a></td>
-          <td>
-            Xinshi Chen
-          </td>
-          <td>2019-11-01</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="Deep neural networks have become invaluable tools for supervised machine learning, e.g. classification of text or images. While often offering superior results over traditional techniques and successfully expressing complicated patterns in data, deep architectures are known to be challenging to design and train such that they generalize well to new data. Critical issues with deep architectures are numerical instabilities in derivative-based learning algorithms commonly called exploding or vanishing gradients. In this paper, we propose new forward propagation techniques inspired by systems of ordinary differential equations (ODE) that overcome this challenge and lead to well-posed learning problems for arbitrarily deep networks. The backbone of our approach is our interpretation of deep learning as a parameter estimation problem of nonlinear dynamical systems. Given this formulation, we analyze stability and well-posedness of deep learning and use this new understanding to develop new network architectures. We relate the exploding and vanishing gradient phenomenon to the stability of the discrete ODE and present several strategies for stabilizing deep learning for very deep networks. While our new architectures restrict the solution space, several numerical experiments show their competitiveness with state-of-the-art networks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/37be889f4654312109dc9c53395fe117adb0f72b" target='_blank'>Stable architectures for deep neural networks</a></td>
-          <td>
-            E. Haber, Lars Ruthotto
-          </td>
-          <td>2017-05-09</td>
-          <td>Inverse Problems</td>
-          <td>642</td>
-          <td>45</td>
-        </tr>
-    
-        <tr id="Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs). In the context of machine learning, differentiable solvers are central for Neural ODEs (NODEs), a class of deep learning models with continuous depth, rather than discrete layers. However, these integrators can be unsatisfactorily slow and inaccurate when learning systems of ODEs from long sequences, or when solutions of the system vary at widely different timescales in each dimension. In this paper we propose an alternative approach to learning ODEs from data: we represent the underlying ODE as a vector field that is related to another base vector field by a differentiable bijection, modelled by an invertible neural network. By restricting the base ODE to be amenable to integration, we can drastically speed up and improve the robustness of integration. We demonstrate the efficacy of our method in training and evaluating continuous neural networks models, as well as in learning benchmark ODE systems. We observe improvements of up to two orders of magnitude when integrating learned ODEs with GPUs computation.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/32dd91add21327c9726a0fd74982182f3a9ffd00" target='_blank'>Learning ODEs via Diffeomorphisms for Fast and Robust Integration</a></td>
-          <td>
-            Weiming Zhi, Tin Lai, Lionel Ott, Edwin V. Bonilla, Fabio Ramos
-          </td>
-          <td>2021-07-04</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>26</td>
-        </tr>
-    
-        <tr id="Neural Ordinary Differential Equations (ODEs) are elegant reinterpretations of deep networks where continuous time can replace the discrete notion of depth, ODE solvers perform forward propagation, and the adjoint method enables efficient, constant memory backpropagation. Neural ODEs are universal approximators only when they are non-autonomous, that is, the dynamics depends explicitly on time. We propose a novel family of Neural ODEs with time-varying weights, where time-dependence is non-parametric, and the smoothness of weight trajectories can be explicitly controlled to allow a tradeoff between expressiveness and efficiency. Using this enhanced expressiveness, we outperform previous Neural ODE variants in both speed and representational capacity, ultimately outperforming standard ResNet and CNN models on select image classification and video prediction tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b3fe9f3ca944cea48d73544aa64c0e25f2e2a837" target='_blank'>Time Dependence in Non-Autonomous Neural ODEs</a></td>
-          <td>
-            Jared Davis, K. Choromanski, Jacob Varley, Honglak Lee, J. Slotine, Valerii Likhosterov, Adrian Weller, A. Makadia, Vikas Sindhwani
-          </td>
-          <td>2020-02-26</td>
-          <td>ArXiv</td>
-          <td>14</td>
-          <td>87</td>
-        </tr>
-    
-        <tr id="We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/449310e3538b08b43227d660227dfd2875c3c3c1" target='_blank'>Neural Ordinary Differential Equations</a></td>
-          <td>
-            T. Chen, Yulia Rubanova, J. Bettencourt, D. Duvenaud
-          </td>
-          <td>2018-06-19</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>3942</td>
-          <td>48</td>
-        </tr>
-    
-  </tbody>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <i class="footer">This page was last updated on 2024-07-22 06:06:38 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Variational Approach for Learning Markov Processes from Time Series Data</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Abstract Transfer operators such as Perron–Frobenius and Koopman operator play a key role in modeling and analysis of complex dynamical systems, which allow linear representations of nonlinear dynamics by transforming the original state variables to feature spaces. However, it remains challenging to identify the optimal low-dimensional feature mappings from data. The variational approach for Markov processes (VAMP) provides a comprehensive framework for the evaluation and optimization of feature mappings based on the variational estimation of modeling errors, but it still suffers from a flawed assumption on the transfer operator and therefore sometimes fails to capture the essential structure of system dynamics. In this paper, we develop a powerful alternative to VAMP, called kernel embedding based variational approach for dynamical systems (KVAD). By using the distance measure of functions in the kernel embedding space, KVAD effectively overcomes theoretical and practical limitations of VAMP. In addition, we develop a data-driven KVAD algorithm for seeking the ideal feature mapping within a subspace spanned by given basis functions, and numerical experiments show that the proposed algorithm can significantly improve the modeling accuracy compared to VAMP.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/57e2a99eaae34cc67acf8d0203cf44493ccdecd3" target='_blank'>Kernel Embedding Based Variational Approach for Low-Dimensional Approximation of Dynamical Systems</a></td>
-          <td>
-            Wenchong Tian, Hao Wu
-          </td>
-          <td>2020-08-07</td>
-          <td>Computational Methods in Applied Mathematics</td>
-          <td>11</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="The long-timescale behavior of complex dynamical systems can be described by linear Markov or Koopman models in a suitable latent space. Recent variational approaches allow the latent space representation and the linear dynamical model to be optimized via unsupervised machine learning methods. Incorporation of physical constraints such as time-reversibility or stochasticity into the dynamical model has been established for a linear, but not for arbitrarily nonlinear (deep learning) representations of the latent space. Here we develop theory and methods for deep learning Markov and Koopman models that can bear such physical constraints. We prove that the model is an universal approximator for reversible Markov processes and that it can be optimized with either maximum likelihood or the variational approach of Markov processes (VAMP). We demonstrate that the model performs equally well for equilibrium and systematically better for biased data compared to existing approaches, thus providing a tool to study the long-timescale processes of dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3f98344f6fc1fe8402a3f24943590e37a74873d9" target='_blank'>Deep learning Markov and Koopman models with physical constraints</a></td>
-          <td>
-            Andreas Mardt, Luca Pasquali, Frank No'e, Hao Wu
-          </td>
-          <td>2019-12-16</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>25</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are however difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended $\beta$-variational autoencoder architecture. By means of simulated datasets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables for the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5e660b3335f6a2a1d8592c6bfd048b1d1aaa6021" target='_blank'>Learning minimal representations of stochastic processes with variational autoencoders</a></td>
-          <td>
-            Gabriel Fern'andez-Fern'andez, Carlo Manzo, M. Lewenstein, A. Dauphin, Gorka Muñoz-Gil
-          </td>
-          <td>2023-07-21</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>93</td>
-        </tr>
-    
-        <tr id="Latent variable models have been widely applied for the analysis and visualization of large datasets. In the case of sequential data, closed-form inference is possible when the transition and observation functions are linear. However, approximate inference techniques are usually necessary when dealing with nonlinear dynamics and observation functions. Here, we propose a novel variational inference framework for the explicit modeling of time series, Variational Inference for Nonlinear Dynamics (VIND), that is able to uncover nonlinear observation and transition functions from sequential data. The framework includes a structured approximate posterior, and an algorithm that relies on the fixed-point iteration method to find the best estimate for latent trajectories. We apply the method to several datasets and show that it is able to accurately infer the underlying dynamics of these systems, in some cases substantially outperforming state-of-the-art methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3af5f441aa7dfd63dfeea73d4a1918917795b795" target='_blank'>A Novel Variational Family for Hidden Nonlinear Markov Models</a></td>
-          <td>
-            Daniel Hernandez, Antonio Khalil Moretti, Ziqiang Wei, S. Saxena, J. Cunningham, L. Paninski
-          </td>
-          <td>2018-09-27</td>
-          <td>ArXiv</td>
-          <td>16</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their relationship with statistical learning is largely unexplored. We formalize a framework to learn the Koopman operator from finite data trajectories of the dynamical system. We consider the restriction of this operator to a reproducing kernel Hilbert space and introduce a notion of risk, from which different estimators naturally arise. We link the risk with the estimation of the spectral decomposition of the Koopman operator. These observations motivate a reduced-rank operator regression (RRR) estimator. We derive learning bounds for the proposed estimator, holding both in i.i.d. and non i.i.d. settings, the latter in terms of mixing coefficients. Our results suggest RRR might be beneficial over other widely used estimators as confirmed in numerical experiments both for forecasting and mode decomposition.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/63055e2a8b0c03fc2f0f07ea9a9cc58350ef3eb1" target='_blank'>Learning Dynamical Systems via Koopman Operator Regression in Reproducing Kernel Hilbert Spaces</a></td>
-          <td>
-            V. Kostić, P. Novelli, Andreas Maurer, C. Ciliberto, L. Rosasco, M. Pontil
-          </td>
-          <td>2022-05-27</td>
-          <td>ArXiv</td>
-          <td>40</td>
-          <td>70</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/06f56fef0842cb1e777730d93458c3e802f52aa5" target='_blank'>Fitting timeseries by continuous-time Markov chains: A quadratic programming approach</a></td>
-          <td>
-            D. Crommelin, E. Vanden-Eijnden
-          </td>
-          <td>2006-09-20</td>
-          <td>J. Comput. Phys.</td>
-          <td>63</td>
-          <td>64</td>
-        </tr>
-    
-        <tr id="Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are naturally described in continuous time, we present a model based on an Markov jump process modulating a subordinated diffusion process. We provide the exact evolution equations for the prior and posterior marginal densities, the direct solutions of which are however computationally intractable. Therefore, we develop a new continuous-time variational inference algorithm, combining a Gaussian process approximation on the diffusion level with posterior inference for Markov jump processes. By minimizing the path-wise Kullback-Leibler divergence we obtain (i) Bayesian latent state estimates for arbitrary points on the real axis and (ii) point estimates of unknown system parameters, utilizing variational expectation maximization. We extensively evaluate our algorithm under the model assumption and for real-world examples.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/42ea66546091e5b0c47f74e6063ff7d940990681" target='_blank'>Variational Inference for Continuous-Time Switching Dynamical Systems</a></td>
-          <td>
-            Lukas Kohs, Bastian Alt, H. Koeppl
-          </td>
-          <td>2021-09-29</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>28</td>
-        </tr>
-    
-        <tr id="In this work, we present a novel methodology for performing the supervised classification of time-ordered noisy data; we call this methodology Entropic Sparse Probabilistic Approximation with Markov regularization (eSPA-Markov). It is an extension of entropic learning methodologies, allowing the simultaneous learning of segmentation patterns, entropy-optimal feature space discretizations, and Bayesian classification rules. We prove the conditions for the existence and uniqueness of the learning problem solution and propose a one-shot numerical learning algorithm that—in the leading order—scales linearly in dimension. We show how this technique can be used for the computationally scalable identification of persistent (metastable) regime affiliations and regime switches from high-dimensional non-stationary and noisy time series, i.e., when the size of the data statistics is small compared to their dimensionality and when the noise variance is larger than the variance in the signal. We demonstrate its performance on a set of toy learning problems, comparing eSPA-Markov to state-of-the-art techniques, including deep learning and random forests. We show how this technique can be used for the analysis of noisy time series from DNA and RNA Nanopore sequencing.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eadfee466307a1a3b8e63299cb3e600477c1f902" target='_blank'>On Entropic Learning from Noisy Time Series in the Small Data Regime</a></td>
-          <td>
-            Davide Bassetti, Lukáš Pospíšil, I. Horenko
-          </td>
-          <td>2024-06-28</td>
-          <td>Entropy</td>
-          <td>0</td>
-          <td>26</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/bcbcc2e1af8bcf6b07edf866be95116a8ed0bf91.md b/docs/recommendations/bcbcc2e1af8bcf6b07edf866be95116a8ed0bf91.md
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-  <i class="footer">This page was last updated on 2024-05-27 07:02:58 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>UniTS: Building a Unified Time Series Model</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world small-sample scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progresses have been achieved as the emergence of large language models, exhibiting unprecedented ability in few-shot generalization, scalability, and task generality, which is however absent in time series models. To change the current practices of training small models on specific datasets from scratch, this paper aims at an early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), that is pre-trained by autoregressive next token prediction on large multi-domain datasets, and is fine-tuned to downstream scenarios with promising abilities as an LTSM.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6b63b78b8368b5974d69e413291fb86c32d6df96" target='_blank'>Timer: Transformers for Time Series Analysis at Scale</a></td>
-          <td>
-            Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
-          </td>
-          <td>2024-02-04</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="Despite the impressive achievements of pre-trained models in the fields of natural language processing (NLP) and computer vision (CV), progress in the domain of time series analysis has been limited. In contrast to NLP and CV, where a single model can handle various tasks, time series analysis still relies heavily on task-specific methods for activities such as classification, anomaly detection, forecasting, and few-shot learning. The primary obstacle to developing a pre-trained model for time series analysis is the scarcity of sufficient training data. In our research, we overcome this obstacle by utilizing pre-trained models from language or CV, which have been trained on billions of data points, and apply them to time series analysis. We assess the effectiveness of the pre-trained transformer model in two ways. Initially, we maintain the original structure of the self-attention and feedforward layers in the residual blocks of the pre-trained language or image model, using the Frozen Pre-trained Transformer (FPT) for time series analysis with the addition of projection matrices for input and output. Additionally, we introduce four unique adapters, designed specifically for downstream tasks based on the pre-trained model, including forecasting and anomaly detection. These adapters are further enhanced with efficient parameter tuning, resulting in superior performance compared to all state-of-the-art methods.Our comprehensive experimental studies reveal that (a) the simple FPT achieves top-tier performance across various time series analysis tasks; and (b) fine-tuning the FPT with the custom-designed adapters can further elevate its performance, outshining specialized task-specific models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/15bfe54223d28c74f9e39960f7ff1d03167e285f" target='_blank'>One Fits All: Universal Time Series Analysis by Pretrained LM and Specially Designed Adaptors</a></td>
-          <td>
-            Tian Zhou, Peisong Niu, Xue Wang, Liang Sun, Rong Jin
-          </td>
-          <td>2023-11-24</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="Time series data are ubiquitous across various domains, making time series analysis critically important. Traditional time series models are task-specific, featuring singular functionality and limited generalization capacity. Recently, large language foundation models have unveiled their remarkable capabilities for cross-task transferability, zero-shot/few-shot learning, and decision-making explainability. This success has sparked interest in the exploration of foundation models to solve multiple time series challenges simultaneously. There are two main research lines, namely pre-training foundation models from scratch for time series and adapting large language foundation models for time series. They both contribute to the development of a unified model that is highly generalizable, versatile, and comprehensible for time series analysis. This survey offers a 3E analytical framework for comprehensive examination of related research. Specifically, we examine existing works from three dimensions, namely Effectiveness, Efficiency and Explainability. In each dimension, we focus on discussing how related works devise tailored solution by considering unique challenges in the realm of time series. Furthermore, we provide a domain taxonomy to help followers keep up with the domain-specific advancements. In addition, we introduce extensive resources to facilitate the field's development, including datasets, open-source, time series libraries. A GitHub repository is also maintained for resource updates (https://github.com/start2020/Awesome-TimeSeries-LLM-FM).">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/522828823ff726598675971036fff01b57320578" target='_blank'>A Survey of Time Series Foundation Models: Generalizing Time Series Representation with Large Language Model</a></td>
-          <td>
-            Jiexia Ye, Weiqi Zhang, Ke Yi, Yongzi Yu, Ziyue Li, Jia Li, F. Tsung
-          </td>
-          <td>2024-05-03</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>47</td>
-        </tr>
-    
-        <tr id="We introduce MOMENT, a family of open-source foundation models for general-purpose time series analysis. Pre-training large models on time series data is challenging due to (1) the absence of a large and cohesive public time series repository, and (2) diverse time series characteristics which make multi-dataset training onerous. Additionally, (3) experimental benchmarks to evaluate these models, especially in scenarios with limited resources, time, and supervision, are still in their nascent stages. To address these challenges, we compile a large and diverse collection of public time series, called the Time series Pile, and systematically tackle time series-specific challenges to unlock large-scale multi-dataset pre-training. Finally, we build on recent work to design a benchmark to evaluate time series foundation models on diverse tasks and datasets in limited supervision settings. Experiments on this benchmark demonstrate the effectiveness of our pre-trained models with minimal data and task-specific fine-tuning. Finally, we present several interesting empirical observations about large pre-trained time series models. Pre-trained models (AutonLab/MOMENT-1-large) and Time Series Pile (AutonLab/Timeseries-PILE) are available on Huggingface.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/aabfdbd9db5ce9b1d598eae44e0d6250e7f0fc00" target='_blank'>MOMENT: A Family of Open Time-series Foundation Models</a></td>
-          <td>
-            Mononito Goswami, Konrad Szafer, Arjun Choudhry, Yifu Cai, Shuo Li, Artur Dubrawski
-          </td>
-          <td>2024-02-06</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="The field of general time series analysis has recently begun to explore unified modeling, where a common architectural backbone can be retrained on a specific task for a specific dataset. In this work, we approach unification from a complementary vantage point: unification across tasks and domains. To this end, we explore the impact of discrete, learnt, time series data representations that enable generalist, cross-domain training. Our method, TOTEM, or TOkenized Time Series EMbeddings, proposes a simple tokenizer architecture that embeds time series data from varying domains using a discrete vectorized representation learned in a self-supervised manner. TOTEM works across multiple tasks and domains with minimal to no tuning. We study the efficacy of TOTEM with an extensive evaluation on 17 real world time series datasets across 3 tasks. We evaluate both the specialist (i.e., training a model on each domain) and generalist (i.e., training a single model on many domains) settings, and show that TOTEM matches or outperforms previous best methods on several popular benchmarks. The code can be found at: https://github.com/SaberaTalukder/TOTEM.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f9f09c782155ca4f2ae4b6ffcf28514b439226cd" target='_blank'>TOTEM: TOkenized Time Series EMbeddings for General Time Series Analysis</a></td>
-          <td>
-            Sabera Talukder, Yisong Yue, Georgia Gkioxari
-          </td>
-          <td>2024-02-26</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Deep learning for time series forecasting has traditionally operated within a one-model-per-dataset framework, limiting its potential to leverage the game-changing impact of large pre-trained models. The concept of universal forecasting, emerging from pre-training on a vast collection of time series datasets, envisions a single Large Time Series Model capable of addressing diverse downstream forecasting tasks. However, constructing such a model poses unique challenges specific to time series data: i) cross-frequency learning, ii) accommodating an arbitrary number of variates for multivariate time series, and iii) addressing the varying distributional properties inherent in large-scale data. To address these challenges, we present novel enhancements to the conventional time series Transformer architecture, resulting in our proposed Masked Encoder-based Universal Time Series Forecasting Transformer (Moirai). Trained on our newly introduced Large-scale Open Time Series Archive (LOTSA) featuring over 27B observations across nine domains, Moirai achieves competitive or superior performance as a zero-shot forecaster when compared to full-shot models. Code, data, and model weights can be found at https://github.com/SalesforceAIResearch/uni2ts.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4a111f7a3b56d0468f13104999844885157ef17d" target='_blank'>Unified Training of Universal Time Series Forecasting Transformers</a></td>
-          <td>
-            Gerald Woo, Chenghao Liu, Akshat Kumar, Caiming Xiong, Silvio Savarese, Doyen Sahoo
-          </td>
-          <td>2024-02-04</td>
-          <td>ArXiv</td>
-          <td>10</td>
-          <td>21</td>
-        </tr>
-    
-        <tr id="Over the past years, foundation models have caused a paradigm shift in machine learning due to their unprecedented capabilities for zero-shot and few-shot generalization. However, despite the success of foundation models in modalities such as natural language processing and computer vision, the development of foundation models for time series forecasting has lagged behind. We present Lag-Llama, a general-purpose foundation model for univariate probabilistic time series forecasting based on a decoder-only transformer architecture that uses lags as covariates. Lag-Llama is pretrained on a large corpus of diverse time series data from several domains, and demonstrates strong zero-shot generalization capabilities compared to a wide range of forecasting models on downstream datasets across domains. Moreover, when fine-tuned on relatively small fractions of such previously unseen datasets, Lag-Llama achieves state-of-the-art performance, outperforming prior deep learning approaches, emerging as the best general-purpose model on average. Lag-Llama serves as a strong contender to the current state-of-art in time series forecasting and paves the way for future advancements in foundation models tailored to time series data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7c9bb230946cf48a7b9de97fd0281f42fbc51d31" target='_blank'>Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting</a></td>
-          <td>
-            Kashif Rasul, Arjun Ashok, Andrew Robert Williams, Arian Khorasani, George Adamopoulos, Rishika Bhagwatkar, Marin Bilovs, Hena Ghonia, N. Hassen, Anderson Schneider, Sahil Garg, Alexandre Drouin, Nicolas Chapados, Yuriy Nevmyvaka, I. Rish
-          </td>
-          <td>2023-10-12</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>39</td>
-        </tr>
-    
-        <tr id="Time-series data exists in every corner of real-world systems and services, ranging from satellites in the sky to wearable devices on human bodies. Learning representations by extracting and inferring valuable information from these time series is crucial for understanding the complex dynamics of particular phenomena and enabling informed decisions. With the learned representations, we can perform numerous downstream analyses more effectively. Among several approaches, deep learning has demonstrated remarkable performance in extracting hidden patterns and features from time-series data without manual feature engineering. This survey first presents a novel taxonomy based on three fundamental elements in designing state-of-the-art universal representation learning methods for time series. According to the proposed taxonomy, we comprehensively review existing studies and discuss their intuitions and insights into how these methods enhance the quality of learned representations. Finally, as a guideline for future studies, we summarize commonly used experimental setups and datasets and discuss several promising research directions. An up-to-date corresponding resource is available at https://github.com/itouchz/awesome-deep-time-series-representations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/72f38d513a8ab095a3d4f459958cbb31b1f7cdc4" target='_blank'>Universal Time-Series Representation Learning: A Survey</a></td>
-          <td>
-            Patara Trirat, Yooju Shin, Junhyeok Kang, Youngeun Nam, Jihye Na, Minyoung Bae, Joeun Kim, Byunghyun Kim, Jae-Gil Lee
-          </td>
-          <td>2024-01-08</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="Although we have witnessed great success of pre-trained models in natural language processing (NLP) and computer vision (CV), limited progress has been made for general time series analysis. Unlike NLP and CV where a unified model can be used to perform different tasks, specially designed approach still dominates in each time series analysis task such as classification, anomaly detection, forecasting, and few-shot learning. The main challenge that blocks the development of pre-trained model for time series analysis is the lack of a large amount of data for training. In this work, we address this challenge by leveraging language or CV models, pre-trained from billions of tokens, for time series analysis. Specifically, we refrain from altering the self-attention and feedforward layers of the residual blocks in the pre-trained language or image model. This model, known as the Frozen Pretrained Transformer (FPT), is evaluated through fine-tuning on all major types of tasks involving time series. Our results demonstrate that pre-trained models on natural language or images can lead to a comparable or state-of-the-art performance in all main time series analysis tasks, as illustrated in Figure 1. We also found both theoretically and empirically that the self-attention module behaviors similarly to principle component analysis (PCA), an observation that helps explains how transformer bridges the domain gap and a crucial step towards understanding the universality of a pre-trained transformer.The code is publicly available at https://github.com/DAMO-DI-ML/One_Fits_All.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5b7f5488c380cf5085a5dd93e993ad293b225eee" target='_blank'>One Fits All: Power General Time Series Analysis by Pretrained LM</a></td>
-          <td>
-            Tian Zhou, Peisong Niu, Xue Wang, Liang Sun, Rong Jin
-          </td>
-          <td>2023-02-23</td>
-          <td>DBLP, ArXiv</td>
-          <td>92</td>
-          <td>16</td>
-        </tr>
-    
-        <tr id="We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4fb78450650894091b0a55b5504a8b0a6f3dec37" target='_blank'>Chronos: Learning the Language of Time Series</a></td>
-          <td>
-            Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, Yuyang Wang
-          </td>
-          <td>2024-03-12</td>
-          <td>ArXiv</td>
-          <td>10</td>
-          <td>18</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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diff --git a/docs/recommendations/be8d39424a9010bfc0805385cc91edee383c2e24.md b/docs/recommendations/be8d39424a9010bfc0805385cc91edee383c2e24.md
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Message Passing Neural PDE Solvers</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some methods utilize reinforcement learning or supervised learning techniques to create adaptive and dynamic meshes, due to the dynamic nature of these systems. However, these approaches face two primary challenges: (1) the need for expensive optimal mesh data, and (2) the change of the solution space's degree of freedom and topology during mesh refinement. To address these challenges, this paper proposes a neural PDE solver with a neural mesh adapter. To begin with, we introduce a novel data-free neural mesh adaptor, called Data-free Mesh Mover (DMM), with two main innovations. Firstly, it is an operator that maps the solution to adaptive meshes and is trained using the Monge-Amp\`ere equation without optimal mesh data. Secondly, it dynamically changes the mesh by moving existing nodes rather than adding or deleting nodes and edges. Theoretical analysis shows that meshes generated by DMM have the lowest interpolation error bound. Based on DMM, to efficiently and accurately model dynamic systems, we develop a moving mesh based neural PDE solver (MM-PDE) that embeds the moving mesh with a two-branch architecture and a learnable interpolation framework to preserve information within the data. Empirical experiments demonstrate that our method generates suitable meshes and considerably enhances accuracy when modeling widely considered PDE systems. The code can be found at: https://github.com/Peiyannn/MM-PDE.git.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/280271683627def8d021a0cf3d47dd97d30776ef" target='_blank'>Better Neural PDE Solvers Through Data-Free Mesh Movers</a></td>
-          <td>
-            Peiyan Hu, Yue Wang, Zhi-Ming Ma
-          </td>
-          <td>2023-12-09</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1128b76da2bdc5e0275361b5bc3d4d8c38fe9038" target='_blank'>Connections Between Numerical Algorithms for PDEs and Neural Networks</a></td>
-          <td>
-            Tobias Alt, K. Schrader, M. Augustin, Pascal Peter, J. Weickert
-          </td>
-          <td>2021-07-30</td>
-          <td>Journal of Mathematical Imaging and Vision</td>
-          <td>13</td>
-          <td>67</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4350d3b899721a39570228ac57a1c71dc0db462f" target='_blank'>Translating Numerical Concepts for PDEs into Neural Architectures</a></td>
-          <td>
-            Tobias Alt, Pascal Peter, J. Weickert, K. Schrader
-          </td>
-          <td>2021-03-29</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>67</td>
-        </tr>
-    
-        <tr id="A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models actually depend on the specific numerical method used during training. If the trained model is supposed to be a flow generated from an ODE, it should be possible to choose another numerical solver with equal or smaller numerical error without loss of performance. We observe that if training relies on a solver with overly coarse discretization, then testing with another solver of equal or smaller numerical error results in a sharp drop in accuracy. In such cases, the combination of vector field and numerical method cannot be interpreted as a flow generated from an ODE, which arguably poses a fatal breakdown of the Neural ODE concept. We observe, however, that there exists a critical step size beyond which the training yields a valid ODE vector field. We propose a method that monitors the behavior of the ODE solver during training to adapt its step size, aiming to ensure a valid ODE without unnecessarily increasing computational cost. We verify this adaptation algorithm on a common bench mark dataset as well as a synthetic dataset.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bde275692b53051823526bbcc8938c2ffc0126a4" target='_blank'>ResNet After All? Neural ODEs and Their Numerical Solution</a></td>
-          <td>
-            Katharina Ott, P. Katiyar, Philipp Hennig, M. Tiemann
-          </td>
-          <td>2020-07-30</td>
-          <td>ArXiv</td>
-          <td>26</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="Recent developments in the field of neural partial differential equation (PDE) solvers have placed a strong emphasis on neural operators. However, the paper"Message Passing Neural PDE Solver"by Brandstetter et al. published in ICLR 2022 revisits autoregressive models and designs a message passing graph neural network that is comparable with or outperforms both the state-of-the-art Fourier Neural Operator and traditional classical PDE solvers in its generalization capabilities and performance. This blog post delves into the key contributions of this work, exploring the strategies used to address the common problem of instability in autoregressive models and the design choices of the message passing graph neural network architecture.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/15e033f23d2074a9188997e5f7f70231bc214e89" target='_blank'>Autoregressive Renaissance in Neural PDE Solvers</a></td>
-          <td>
-            Yolanne Yi Ran Lee
-          </td>
-          <td>2023-10-30</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="One of the main challenges in solving time-dependent partial differential equations is to develop computationally efficient solvers that are accurate and stable. Here, we introduce a graph neural network approach to finding efficient PDE solvers through learning using message-passing models. We first introduce domain invariant features for PDE-data inspired by classical PDE solvers for an efficient physical representation. Next, we use graphs to represent PDE-data on an unstructured mesh and show that message passing graph neural networks (MPGNN) can parameterize governing equations, and as a result, efficiently learn accurate solver schemes for linear/nonlinear PDEs. We further show that the solvers are independent of the initial trained geometry, i.e. the trained solver can find PDE solution on different complex domains. Lastly, we show that a recurrent graph neural network approach can find a temporal sequence of solutions to a PDE.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/88d15996b0eb81c348ab9e145b14655171d35d67" target='_blank'>Learning time-dependent PDE solver using Message Passing Graph Neural Networks</a></td>
-          <td>
-            Pourya Pilva, A. Zareei
-          </td>
-          <td>2022-04-15</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="In the past years, the application of neural networks as an alternative to classical numerical methods to solve Partial Differential Equations has emerged as a potential paradigm shift in this century-old mathematical field. However, in terms of practical applicability, computational cost remains a substantial bottleneck. Classical approaches try to mitigate this challenge by limiting the spatial resolution on which the PDEs are defined. For neural PDE solvers, we can do better: Here, we investigate the potential of state-of-the-art quantization methods on reducing computational costs. We show that quantizing the network weights and activations can successfully lower the computational cost of inference while maintaining performance. Our results on four standard PDE datasets and three network architectures show that quantization-aware training works across settings and three orders of FLOPs magnitudes. Finally, we empirically demonstrate that Pareto-optimality of computational cost vs performance is almost always achieved only by incorporating quantization.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2b76349e67ea2cfb38346ac9a70a8ef4a1cda7de" target='_blank'>Efficient Neural PDE-Solvers using Quantization Aware Training</a></td>
-          <td>
-            W.V.S.O. van den Dool, Tijmen Blankevoort, M. Welling, Yuki M. Asano
-          </td>
-          <td>2023-08-14</td>
-          <td>2023 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW)</td>
-          <td>3</td>
-          <td>88</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/84217089f7393febd46ebc374570a0ff03b676be" target='_blank'>DiscretizationNet: A Machine-Learning based solver for Navier-Stokes Equations using Finite Volume Discretization</a></td>
-          <td>
-            Rishikesh Ranade, C. Hill, Jay Pathak
-          </td>
-          <td>2020-05-17</td>
-          <td>ArXiv</td>
-          <td>91</td>
-          <td>10</td>
-        </tr>
-    
-        <tr id="In this study, we introduce a domain-decomposition-based distributed training and inference approach for message-passing neural networks (MPNN). Our objective is to address the challenge of scaling edge-based graph neural networks as the number of nodes increases. Through our distributed training approach, coupled with Nystr\"om-approximation sampling techniques, we present a scalable graph neural network, referred to as DS-MPNN (D and S standing for distributed and sampled, respectively), capable of scaling up to $O(10^5)$ nodes. We validate our sampling and distributed training approach on two cases: (a) a Darcy flow dataset and (b) steady RANS simulations of 2-D airfoils, providing comparisons with both single-GPU implementation and node-based graph convolution networks (GCNs). The DS-MPNN model demonstrates comparable accuracy to single-GPU implementation, can accommodate a significantly larger number of nodes compared to the single-GPU variant (S-MPNN), and significantly outperforms the node-based GCN.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f658f479ac42373f03d1f186c476461f7369ad63" target='_blank'>Sampling-based Distributed Training with Message Passing Neural Network</a></td>
-          <td>
-            P. Kakka, S. Nidhan, Rishikesh Ranade, J. MacArt
-          </td>
-          <td>2024-02-23</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>10</td>
-        </tr>
-    
-        <tr id="We motivate the use of neural networks for the construction of numerical solutions to differential equations. We prove that there exists a feed-forward neural network that can arbitrarily minimise an objective function that is zero at the solution of Poisson’s equation, allowing us to guarantee that neural network solution estimates can get arbitrarily close to the exact solutions. We also show how these estimates can be appreciably enhanced through various strategies, in particular through the construction of error correction networks, for which we propose a general method. We conclude by providing numerical experiments that attest to the validity of all such strategies for variants of Poisson’s equation. The source code for this project can be found at https://github.com/mjhwright/error-correction .">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/83b04e006290360cc8e466253924fc1aeccee65c" target='_blank'>Enhancing Neural Network Differential Equation Solvers</a></td>
-          <td>
-            Matthew J. H. Wright
-          </td>
-          <td>2022-12-28</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-    Recommendations for the article <i>A Unified Framework for Sparse Relaxed Regularized Regression: SR3</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications, variable selection, and high-dimensional analysis. We propose a new and highly effective approach for regularized regression, called SR3. The key idea is to solve a relaxation of the regularized problem, which has three advantages over the state-of-the-art: (1) solutions of the relaxed problem are superior with respect to errors, false positives, and conditioning, (2) relaxation allows extremely fast algorithms for both convex and nonconvex formulations, and (3) the methods apply to composite regularizers such as total variation (TV) and its nonconvex variants. We demonstrate the improved performance of SR3 across a range of regularized regression problems with synthetic and real data, including compressed sensing, LASSO, matrix completion and TV regularization. To promote reproducible research, we include a companion MATLAB package that implements these popular applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4395eb13c70bf57c074a857f00a05b97174945c2" target='_blank'>Sparse Relaxed Regularized Regression: SR3</a></td>
-          <td>
-            P. Zheng, T. Askham, S. Brunton, J. Kutz, A. Aravkin
-          </td>
-          <td>2018-07-14</td>
-          <td>ArXiv</td>
-          <td>9</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the estimators is a challenging (\NP-hard) non-convex optimization problem. In this paper, we derive new strong convex relaxations for sparse regression. These relaxations are based on the ideal (convex-hull) formulations for rank-one quadratic terms with indicator variables. The new relaxations can be formulated as semidefinite optimization problems in an extended space and are stronger and more general than the state-of-the-art formulations, including the perspective reformulation and formulations with the reverse Huber penalty and the minimax concave penalty functions. Furthermore, the proposed rank-one strengthening can be interpreted as a \textit{non-separable, non-convex, unbiased} sparsity-inducing regularizer, which dynamically adjusts its penalty according to the shape of the error function without inducing bias for the sparse solutions. In our computational experiments with benchmark datasets, the proposed conic formulations are solved within seconds and result in near-optimal solutions (with 0.4\% optimality gap) for non-convex $\ell_0$-problems. Moreover, the resulting estimators also outperform alternative convex approaches from a statistical perspective, achieving high prediction accuracy and good interpretability.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fdaa7e10a914707c5aa2c9b8a8ade26f658a28eb" target='_blank'>Rank-one Convexification for Sparse Regression</a></td>
-          <td>
-            Alper Atamtürk, A. Gómez
-          </td>
-          <td>2019-01-29</td>
-          <td>ArXiv</td>
-          <td>49</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class of models with partial regularizers for recovering a sparse solution of a linear system. We show that every local minimizer of these models is sufficiently sparse or the magnitude of all its nonzero entries is above a uniform constant depending only on the data of the linear system. Moreover, for a class of partial regularizers, any global minimizer of these models is a sparsest solution to the linear system. We also establish some sufficient conditions for local or global recovery of the sparsest solution to the linear system, among which one of the conditions is weaker than the best known restricted isometry property (RIP) condition for sparse recovery by $\ell_1$. In addition, a first-order feasible augmented Lagrangian (FAL) method is proposed for solving these models, in which each subproblem is solved by a nonmonotone proximal gradient (NPG) method. Despite the complication of the partial regularizers, we show that each proximal subproblem in NPG can be solved as a certain number of one-dimensional optimization problems, which usually have a closed-form solution. We also show that any accumulation point of the sequence generated by FAL is a first-order stationary point of the models. Numerical results on compressed sensing and sparse logistic regression demonstrate that the proposed models substantially outperform the widely used ones in the literature in terms of solution quality.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/27e034273ffd12e1405e01baf2550cac744cfacf" target='_blank'>Sparse Recovery via Partial Regularization: Models, Theory and Algorithms</a></td>
-          <td>
-            Zhaosong Lu, Xiaorui Li
-          </td>
-          <td>2015-11-23</td>
-          <td>ArXiv</td>
-          <td>35</td>
-          <td>32</td>
-        </tr>
-    
-        <tr id="Regularization is a widely used technique throughout statistics, machine learning, and applied mathematics. Modern applications in science and engineering lead to massive and complex data sets, which motivate the use of more structured types of regularizers. This survey provides an overview of the use of structured regularization in high-dimensional statistics, including regularizers for group-structured and hierarchical sparsity, low-rank matrices, additive and multiplicative matrix decomposition, and high-dimensional nonparametric models. It includes various examples with motivating applications; it also covers key aspects of statistical theory and provides some discussion of efficient algorithms.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/663764ed0282809df64f480c5c5e8b083f0e82c0" target='_blank'>Structured Regularizers for High-Dimensional Problems: Statistical and Computational Issues</a></td>
-          <td>
-            M. Wainwright
-          </td>
-          <td>2014-01-03</td>
-          <td></td>
-          <td>58</td>
-          <td>94</td>
-        </tr>
-    
-        <tr id="High-dimensional sparse linear regression is a basic problem in machine learning and statistics. Consider a linear model $y = X\theta^\star + w$, where $y \in \mathbb{R}^n$ is the vector of observations, $X \in \mathbb{R}^{n \times d}$ is the covariate matrix and $w \in \mathbb{R}^n$ is an unknown noise vector. In many applications, the linear regression model is high-dimensional in nature, meaning that the number of observations $n$ may be substantially smaller than the number of covariates $d$. In these cases, it is common to assume that $\theta^\star$ is sparse, and the goal in sparse linear regression is to estimate this sparse $\theta^\star$, given $(X,y)$. 
-In this paper, we study a variant of the traditional sparse linear regression problem where each of the $n$ covariate vectors in $\mathbb{R}^d$ are individually projected by a random linear transformation to $\mathbb{R}^m$ with $m \ll d$. Such transformations are commonly applied in practice for computational savings in resources such as storage space, transmission bandwidth, and processing time. Our main result shows that one can estimate $\theta^\star$ with a low $\ell_2$-error, even with access to only these projected covariate vectors, under some mild assumptions on the problem instance. Our approach is based on solving a variant of the popular Lasso optimization problem. While the conditions (such as the restricted eigenvalue condition on $X$) for success of a Lasso formulation in estimating $\theta^\star$ are well-understood, we investigate conditions under which this variant of Lasso estimates $\theta^\star$. 
-As a simple consequence, our approach also provides a new way for estimating $\theta^\star$ in the traditional sparse linear regression problem setting, which operates (even) under a weaker assumption on the design matrix than previously known, albeit achieving a weaker convergence bound.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/490480bb749d41dce1f42dabf0c6763dcc085223" target='_blank'>Compressed Sparse Linear Regression</a></td>
-          <td>
-            S. Kasiviswanathan, M. Rudelson
-          </td>
-          <td>2017-07-25</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>29</td>
-        </tr>
-    
-        <tr id="Reconstruction of signals from undersampled and noisy measurements is a topic of considerable interest. Sharpness conditions directly control the recovery performance of restart schemes for first-order methods without the need for restrictive assumptions such as strong convexity. However, they are challenging to apply in the presence of noise or approximate model classes (e.g., approximate sparsity). We provide a first-order method: Weighted, Accelerated and Restarted Primal-dual (WARPd), based on primal-dual iterations and a novel restart-reweight scheme. Under a generic approximate sharpness condition, WARPd achieves stable linear convergence to the desired vector. Many problems of interest fit into this framework. For example, we analyze sparse recovery in compressed sensing, low-rank matrix recovery, matrix completion, TV regularization, minimization of $\|Bx\|_{l^1}$ under constraints ($l^1$-analysis problems for general $B$), and mixed regularization problems. We show how several quantities controlling recovery performance also provide explicit approximate sharpness constants. Numerical experiments show that WARPd compares favorably with specialized state-of-the-art methods and is ideally suited for solving large-scale problems. We also present a noise-blind variant based on the Square-Root LASSO decoder. Finally, we show how to unroll WARPd as neural networks. This approximation theory result provides lower bounds for stable and accurate neural networks for inverse problems and sheds light on architecture choices. Code and a gallery of examples are made available online as a MATLAB package.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6fb4013825fdf1703f38356d74af6dc837fac235" target='_blank'>WARPd: A linearly convergent first-order method for inverse problems with approximate sharpness conditions</a></td>
-          <td>
-            Matthew J. Colbrook
-          </td>
-          <td>2021-10-24</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>16</td>
-        </tr>
-    
-        <tr id="This paper addresses the robust reconstruction problem of a sparse signal from compressed measurements. We propose a robust formulation for sparse reconstruction that employs the <inline-formula><tex-math notation="LaTeX">$\ell _1$ </tex-math></inline-formula>-norm as the loss function for the residual error and utilizes a generalized nonconvex penalty for sparsity inducing. The <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math></inline-formula> -loss is less sensitive to outliers in the measurements than the popular <inline-formula><tex-math notation="LaTeX"> $\ell _2$</tex-math></inline-formula>-loss, while the nonconvex penalty has the capability of ameliorating the bias problem of the popular convex LASSO penalty and thus can yield more accurate recovery. To solve this nonconvex and nonsmooth minimization formulation efficiently, we propose a first-order algorithm based on alternating direction method of multipliers. A smoothing strategy on the <inline-formula><tex-math notation="LaTeX">$\ell _1$</tex-math> </inline-formula>-loss function has been used in deriving the new algorithm to make it convergent. Further, a sufficient condition for the convergence of the new algorithm has been provided for generalized nonconvex regularization. In comparison with several state-of-the-art algorithms, the new algorithm showed better performance in numerical experiments in recovering sparse signals and compressible images. The new algorithm scales well for large-scale problems, as often encountered in image processing.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/068d960bb7a2df7e12fee685d9a8afb7b1bfcc50" target='_blank'>Efficient and Robust Recovery of Sparse Signal and Image Using Generalized Nonconvex Regularization</a></td>
-          <td>
-            Fei Wen, L. Pei, Yuan Yang, Wenxian Yu, Peilin Liu
-          </td>
-          <td>2017-03-23</td>
-          <td>IEEE Transactions on Computational Imaging</td>
-          <td>83</td>
-          <td>30</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/10d6de4fab447cbb4279a5206d5b2c276162c656" target='_blank'>Regularizers for structured sparsity</a></td>
-          <td>
-            C. Micchelli, Jean Morales, M. Pontil
-          </td>
-          <td>2010-10-04</td>
-          <td>Advances in Computational Mathematics</td>
-          <td>79</td>
-          <td>70</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/10d6de4fab447cbb4279a5206d5b2c276162c656" target='_blank'>Regularizers for structured sparsity</a></td>
-          <td>
-            C. Micchelli, Jean Morales, M. Pontil
-          </td>
-          <td>2010-10-04</td>
-          <td>Advances in Computational Mathematics</td>
-          <td>79</td>
-          <td>70</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
-
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-  <tbody>
-    
-        <tr id="We present the first whiteness test for graphs, i.e., a whiteness test for multivariate time series associated with the nodes of a dynamic graph. The statistical test aims at finding serial dependencies among close-in-time observations, as well as spatial dependencies among neighboring observations given the underlying graph. The proposed test is a spatio-temporal extension of traditional tests from the system identification literature and finds applications in similar, yet more general, application scenarios involving graph signals. The AZ-test is versatile, allowing the underlying graph to be dynamic, changing in topology and set of nodes, and weighted, thus accounting for connections of different strength, as is the case in many application scenarios like transportation networks and sensor grids. The asymptotic distribution -- as the number of graph edges or temporal observations increases -- is known, and does not assume identically distributed data. We validate the practical value of the test on both synthetic and real-world problems, and show how the test can be employed to assess the quality of spatio-temporal forecasting models by analyzing the prediction residuals appended to the graphs stream.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/44a9610f927230a711176e4ad7008324abacd65b" target='_blank'>AZ-whiteness test: a test for uncorrelated noise on spatio-temporal graphs</a></td>
-          <td>
-            Daniele Zambon, C. Alippi
-          </td>
-          <td>2022-04-23</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9" target='_blank'>A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection</a></td>
-          <td>
-            Ming Jin, Huan Yee Koh, Qingsong Wen, Daniele Zambon, C. Alippi, G. I. Webb, Irwin King, Shirui Pan
-          </td>
-          <td>2023-07-07</td>
-          <td>ArXiv</td>
-          <td>61</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="Spatio-temporal forecasting of future values of spatially correlated time series is important across many cyber-physical systems (CPS). Recent studies offer evidence that the use of graph neural networks to capture latent correlations between time series holds a potential for enhanced forecasting. However, most existing methods rely on predefined or self-learning graphs, which are either static or unintentionally dynamic, and thus cannot model the time-varying correlations that exhibit trends and periodicities caused by the regularity of the underlying processes in CPS. To tackle such limitation, we propose Time-aware Graph Structure Learning (TagSL), which extracts time-aware correlations among time series by measuring the interaction of node and time representations in high-dimensional spaces. Notably, we introduce time discrepancy learning that utilizes contrastive learning with distance-based regularization terms to constrain learned spatial correlations to a trend sequence. Additionally, we propose a periodic discriminant function to enable the capture of periodic changes from the state of nodes. Next, we present a Graph Convolution-based Gated Recurrent Unit (GCGRU) that jointly captures spatial and temporal dependencies while learning time-aware and node-specific patterns. Finally, we introduce a unified framework named Time-aware Graph Convolutional Recurrent Network (TGCRN), combining TagSL, and GCGRU in an encoder-decoder architecture for multi-step spatiotemporal forecasting. We report on experiments with TGCRN and popular existing approaches on five real-world datasets, thus providing evidence that TGCRN is capable of advancing the state-of-the-art. We also cover a detailed ablation study and visualization analysis, offering detailed insight into the effectiveness of time-aware structure learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2e635d42e768aec7be29fbd203a605c1f011a44d" target='_blank'>Learning Time-Aware Graph Structures for Spatially Correlated Time Series Forecasting</a></td>
-          <td>
-            Minbo Ma, Jilin Hu, Christian S. Jensen, Fei Teng, Peng Han, Zhiqiang Xu, Tian-Jie Li
-          </td>
-          <td>2023-12-27</td>
-          <td>2024 IEEE 40th International Conference on Data Engineering (ICDE)</td>
-          <td>0</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8af9708e610256bd5f2315fc83b8c55cd1482901" target='_blank'>Graph construction on complex spatiotemporal data for enhancing graph neural network-based approaches</a></td>
-          <td>
-            Stefan Bloemheuvel, J. Hoogen, Martin Atzmueller
-          </td>
-          <td>2023-09-25</td>
-          <td>International Journal of Data Science and Analytics</td>
-          <td>0</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatiotemporal information in these signals is essential for the downstream tasks. Previous studies have used the smoothness of the temporal differences of such graph signals as an initial assumption. Nevertheless, this smoothness assumption could result in a degradation of performance in the corresponding application when the prior does not hold. In this work, we relax the requirement of this hypothesis by including a learning module. We propose a Time Graph Neural Network (TimeGNN) for the recovery of time-varying graph signals. Our algorithm uses an encoder-decoder architecture with a specialized loss composed of a mean squared error function and a Sobolev smoothness operator. TimeGNN shows competitive performance against previous methods in real datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a320892b1bc4ef98c47edf416d6921a64d0b4b77" target='_blank'>Time-Varying Signals Recovery Via Graph Neural Networks</a></td>
-          <td>
-            Jhon A. Castro-Correa, Jhony H. Giraldo, Anindya Mondal, M. Badiey, T. Bouwmans, Fragkiskos D. Malliaros
-          </td>
-          <td>2023-02-22</td>
-          <td>ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</td>
-          <td>4</td>
-          <td>42</td>
-        </tr>
-    
-        <tr id="Devising and analysing learning models for spatiotemporal network data is of importance for tasks including forecasting, anomaly detection, and multi-agent coordination, among others. Graph Convolutional Neural Networks (GCNNs) are an established approach to learn from time-invariant network data. The graph convolution operation offers a principled approach to aggregate information and offers mathematical analysis by exploring tools from graph signal processing. This analysis provides insights into the equivariance properties of GCNNs; spectral behaviour of the learned filters; and the stability to graph perturbations, which arise from support perturbations or uncertainties. However, extending the convolutional learning and respective analysis to the spatiotemporal domain is challenging because spatiotemporal data have more intrinsic dependencies. Hence, a higher flexibility to capture jointly the spatial and temporal dependencies is required to learn meaningful higher-order representations. Here, we leverage product graphs to represent the spatiotemporal dependencies in the data and introduce Graph-Time Convolutional Neural Networks (GTCNNs) as a principled architecture. We also introduce a parametric product graph to learn the spatiotemporal coupling. The convolution principle further allows a similar mathematical tractability as for GCNNs. In particular, the stability result shows GTCNNs are stable to spatial perturbations. owever, there is an implicit trade-off between discriminability and robustness; i.e., the more complex the model, the less stable. Extensive numerical results on benchmark datasets corroborate our findings and show the GTCNN compares favorably with state-of-the-art solutions. We anticipate the GTCNN to be a starting point for more sophisticated models that achieve good performance but are also fundamentally grounded.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/41a11baa108f2e022357c92b4e71750b9f585639" target='_blank'>Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis</a></td>
-          <td>
-            Mohammad Sabbaqi, E. Isufi
-          </td>
-          <td>2022-06-30</td>
-          <td>IEEE Transactions on Pattern Analysis and Machine Intelligence</td>
-          <td>7</td>
-          <td>20</td>
-        </tr>
-    
-        <tr id="Multivariate time series forecasting has long received significant attention in real-world applications, such as energy consumption and traffic prediction. While recent methods demonstrate good forecasting abilities, they have three fundamental limitations. (i). <italic>Discrete neural architectures:</italic> Interlacing individually parameterized spatial and temporal blocks to encode rich underlying patterns leads to discontinuous latent state trajectories and higher forecasting numerical errors. (ii). <italic>High complexity:</italic> Discrete approaches complicate models with dedicated designs and redundant parameters, leading to higher computational and memory overheads. (iii). <italic>Reliance on graph priors:</italic> Relying on predefined static graph structures limits their effectiveness and practicability in real-world applications. In this paper, we address all the above limitations by proposing a continuous model to forecast <underline><bold>M</bold></underline>ultivariate <underline><bold>T</bold></underline>ime series with dynamic <underline><bold>G</bold></underline>raph neural <underline><bold>O</bold></underline>rdinary <underline><bold>D</bold></underline>ifferential <underline><bold>E</bold></underline>quations (<monospace>MTGODE</monospace>). Specifically, we first abstract multivariate time series into dynamic graphs with time-evolving node features and unknown graph structures. Then, we design and solve a neural ODE to complement missing graph topologies and unify both spatial and temporal message passing, allowing deeper graph propagation and fine-grained temporal information aggregation to characterize stable and precise latent spatial-temporal dynamics. Our experiments demonstrate the superiorities of <monospace>MTGODE</monospace> from various perspectives on five time series benchmark datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b02a5aebd9598ddbb2b4021b5576cedb5519d436" target='_blank'>Multivariate Time Series Forecasting With Dynamic Graph Neural ODEs</a></td>
-          <td>
-            Ming Jin, Yu Zheng, Yuanhao Li, Siheng Chen, B. Yang, Shirui Pan
-          </td>
-          <td>2022-02-17</td>
-          <td>IEEE Transactions on Knowledge and Data Engineering</td>
-          <td>54</td>
-          <td>42</td>
-        </tr>
-    
-        <tr id="Existing multivariate time series anomaly detection methods utilize graph neural networks to model inter-sensor dependencies and achieve satisfactory results. However, these methods often employ a predefined or self-learning static adjacency matrix for graph information aggregation, disregarding the dynamic characteristics of inter-sensor dependencies in the real world, which change over time and are observable at different time scales as dynamic changing graph structure information. Furthermore, existing techniques struggle to capture long-term temporal contextual relationships. To address these issues, we propose a Dynamic Graph Learning with Long and Short-term time model (DGL-LS) for multivariate time series anomaly detection. The network integrates a dynamic graph structure learning method among sensors in multi-time mode and long- and short-term temporal context information to enhance the prediction of multivariate time series anomalies. We propose a strategy for learning dynamic graphs that aggregates sensor node representations at various time intervals, and then uses an attention-based gating unit to evolve the node dynamic characterization and construct a series of adjacency matrices that describe the dynamic changes in graph structure over time. Moreover, we formulate a long-short time convolution to capture the long-term and short-term temporal dependencies within the time series. We demonstrate the superiority of our approach over other state-of-the-art methods by conducting extensive experiments on three publicly available datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/379f54e4519d51a31de25e26fa651b3bd21d6530" target='_blank'>Dynamic Graph Learning with Long and Short-Term for Multivariate Time Series Anomaly Detection</a></td>
-          <td>
-            Yuyin Tian, Rong Gao, Lingyu Yan, Donghua Liu, Zhiwei Ye
-          </td>
-          <td>2023-09-07</td>
-          <td>2023 IEEE 12th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS)</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-  </tbody>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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-  <i class="footer">This page was last updated on 2024-07-22 06:06:23 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Learning to Simulate Complex Physics with Graph Networks</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We develop a PyTorch-based Graph Network Simulator (GNS) that learns physics and predicts the flow behavior of particulate and fluid systems. GNS discretizes the domain with nodes representing a collection of material points and the links connecting the nodes representing the local interaction between particles or clusters of particles. The GNS learns the interaction laws through message passing on the graph. GNS has three components: (a) Encoder, which embeds particle information to a latent graph, the edges are learned functions; (b) Processor, which allows data propagation and computes the nodal interactions across steps; and (c) Decoder, which extracts the relevant dynamics (e.g., particle acceleration) from the graph. We introduce physics-inspired simple inductive biases, such as an inertial frame that allows learning algorithms to prioritize one solution (constant gravitational acceleration) over another, reducing learning time. The GNS implementation uses semi-implicit Euler integration to update the next state based on the predicted accelerations. GNS trained on trajectory data is generalizable to predict particle kinematics in complex boundary conditions not seen during training. The trained model accurately predicts within a 5\% error of its associated material point method (MPM) simulation. The predictions are 5,000x faster than traditional MPM simulations (2.5 hours for MPM simulations versus 20 s for GNS simulation of granular flow). GNS surrogates are popular for solving optimization, control, critical-region prediction for in situ viz, and inverse-type problems. The GNS code is available under the open-source MIT license at https://github.com/geoelements/gns.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8d0ad8be491a5dad5af49f7c7f6c4dde40ee3f25" target='_blank'>GNS: A generalizable Graph Neural Network-based simulator for particulate and fluid modeling</a></td>
-          <td>
-            Krishna Kumar, J. Vantassel
-          </td>
-          <td>2022-11-18</td>
-          <td>J. Open Source Softw.</td>
-          <td>7</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="Simulation of the dynamics of physical systems is essential to the development of both science and engineering. Recently there is an increasing interest in learning to simulate the dynamics of physical systems using neural networks. However, existing approaches fail to generalize to physical substances not in the training set, such as liquids with different viscosities or elastomers with different elasticities. Here we present a machine learning method embedded with physical priors and material parameters, which we term as"Graph-based Physics Engine"(GPE), to efficiently model the physical dynamics of different substances in a wide variety of scenarios. We demonstrate that GPE can generalize to materials with different properties not seen in the training set and perform well from single-step predictions to multi-step roll-out simulations. In addition, introducing the law of momentum conservation in the model significantly improves the efficiency and stability of learning, allowing convergence to better models with fewer training steps.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68c9deb6d474b34c5cf947b30c519640b0d4fd45" target='_blank'>Learning to Simulate Unseen Physical Systems with Graph Neural Networks</a></td>
-          <td>
-            Ce Yang, Weihao Gao, Di Wu, Chong Wang
-          </td>
-          <td>2022-01-28</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>15</td>
-        </tr>
-    
-        <tr id="Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for physical systems with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. Finally, we demonstrate that our method also performs well when taking discontinuous effects into account such as collisions between individual rods. A video showing dynamic results of our graph learning assisted simulations of elastic rods can be found on the project website available at this http URL .">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0bf48ff5241fcf7116db676d87d98188dfcac175" target='_blank'>Accurately Solving Physical Systems with Graph Learning</a></td>
-          <td>
-            Han Shao, Tassilo Kugelstadt, Wojciech Palubicki, Jan Bender, S. Pirk, D. Michels
-          </td>
-          <td>2020-06-06</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>27</td>
-        </tr>
-    
-        <tr id="Simulating complex dynamics like fluids with traditional simulators is computationally challenging. Deep learning models have been proposed as an efficient alternative, extending or replacing parts of traditional simulators. We investigate graph neural networks (GNNs) for learning fluid dynamics and find that their generalization capability is more limited than previous works would suggest. We also challenge the current practice of adding random noise to the network inputs in order to improve its generalization capability and simulation stability. We find that inserting the real data distribution, e.g. by unrolling multiple simulation steps, improves accuracy and that hiding all domain-specific features from the learning model improves generalization. Our results indicate that learning models, such as GNNs, fail to learn the exact underlying dynamics unless the training set is devoid of any other problem-specific correlations that could be used as shortcuts.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/218168b5d4ad7c61f5db656339e3b499fec02cf1" target='_blank'>Simulating Liquids with Graph Networks</a></td>
-          <td>
-            Jonathan Klimesch, Philipp Holl, Nils Thuerey
-          </td>
-          <td>2022-03-14</td>
-          <td>ArXiv</td>
-          <td>8</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="Learning system dynamics directly from observations is a promising direction in machine learning due to its potential to significantly enhance our ability to understand physical systems. However, the dynamics of many real-world systems are challenging to learn due to the presence of nonlinear potentials and a number of interactions that scales quadratically with the number of particles N, as in the case of the N-body problem. In this work we introduce an approach that transforms a fully-connected interaction graph into a hierarchical one which reduces the number of edges to O(N). This results in a linear time and space complexity while the pre-computation of the hierarchical graph requires O(N log (N)) time and O(N) space. Using our approach, we are able to train models on much larger particle counts, even on a single GPU. We evaluate how the phase space position accuracy and energy conservation depend on the number of simulated particles. Our approach retains high accuracy and efficiency even on large-scale gravitational N-body simulations which are impossible to run on a single machine if a fully-connected graph is used. Similar results are also observed when simulating Coulomb interactions. Furthermore, we make several important observations regarding the performance of this new hierarchical model, including: i) its accuracy tends to improve with the number of particles in the simulation and ii) its generalisation to unseen particle counts is also much better than for models that use all O(N^2) interactions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/56f6708f22cbedcc1c600d78408bfbb46669d483" target='_blank'>Scalable Graph Networks for Particle Simulations</a></td>
-          <td>
-            Karolis Martinkus, Aurélien Lucchi, Nathanael Perraudin
-          </td>
-          <td>2020-10-14</td>
-          <td>MAG, ArXiv, DBLP</td>
-          <td>10</td>
-          <td>39</td>
-        </tr>
-    
-        <tr id="Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9e20f6874feaaf7c9994f9875b1d9cab17a2fd59" target='_blank'>Learning Mesh-Based Simulation with Graph Networks</a></td>
-          <td>
-            T. Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, P. Battaglia
-          </td>
-          <td>2020-10-07</td>
-          <td>ArXiv</td>
-          <td>559</td>
-          <td>46</td>
-        </tr>
-    
-        <tr id="Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d7952de05e25e90a08b79431116ca6d2ec85e710" target='_blank'>Unravelling the Performance of Physics-informed Graph Neural Networks for Dynamical Systems</a></td>
-          <td>
-            A. Thangamuthu, Gunjan Kumar, S. Bishnoi, Ravinder Bhattoo, N. Krishnan, Sayan Ranu
-          </td>
-          <td>2022-11-10</td>
-          <td>ArXiv</td>
-          <td>12</td>
-          <td>21</td>
-        </tr>
-    
-        <tr id="In recent years, there has been a growing interest in using machine learning to overcome the high cost of numerical simulation, with some learned models achieving impressive speed-ups over classical solvers whilst maintaining accuracy. However, these methods are usually tested at low-resolution settings, and it remains to be seen whether they can scale to the costly high-resolution simulations that we ultimately want to tackle. In this work, we propose two complementary approaches to improve the framework from MeshGraphNets, which demonstrated accurate predictions in a broad range of physical systems. MeshGraphNets relies on a message passing graph neural network to propagate information, and this structure becomes a limiting factor for high-resolution simulations, as equally distant points in space become further apart in graph space. First, we demonstrate that it is possible to learn accurate surrogate dynamics of a high-resolution system on a much coarser mesh, both removing the message passing bottleneck and improving performance; and second, we introduce a hierarchical approach (MultiScale MeshGraphNets) which passes messages on two different resolutions (fine and coarse), significantly improving the accuracy of MeshGraphNets while requiring less computational resources.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b6841ed68e0e6d9cabeb28e9dfca22ffa853f30f" target='_blank'>MultiScale MeshGraphNets</a></td>
-          <td>
-            Meire Fortunato, Tobias Pfaff, Peter Wirnsberger, A. Pritzel, Peter W. Battaglia
-          </td>
-          <td>2022-10-02</td>
-          <td>ArXiv</td>
-          <td>45</td>
-          <td>27</td>
-        </tr>
-    
-        <tr id="Continuum mechanics simulators, numerically solving one or more partial differential equations, are essential tools in many areas of science and engineering, but their performance often limits application in practice. Recent modern machine learning approaches have demonstrated their ability to accelerate spatio-temporal predictions, although, with only moderate accuracy in comparison. Here we introduce MultiScaleGNN, a novel multi-scale graph neural network model for learning to infer unsteady continuum mechanics. MultiScaleGNN represents the physical domain as an unstructured set of nodes, and it constructs one or more graphs, each of them encoding different scales of spatial resolution. Successive learnt message passing between these graphs improves the ability of GNNs to capture and forecast the system state in problems encompassing a range of length scales. Using graph representations, MultiScaleGNN can impose periodic boundary conditions as an inductive bias on the edges in the graphs, and achieve independence to the nodes' positions. We demonstrate this method on advection problems and incompressible fluid dynamics. Our results show that the proposed model can generalise from uniform advection fields to high-gradient fields on complex domains at test time and infer long-term Navier-Stokes solutions within a range of Reynolds numbers. Simulations obtained with MultiScaleGNN are between two and four orders of magnitude faster than the ones on which it was trained.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bc9df947dee9aa269ef9d5fcd06980598293aea5" target='_blank'>Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks</a></td>
-          <td>
-            Mario Lino, C. Cantwell, A. Bharath, Stathi Fotiadis
-          </td>
-          <td>2021-06-09</td>
-          <td>ArXiv</td>
-          <td>37</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="We introduce an approach for imposing physically informed inductive biases in learned simulation models. We combine graph networks with a differentiable ordinary differential equation integrator as a mechanism for predicting future states, and a Hamiltonian as an internal representation. We find that our approach outperforms baselines without these biases in terms of predictive accuracy, energy accuracy, and zero-shot generalization to time-step sizes and integrator orders not experienced during training. This advances the state-of-the-art of learned simulation, and in principle is applicable beyond physical domains.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/57784e5db3504d549d16382de8f7f4ad222b3d71" target='_blank'>Hamiltonian Graph Networks with ODE Integrators</a></td>
-          <td>
-            Alvaro Sanchez-Gonzalez, V. Bapst, Kyle Cranmer, P. Battaglia
-          </td>
-          <td>2019-09-27</td>
-          <td>ArXiv</td>
-          <td>161</td>
-          <td>46</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a.md b/docs/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a.md
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Graph Deep Learning for Time Series Forecasting</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Time series forecasting lies at the core of important real-world applications in many fields of science and engineering. The abundance of large time series datasets that consist of complex patterns and long-term dependencies has led to the development of various neural network architectures. Graph neural network approaches, which jointly learn a graph structure based on the correlation of raw values of multivariate time series while forecasting, have recently seen great success. However, such solutions are often costly to train and difficult to scale. In this paper, we propose TimeGNN, a method that learns dynamic temporal graph representations that can capture the evolution of inter-series patterns along with the correlations of multiple series. TimeGNN achieves inference times 4 to 80 times faster than other state-of-the-art graph-based methods while achieving comparable forecasting performance">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d9916caa8da69496ecc8e0b1c229c73a60d6f861" target='_blank'>TimeGNN: Temporal Dynamic Graph Learning for Time Series Forecasting</a></td>
-          <td>
-            Nancy R. Xu, Chrysoula Kosma, M. Vazirgiannis
-          </td>
-          <td>2023-07-27</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>54</td>
-        </tr>
-    
-        <tr id="Accurate forecasting of multivariate time series is an extensively studied subject in finance, transportation, and computer science. Fully mining the correlation and causation between the variables in a multivariate time series exhibits noticeable results in improving the performance of a time series model. Recently, some models have explored the dependencies between variables through end-to-end graph structure learning without the need for predefined graphs. However, current models do not incorporate the trade-off between efficiency and flexibility and lack the guidance of domain knowledge in the design of graph structure learning algorithms. This paper alleviates the above issues by proposing Balanced Graph Structure Learning for Forecasting (BGSLF), a novel deep learning model that joins graph structure learning and forecasting. Technically, BGSLF leverages the spatial information into convolutional operations and extracts temporal dynamics using the diffusion convolutional recurrent network. The proposed framework balance the trade-off between efficiency and flexibility by introducing Multi-Graph Generation Network (MGN) and Graph Selection Module. In addition, a method named Smooth Sparse Unit (SSU) is designed to sparse the learned graph structures, which conforms to the sparse spatial correlations in the real world. Extensive experiments on four real-world datasets demonstrate that our model achieves state-of-the-art performances with minor trainable parameters. Code will be made publicly available.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cf803de5a63ec6893960af15756a8e4766c99e0d" target='_blank'>Balanced Graph Structure Learning for Multivariate Time Series Forecasting</a></td>
-          <td>
-            Weijun Chen, Yanze Wang, Chengshuo Du, Zhenglong Jia, Feng Liu, Ran Chen
-          </td>
-          <td>2022-01-24</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>10</td>
-        </tr>
-    
-        <tr id="Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational information characterizing the underlying data-generating process is unavailable and the practitioner is left with the problem of inferring from data which relational graph to use in the subsequent processing stages. We propose novel, principled - yet practical - probabilistic score-based methods that learn the relational dependencies as distributions over graphs while maximizing end-to-end the performance at task. The proposed graph learning framework is based on consolidated variance reduction techniques for Monte Carlo score-based gradient estimation, is theoretically grounded, and, as we show, effective in practice. In this paper, we focus on the time series forecasting problem and show that, by tailoring the gradient estimators to the graph learning problem, we are able to achieve state-of-the-art performance while controlling the sparsity of the learned graph and the computational scalability. We empirically assess the effectiveness of the proposed method on synthetic and real-world benchmarks, showing that the proposed solution can be used as a stand-alone graph identification procedure as well as a graph learning component of an end-to-end forecasting architecture.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0d01d21137a5af9f04e4b16a55a0f732cb8a540b" target='_blank'>Sparse Graph Learning from Spatiotemporal Time Series</a></td>
-          <td>
-            Andrea Cini, Daniele Zambon, C. Alippi
-          </td>
-          <td>2022-05-26</td>
-          <td>J. Mach. Learn. Res.</td>
-          <td>11</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="The challenge of effectively learning inter-series correlations for multivariate time series forecasting remains a substantial and unresolved problem. Traditional deep learning models, which are largely dependent on the Transformer paradigm for modeling long sequences, often fail to integrate information from multiple time series into a coherent and universally applicable model. To bridge this gap, our paper presents ForecastGrapher, a framework reconceptualizes multivariate time series forecasting as a node regression task, providing a unique avenue for capturing the intricate temporal dynamics and inter-series correlations. Our approach is underpinned by three pivotal steps: firstly, generating custom node embeddings to reflect the temporal variations within each series; secondly, constructing an adaptive adjacency matrix to encode the inter-series correlations; and thirdly, augmenting the GNNs' expressive power by diversifying the node feature distribution. To enhance this expressive power, we introduce the Group Feature Convolution GNN (GFC-GNN). This model employs a learnable scaler to segment node features into multiple groups and applies one-dimensional convolutions with different kernel lengths to each group prior to the aggregation phase. Consequently, the GFC-GNN method enriches the diversity of node feature distribution in a fully end-to-end fashion. Through extensive experiments and ablation studies, we show that ForecastGrapher surpasses strong baselines and leading published techniques in the domain of multivariate time series forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/60560da7e2483d4f788c228ebd5e226ae1f40002" target='_blank'>ForecastGrapher: Redefining Multivariate Time Series Forecasting with Graph Neural Networks</a></td>
-          <td>
-            Wanlin Cai, Kun Wang, Hao Wu, Xiaoxu Chen, Yuankai Wu
-          </td>
-          <td>2024-05-28</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Modeling multivariate time series has long been a subject that has attracted researchers from a diverse range of fields including economics, finance, and traffic. A basic assumption behind multivariate time series forecasting is that its variables depend on one another but, upon looking closely, it is fair to say that existing methods fail to fully exploit latent spatial dependencies between pairs of variables. In recent years, meanwhile, graph neural networks (GNNs) have shown high capability in handling relational dependencies. GNNs require well-defined graph structures for information propagation which means they cannot be applied directly for multivariate time series where the dependencies are not known in advance. In this paper, we propose a general graph neural network framework designed specifically for multivariate time series data. Our approach automatically extracts the uni-directed relations among variables through a graph learning module, into which external knowledge like variable attributes can be easily integrated. A novel mix-hop propagation layer and a dilated inception layer are further proposed to capture the spatial and temporal dependencies within the time series. The graph learning, graph convolution, and temporal convolution modules are jointly learned in an end-to-end framework. Experimental results show that our proposed model outperforms the state-of-the-art baseline methods on 3 of 4 benchmark datasets and achieves on-par performance with other approaches on two traffic datasets which provide extra structural information.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/75e924bd79d27a23f3f93d9b1ab62a779505c8d2" target='_blank'>Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks</a></td>
-          <td>
-            Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, Xiaojun Chang, Chengqi Zhang
-          </td>
-          <td>2020-05-24</td>
-          <td>Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining</td>
-          <td>938</td>
-          <td>54</td>
-        </tr>
-    
-        <tr id="Graph Neural Networks (GNN) have gained significant traction in the forecasting domain, especially for their capacity to simultaneously account for intra-series temporal correlations and inter-series relationships. This paper introduces a novel Hierarchical GNN (DeepHGNN) framework, explicitly designed for forecasting in complex hierarchical structures. The uniqueness of DeepHGNN lies in its innovative graph-based hierarchical interpolation and an end-to-end reconciliation mechanism. This approach ensures forecast accuracy and coherence across various hierarchical levels while sharing signals across them, addressing a key challenge in hierarchical forecasting. A critical insight in hierarchical time series is the variance in forecastability across levels, with upper levels typically presenting more predictable components. DeepHGNN capitalizes on this insight by pooling and leveraging knowledge from all hierarchy levels, thereby enhancing the overall forecast accuracy. Our comprehensive evaluation set against several state-of-the-art models confirm the superior performance of DeepHGNN. This research not only demonstrates DeepHGNN's effectiveness in achieving significantly improved forecast accuracy but also contributes to the understanding of graph-based methods in hierarchical time series forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/699d32e116b67bd6f64d689ce7ed97a0aef60ad6" target='_blank'>DeepHGNN: Study of Graph Neural Network based Forecasting Methods for Hierarchically Related Multivariate Time Series</a></td>
-          <td>
-            Abishek Sriramulu, Nicolas Fourrier, Christoph Bergmeir
-          </td>
-          <td>2024-05-29</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="Multivariate time series (MTS) forecasting has shown great importance in numerous industries. Current state-of-the-art graph neural network (GNN)-based forecasting methods usually require both graph networks (e.g., GCN) and temporal networks (e.g., LSTM) to capture inter-series (spatial) dynamics and intra-series (temporal) dependencies, respectively. However, the uncertain compatibility of the two networks puts an extra burden on handcrafted model designs. Moreover, the separate spatial and temporal modeling naturally violates the unified spatiotemporal inter-dependencies in real world, which largely hinders the forecasting performance. To overcome these problems, we explore an interesting direction of directly applying graph networks and rethink MTS forecasting from a pure graph perspective. We first define a novel data structure, hypervariate graph, which regards each series value (regardless of variates or timestamps) as a graph node, and represents sliding windows as space-time fully-connected graphs. This perspective considers spatiotemporal dynamics unitedly and reformulates classic MTS forecasting into the predictions on hypervariate graphs. Then, we propose a novel architecture Fourier Graph Neural Network (FourierGNN) by stacking our proposed Fourier Graph Operator (FGO) to perform matrix multiplications in Fourier space. FourierGNN accommodates adequate expressiveness and achieves much lower complexity, which can effectively and efficiently accomplish the forecasting. Besides, our theoretical analysis reveals FGO's equivalence to graph convolutions in the time domain, which further verifies the validity of FourierGNN. Extensive experiments on seven datasets have demonstrated our superior performance with higher efficiency and fewer parameters compared with state-of-the-art methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9dbcb0893d05e6176353eee401afa4929b570cf6" target='_blank'>FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective</a></td>
-          <td>
-            Kun Yi, Qi Zhang, Wei Fan, Hui He, Liang Hu, Pengyang Wang, Ning An, Longbin Cao, Zhendong Niu
-          </td>
-          <td>2023-11-10</td>
-          <td>ArXiv</td>
-          <td>25</td>
-          <td>4</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Continuous PDE Dynamics Forecasting with Implicit Neural Representations</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an efficient probabilistic framework and a novel encoder design for improved data efficiency and grid independence. The latent state dynamics are governed by a PDE model that combines the collocation method and the method of lines. We employ amortized variational inference for approximate posterior estimation and utilize a multiple shooting technique for enhanced training speed and stability. Our model demonstrates state-of-the-art performance on complex synthetic and real-world datasets, overcoming limitations of previous approaches and effectively handling partially-observed data. The proposed model outperforms recent methods, showing its potential to advance data-driven PDE modeling and enabling robust, grid-independent modeling of complex partially-observed dynamic processes.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/18fc14bf5e659e56f4c5cc3ccd593462dd28c383" target='_blank'>Learning Space-Time Continuous Neural PDEs from Partially Observed States</a></td>
-          <td>
-            V. Iakovlev, Markus Heinonen, H. Lähdesmäki
-          </td>
-          <td>2023-07-09</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>48</td>
-        </tr>
-    
-        <tr id="Significance In many physical systems, the governing equations are known with high confidence, but direct numerical solution is prohibitively expensive. Often this situation is alleviated by writing effective equations to approximate dynamics below the grid scale. This process is often impossible to perform analytically and is often ad hoc. Here we propose data-driven discretization, a method that uses machine learning to systematically derive discretizations for continuous physical systems. On a series of model problems, data-driven discretization gives accurate solutions with a dramatic drop in required resolution. The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length- and timescales. Often, it is computationally intractable to resolve the finest features in the solution. The only recourse is to use approximate coarse-grained representations, which aim to accurately represent long-wavelength dynamics while properly accounting for unresolved small-scale physics. Deriving such coarse-grained equations is notoriously difficult and often ad hoc. Here we introduce data-driven discretization, a method for learning optimized approximations to PDEs based on actual solutions to the known underlying equations. Our approach uses neural networks to estimate spatial derivatives, which are optimized end to end to best satisfy the equations on a low-resolution grid. The resulting numerical methods are remarkably accurate, allowing us to integrate in time a collection of nonlinear equations in 1 spatial dimension at resolutions 4× to 8× coarser than is possible with standard finite-difference methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9a43842478bf9d1aff71e964f584af4eeb196073" target='_blank'>Learning data-driven discretizations for partial differential equations</a></td>
-          <td>
-            Yohai Bar-Sinai, Stephan Hoyer, Jason Hickey, M. Brenner
-          </td>
-          <td>2018-08-15</td>
-          <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>430</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and predicts its evolution using sparsely distributed data sites. Deep learning has shown promising results in modeling physical dynamics in recent years. However, most of the existing deep learning methods for modeling physical dynamics either focus on solving known PDEs or require data in a dense grid when the governing PDEs are unknown. In contrast, our method focuses on learning prediction models for unknown PDE-driven dynamics only from sparsely observed data. The proposed method is spatial dimension-independent and geometrically flexible. We demonstrate our method in the forecasting task for the two-dimensional wave equation and the Burgers-Fisher equation in multiple geometries with different boundary conditions, and the ten-dimensional heat equation.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e00fa719a36548c833fe2abe1c2180ecaf3e8e0f" target='_blank'>A Deep Learning Approach for Predicting Spatiotemporal Dynamics From Sparsely Observed Data</a></td>
-          <td>
-            Priyabrata Saha, S. Mukhopadhyay
-          </td>
-          <td>2020-12-01</td>
-          <td>IEEE Access</td>
-          <td>4</td>
-          <td>45</td>
-        </tr>
-    
-        <tr id="Recent advances in incorporating physical knowledge into deep neural networks can estimate previously unknown governing partial differential equations (PDEs) in a data-driven way. They have shown promising results in spatiotemporal predictive learning. However, these methods typically assume universal governing PDEs across space, which is impractical for modeling complex spatiotemporal phenomena with high spatial variability (e.g., climate). Also, they cannot effectively model the evolution of potential errors in estimating the physical dynamics over time. This paper introduces a physics-guided neural network, SVPNet, which learns effective physical representations by estimating the error evolution in physics states for correction and modeling spatially varying physical dynamics to predict the next state. Experiments carried out in four scenarios, including benchmarks and real-world datasets, show that SVPNet outperforms state-of-the-art methods in spatiotemporal prediction tasks for natural processes and significantly improves prediction when training data are limited. Ablation studies also highlight that SVPNet is powerful in capturing physical dynamics in complex physical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a79653a75c7412044433ab2757edce70b964019a" target='_blank'>Modeling Spatially Varying Physical Dynamics for Spatiotemporal Predictive Learning</a></td>
-          <td>
-            Yijun Lin, Yao-Yi Chiang
-          </td>
-          <td>2023-11-13</td>
-          <td>Proceedings of the 31st ACM International Conference on Advances in Geographic Information Systems</td>
-          <td>0</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make specific assumptions on the type of DEs, making the model specialized for particular problems. This work presents a partial differential equation (PDE) based framework which improves the dynamics modeling capability. Building upon the recent Fourier neural operator, we propose a neural operator that can handle time continuously without requiring iterative operations or specific grids of temporal discretization. A theoretical result demonstrating its universality is provided. We also uncover an intrinsic property of neural operators that improves data efficiency and model generalization by ensuring stability. Our model achieves superior accuracy in dealing with time-dependent PDEs compared to existing models. Furthermore, several numerical pieces of evidence validate that our method better represents a wide range of dynamics and outperforms state-of-the-art DE-based models in real-time-series applications. Our framework opens up a new way for a continuous representation of neural networks that can be readily adopted for real-world applications.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1095fbfe9feb9117819a6d899faf624f2e943e73" target='_blank'>Learning PDE Solution Operator for Continuous Modeling of Time-Series</a></td>
-          <td>
-            Yesom Park, Jaemoo Choi, Changyeon Yoon, Changhoon Song, Myung-joo Kang
-          </td>
-          <td>2023-02-02</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="Recently, Conditional Neural Fields (NeFs) have emerged as a powerful modelling paradigm for PDEs, by learning solutions as flows in the latent space of the Conditional NeF. Although benefiting from favourable properties of NeFs such as grid-agnosticity and space-time-continuous dynamics modelling, this approach limits the ability to impose known constraints of the PDE on the solutions -- e.g. symmetries or boundary conditions -- in favour of modelling flexibility. Instead, we propose a space-time continuous NeF-based solving framework that - by preserving geometric information in the latent space - respects known symmetries of the PDE. We show that modelling solutions as flows of pointclouds over the group of interest $G$ improves generalization and data-efficiency. We validated that our framework readily generalizes to unseen spatial and temporal locations, as well as geometric transformations of the initial conditions - where other NeF-based PDE forecasting methods fail - and improve over baselines in a number of challenging geometries.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9c8295fdfb6de078027cabc7d49b319df8abb0ee" target='_blank'>Space-Time Continuous PDE Forecasting using Equivariant Neural Fields</a></td>
-          <td>
-            David M. Knigge, David R. Wessels, Riccardo Valperga, Samuele Papa, J. Sonke, E. Gavves, E. J. Bekkers
-          </td>
-          <td>2024-06-10</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>56</td>
-        </tr>
-    
-        <tr id="We present AROMA (Attentive Reduced Order Model with Attention), a framework designed to enhance the modeling of partial differential equations (PDEs) using local neural fields. Our flexible encoder-decoder architecture can obtain smooth latent representations of spatial physical fields from a variety of data types, including irregular-grid inputs and point clouds. This versatility eliminates the need for patching and allows efficient processing of diverse geometries. The sequential nature of our latent representation can be interpreted spatially and permits the use of a conditional transformer for modeling the temporal dynamics of PDEs. By employing a diffusion-based formulation, we achieve greater stability and enable longer rollouts compared to conventional MSE training. AROMA's superior performance in simulating 1D and 2D equations underscores the efficacy of our approach in capturing complex dynamical behaviors.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ed3fa74ebc0adcad4aee915c4625b384eaddbc91" target='_blank'>AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields</a></td>
-          <td>
-            Louis Serrano, Thomas X. Wang, E. L. Naour, Jean-Noël Vittaut, P. Gallinari
-          </td>
-          <td>2024-06-04</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>48</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6645028d3aad0592fe663469862fa3a2b05e73c3" target='_blank'>STENCIL-NET for equation-free forecasting from data</a></td>
-          <td>
-            S. Maddu, D. Sturm, B. Cheeseman, Christian L. Müller, I. Sbalzarini
-          </td>
-          <td>2023-08-07</td>
-          <td>Scientific Reports</td>
-          <td>3</td>
-          <td>38</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c3d769578637c4eebda2ace167b51a0a3ff7698d" target='_blank'>NeuralPDE: Modelling Dynamical Systems from Data</a></td>
-          <td>
-            Andrzej Dulny, A. Hotho, Anna Krause
-          </td>
-          <td>2021-11-15</td>
-          <td>ArXiv</td>
-          <td>8</td>
-          <td>53</td>
-        </tr>
-    
-        <tr id="Numerical methods for approximately solving partial differential equations (PDE) are at the core of scientific computing. Often, this requires high-resolution or adaptive discretization grids to capture relevant spatio-temporal features in the PDE solution, e.g., in applications like turbulence, combustion, and shock propagation. Numerical approximation also requires knowing the PDE in order to construct problem-specific discretizations. Systematically deriving such solution-adaptive discrete operators, however, is a current challenge. Here we present STENCIL-NET, an artificial neural network architecture for data-driven learning of problem- and resolution-specific local discretizations of nonlinear PDEs. STENCIL-NET achieves numerically stable discretization of the operators in an unknown nonlinear PDE by spatially and temporally adaptive parametric pooling on regular Cartesian grids, and by incorporating knowledge about discrete time integration. Knowing the actual PDE is not necessary, as solution data is sufficient to train the network to learn the discrete operators. A once-trained STENCIL-NET model can be used to predict solutions of the PDE on larger spatial domains and for longer times than it was trained for, hence addressing the problem of PDE-constrained extrapolation from data. To support this claim, we present numerical experiments on long-term forecasting of chaotic PDE solutions on coarse spatio-temporal grids. We also quantify the speed-up achieved by substituting base-line numerical methods with equation-free STENCIL-NET predictions on coarser grids with little compromise on accuracy.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9892628c5207890a3987a196304fc32a2bbacafd" target='_blank'>STENCIL-NET: Data-driven solution-adaptive discretization of partial differential equations</a></td>
-          <td>
-            S. Maddu, D. Sturm, B. Cheeseman, Christian L. Müller, I. Sbalzarini
-          </td>
-          <td>2021-01-15</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>38</td>
-        </tr>
-    
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-        <th>Title</th>
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-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
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-        <th>Publication Date</th>
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-        <tr id="Time-series and graphs have been extensively studied for their ubiquitous existence in numerous domains. Both topics have been separately explored in the field of deep learning. For time-series modeling, recurrent neural networks or convolutional neural networks model the relations between values across timesteps, while for graph modeling, graph neural networks model the inter-relations between nodes. Recent research in deep learning requires simultaneous modeling for time-series and graphs when both representations are present. For example, both types of modeling are necessary for time-series classification, regression, and anomaly detection in graphs. This article aims to provide a comprehensive summary of these models, which we call graph time-series models. To the best of our knowledge, this is the first survey article that provides a picture of related models from the perspective of deep graph time-series modeling to address a range of time-series tasks, including regression, classification, and anomaly detection. Graph time-series models are split into two categories: (a) graph recurrent/convolutional neural networks and (b) graph attention neural networks. Under each category, we further categorize models based on their properties. Additionally, we compare representative models and discuss how distinctive model characteristics are utilized with respect to various model components and data challenges. Pointers to commonly used datasets and code are included to facilitate access for further research. In the end, we discuss potential directions for future research.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2fb8c64bd14f62d2f65377ee3835555a748a8ada" target='_blank'>Graph Time-series Modeling in Deep Learning: A Survey</a></td>
-          <td>
-            Hongjie Chen, Hoda Eldardiry
-          </td>
-          <td>2023-12-23</td>
-          <td>ACM Transactions on Knowledge Discovery from Data</td>
-          <td>1</td>
-          <td>14</td>
-        </tr>
-    
-        <tr id="Time series forecasting lies at the core of important real-world applications in many fields of science and engineering. The abundance of large time series datasets that consist of complex patterns and long-term dependencies has led to the development of various neural network architectures. Graph neural network approaches, which jointly learn a graph structure based on the correlation of raw values of multivariate time series while forecasting, have recently seen great success. However, such solutions are often costly to train and difficult to scale. In this paper, we propose TimeGNN, a method that learns dynamic temporal graph representations that can capture the evolution of inter-series patterns along with the correlations of multiple series. TimeGNN achieves inference times 4 to 80 times faster than other state-of-the-art graph-based methods while achieving comparable forecasting performance">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d9916caa8da69496ecc8e0b1c229c73a60d6f861" target='_blank'>TimeGNN: Temporal Dynamic Graph Learning for Time Series Forecasting</a></td>
-          <td>
-            Nancy R. Xu, Chrysoula Kosma, M. Vazirgiannis
-          </td>
-          <td>2023-07-27</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>54</td>
-        </tr>
-    
-        <tr id="Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ccea298edb788edf821aef58f0952c3e8debc25a" target='_blank'>Graph Deep Learning for Time Series Forecasting</a></td>
-          <td>
-            Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi
-          </td>
-          <td>2023-10-24</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="With the recent advances in technology, a wide range of systems continue to collect a large amount of data over time and thus generate time series. Time-Series Anomaly Detection (TSAD) is an important task in various time-series applications such as e-commerce, cybersecurity, vehicle maintenance, and healthcare monitoring. However, this task is very challenging as it requires considering both the intra-variable dependency and the inter-variable dependency, where a variable can be defined as an observation in time-series data. Recent graph-based approaches have made impressive progress in tackling the challenges of this field. In this survey, we conduct a comprehensive and up-to-date review of TSAD using graphs, referred to as G-TSAD. First, we explore the significant potential of graph representation learning for time-series data. Then, we review state-of-the-art graph anomaly detection techniques in the context of time series and discuss their strengths and drawbacks. Finally, we discuss the technical challenges and potential future directions for possible improvements in this research field.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cf0eaa1b8d9cdc56f6cef0d95fa4007adb57aff7" target='_blank'>Graph Anomaly Detection in Time Series: A Survey</a></td>
-          <td>
-            Thi Kieu Khanh Ho, Ali Karami, N. Armanfard
-          </td>
-          <td>2023-01-31</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>15</td>
-        </tr>
-    
-        <tr id="Multivariate time series (MTS) forecasting has shown great importance in numerous industries. Current state-of-the-art graph neural network (GNN)-based forecasting methods usually require both graph networks (e.g., GCN) and temporal networks (e.g., LSTM) to capture inter-series (spatial) dynamics and intra-series (temporal) dependencies, respectively. However, the uncertain compatibility of the two networks puts an extra burden on handcrafted model designs. Moreover, the separate spatial and temporal modeling naturally violates the unified spatiotemporal inter-dependencies in real world, which largely hinders the forecasting performance. To overcome these problems, we explore an interesting direction of directly applying graph networks and rethink MTS forecasting from a pure graph perspective. We first define a novel data structure, hypervariate graph, which regards each series value (regardless of variates or timestamps) as a graph node, and represents sliding windows as space-time fully-connected graphs. This perspective considers spatiotemporal dynamics unitedly and reformulates classic MTS forecasting into the predictions on hypervariate graphs. Then, we propose a novel architecture Fourier Graph Neural Network (FourierGNN) by stacking our proposed Fourier Graph Operator (FGO) to perform matrix multiplications in Fourier space. FourierGNN accommodates adequate expressiveness and achieves much lower complexity, which can effectively and efficiently accomplish the forecasting. Besides, our theoretical analysis reveals FGO's equivalence to graph convolutions in the time domain, which further verifies the validity of FourierGNN. Extensive experiments on seven datasets have demonstrated our superior performance with higher efficiency and fewer parameters compared with state-of-the-art methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9dbcb0893d05e6176353eee401afa4929b570cf6" target='_blank'>FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective</a></td>
-          <td>
-            Kun Yi, Qi Zhang, Wei Fan, Hui He, Liang Hu, Pengyang Wang, Ning An, Longbin Cao, Zhendong Niu
-          </td>
-          <td>2023-11-10</td>
-          <td>ArXiv</td>
-          <td>25</td>
-          <td>4</td>
-        </tr>
-    
-        <tr id="Anomaly detection of time series, especially multivariate time series(time series with multiple sensors), has been focused on for several years. Though existing method has achieved great progress, there are several challenging problems to be solved. Firstly, existing method including neural network only concentrate on the relationship in terms of timestamp. To be exact, they only want to know how does the data in the past influence which in the future. However, one sensor sometimes intervenes in other sensor such as the speed of wind may cause decrease of temperature. Secondly, there exist two categories of model for time series anomaly detection: prediction model and reconstruction model. Prediction model is adept at learning timely representation while short of capability when faced with sparse anomaly. Conversely, reconstruction model is opposite. Therefore, how can we efficiently get the relationship both in terms of both timestamp and sensors becomes our main topic. Our approach uses GAT, which is originated from graph neural network, to obtain connection between sensors. And LSTM is used to obtain relationships timely. Our approach is also designed to be double headed to calculate both prediction loss and reconstruction loss via VAE(Variational Auto-Encoder). In order to take advantage of two sorts of model, multi-task optimization algorithm is used in this model.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2859004fbfeaa7b388b73ee632c1eda77afeafc0" target='_blank'>MGADN: A Multi-task Graph Anomaly Detection Network for Multivariate Time Series</a></td>
-          <td>
-            Wei-Shu Xiong, Xiaochen (Michael) Sun
-          </td>
-          <td>2022-11-22</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Anomalies in univariate time series often refer to abnormal values and deviations from the temporal patterns from majority of historical observations. In multivariate time series, anomalies also refer to abnormal changes in the inter-series relationship, such as correlation, over time. Existing studies have been able to model such inter-series relationships through graph neural networks. However, most works settle on learning a static graph globally or within a context window to assist a time series forecasting task or a reconstruction task, whose objective is not tailored to explicitly detect the abnormal relationship. Some other works detect anomalies based on reconstructing or forecasting a list of inter-series graphs, which inadvertently weakens their power to capture temporal patterns within the data due to the discrete nature of graphs. In this study, we propose DyGraphAD, a multivariate time series anomaly detection framework based upon a list of dynamic inter-series graphs. The core idea is to detect anomalies based on the deviation of inter-series relationships and intra-series temporal patterns from normal to anomalous states, by leveraging the evolving nature of the graphs in order to assist a graph forecasting task and a time series forecasting task simultaneously. Our numerical experiments on real-world datasets demonstrate that DyGraphAD has superior performance than baseline anomaly detection approaches.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bd2aad6aa8c0b257a0ef98404f58dd541e27e774" target='_blank'>Multivariate Time Series Anomaly Detection via Dynamic Graph Forecasting</a></td>
-          <td>
-            Katrina Chen, M. Feng, T. Wirjanto
-          </td>
-          <td>2023-02-04</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>22</td>
-        </tr>
-    
-        <tr id="With the rapid advancement in cyber-physical systems, the increasing number of sensors has significantly complicated manual monitoring of system states. Consequently, graph-based time-series anomaly detection methods have gained attention due to their ability to explicitly represent relationships between sensors. However, these methods often apply a uniform source node representation across all connected target nodes, even when updating different target node representations. Moreover, the graph attention mechanism, commonly used to infer unknown graph structures, could constrain the diversity of source node representations. In this paper, we introduce the Edge Conditional Node-update Graph Neural Network (ECNU-GNN). Our model, equipped with an edge conditional node update module, dynamically transforms source node representations based on connected edges to represent target nodes aptly. We validate performance on three real-world datasets: SWaT, WADI, and PSM. Our model demonstrates 5.4%, 12.4%, and 6.0% higher performance, respectively, compared to best F1 baseline models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/29f738cfaf281d7c863a0dcb3f7603deccd2a97f" target='_blank'>Edge Conditional Node Update Graph Neural Network for Multi-variate Time Series Anomaly Detection</a></td>
-          <td>
-            H. Jo, Seong-Whan Lee
-          </td>
-          <td>2024-01-25</td>
-          <td>Inf. Sci.</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Spatio-temporal forecasting of future values of spatially correlated time series is important across many cyber-physical systems (CPS). Recent studies offer evidence that the use of graph neural networks to capture latent correlations between time series holds a potential for enhanced forecasting. However, most existing methods rely on predefined or self-learning graphs, which are either static or unintentionally dynamic, and thus cannot model the time-varying correlations that exhibit trends and periodicities caused by the regularity of the underlying processes in CPS. To tackle such limitation, we propose Time-aware Graph Structure Learning (TagSL), which extracts time-aware correlations among time series by measuring the interaction of node and time representations in high-dimensional spaces. Notably, we introduce time discrepancy learning that utilizes contrastive learning with distance-based regularization terms to constrain learned spatial correlations to a trend sequence. Additionally, we propose a periodic discriminant function to enable the capture of periodic changes from the state of nodes. Next, we present a Graph Convolution-based Gated Recurrent Unit (GCGRU) that jointly captures spatial and temporal dependencies while learning time-aware and node-specific patterns. Finally, we introduce a unified framework named Time-aware Graph Convolutional Recurrent Network (TGCRN), combining TagSL, and GCGRU in an encoder-decoder architecture for multi-step spatiotemporal forecasting. We report on experiments with TGCRN and popular existing approaches on five real-world datasets, thus providing evidence that TGCRN is capable of advancing the state-of-the-art. We also cover a detailed ablation study and visualization analysis, offering detailed insight into the effectiveness of time-aware structure learning.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2e635d42e768aec7be29fbd203a605c1f011a44d" target='_blank'>Learning Time-Aware Graph Structures for Spatially Correlated Time Series Forecasting</a></td>
-          <td>
-            Minbo Ma, Jilin Hu, Christian S. Jensen, Fei Teng, Peng Han, Zhiqiang Xu, Tian-Jie Li
-          </td>
-          <td>2023-12-27</td>
-          <td>2024 IEEE 40th International Conference on Data Engineering (ICDE)</td>
-          <td>0</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="Multivariate time-series anomaly detection is critically important in many applications, including retail, transportation, power grid, and water treatment plants. Existing approaches for this problem mostly employ either statistical models which cannot capture the nonlinear relations well or conventional deep learning (DL) models e.g., convolutional neural network (CNN) and long short-term memory (LSTM) that do not explicitly learn the pairwise correlations among variables. To overcome these limitations, we propose a novel method, correlation-aware spatial-temporal graph learning (termed ), for time-series anomaly detection. explicitly captures the pairwise correlations via a correlation learning (MTCL) module based on which a spatial-temporal graph neural network (STGNN) can be developed. Then, by employing a graph convolution network (GCN) that exploits one-and multihop neighbor information, our STGNN component can encode rich spatial information from complex pairwise dependencies between variables. With a temporal module that consists of dilated convolutional functions, the STGNN can further capture long-range dependence over time. A novel anomaly scoring component is further integrated into to estimate the degree of an anomaly in a purely unsupervised manner. Experimental results demonstrate that can detect and diagnose anomalies effectively in general settings as well as enable early detection across different time delays. Our code is available at https://github.com/huankoh/CST-GL.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eb46fe40562fe20eac559174dacd98614d80d1e4" target='_blank'>Correlation-aware Spatial-Temporal Graph Learning for Multivariate Time-series Anomaly Detection</a></td>
-          <td>
-            Yu Zheng, Huan Yee Koh, Ming Jin, Lianhua Chi, Khoa T. Phan, Shirui Pan, Yi-Ping Phoebe Chen, Wei Xiang
-          </td>
-          <td>2023-07-17</td>
-          <td>IEEE transactions on neural networks and learning systems</td>
-          <td>8</td>
-          <td>18</td>
-        </tr>
-    
-  </tbody>
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-        <th>Title</th>
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-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Learning rigid dynamics with face interaction graph networks</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6c7dbbb11ba59c09bf73869f9fa5f73fd5d17e72" target='_blank'>Learning Flexible Body Collision Dynamics with Hierarchical Contact Mesh Transformer</a></td>
-          <td>
-            Youn-Yeol Yu, Jeongwhan Choi, Woojin Cho, Kookjin Lee, Nayong Kim, Kiseok Chang, ChangSeung Woo, Ilho Kim, Seok-Woo Lee, Joon Young Yang, S. Yoon, Noseong Park
-          </td>
-          <td>2023-12-19</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>8</td>
-        </tr>
-    
-        <tr id="Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9e20f6874feaaf7c9994f9875b1d9cab17a2fd59" target='_blank'>Learning Mesh-Based Simulation with Graph Networks</a></td>
-          <td>
-            T. Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, P. Battaglia
-          </td>
-          <td>2020-10-07</td>
-          <td>ArXiv</td>
-          <td>559</td>
-          <td>46</td>
-        </tr>
-    
-        <tr id="Simulating large scenes with many rigid objects is crucial for a variety of applications, such as robotics, engineering, film and video games. Rigid interactions are notoriously hard to model: small changes to the initial state or the simulation parameters can lead to large changes in the final state. Recently, learned simulators based on graph networks (GNNs) were developed as an alternative to hand-designed simulators like MuJoCo and PyBullet. They are able to accurately capture dynamics of real objects directly from real-world observations. However, current state-of-the-art learned simulators operate on meshes and scale poorly to scenes with many objects or detailed shapes. Here we present SDF-Sim, the first learned rigid-body simulator designed for scale. We use learned signed-distance functions (SDFs) to represent the object shapes and to speed up distance computation. We design the simulator to leverage SDFs and avoid the fundamental bottleneck of the previous simulators associated with collision detection. For the first time in literature, we demonstrate that we can scale the GNN-based simulators to scenes with hundreds of objects and up to 1.1 million nodes, where mesh-based approaches run out of memory. Finally, we show that SDF-Sim can be applied to real world scenes by extracting SDFs from multi-view images.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ce2992a1d7c057b170909cc2f7db442f0d32f5dc" target='_blank'>Learning rigid-body simulators over implicit shapes for large-scale scenes and vision</a></td>
-          <td>
-            Yulia Rubanova, Tatiana Lopez-Guevara, Kelsey R. Allen, William F. Whitney, Kimberly L. Stachenfeld, Tobias Pfaff
-          </td>
-          <td>2024-05-22</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. However, they still encounter several challenges: 1) Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization and should be incorporated into the model design. Existing simulators either consider insufficient symmetry, or enforce excessive equivariance in practice when symmetry is partially broken by gravity. 2) Objects in the physical world possess diverse shapes, sizes, and properties, which should be appropriately processed by the model. To tackle these difficulties, we propose a novel backbone, Subequivariant Graph Neural Network, which 1) relaxes equivariance to subequivariance by considering external fields like gravity, where the universal approximation ability holds theoretically; 2) introduces a new subequivariant object-aware message passing for learning physical interactions between multiple objects of various shapes in the particle-based representation; 3) operates in a hierarchical fashion, allowing for modeling long-range and complex interactions. Our model achieves on average over 3% enhancement in contact prediction accuracy across 8 scenarios on Physion and 2X lower rollout MSE on RigidFall compared with state-of-the-art GNN simulators, while exhibiting strong generalization and data efficiency.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/91090894c7fda3a19000f7224349e9168f9d7d42" target='_blank'>Learning Physical Dynamics with Subequivariant Graph Neural Networks</a></td>
-          <td>
-            Jiaqi Han, Wenbing Huang, Hengbo Ma, Jiachen Li, J. Tenenbaum, Chuang Gan
-          </td>
-          <td>2022-10-13</td>
-          <td>ArXiv</td>
-          <td>21</td>
-          <td>124</td>
-        </tr>
-    
-        <tr id="We present a robust learning algorithm to detect and handle collisions in 3D deforming meshes. Our collision detector is represented as a bilevel deep autoencoder with an attention mechanism that identifies colliding mesh sub-parts. We use a numerical optimization algorithm to resolve penetrations guided by the network. Our learned collision handler can resolve collisions for unseen, high-dimensional meshes with thousands of vertices. To obtain stable network performance in such large and unseen spaces, we progressively insert new collision data based on the errors in network inferences. We automatically label these data using an analytical collision detector and progressively fine-tune our detection networks. We evaluate our method for collision handling of complex, 3D meshes coming from several datasets with different shapes and topologies, including datasets corresponding to dressed and undressed human poses, cloth simulations, and human hand poses acquired using multiview capture systems. Our approach outperforms supervised learning methods and achieves $93.8-98.1\%$ accuracy compared to the groundtruth by analytic methods. Compared to prior learning methods, our approach results in a $5.16\%-25.50\%$ lower false negative rate in terms of collision checking and a $9.65\%-58.91\%$ higher success rate in collision handling.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2558e6159ac733bd36199a0a99e964193d59ac9b" target='_blank'>Active Learning of Neural Collision Handler for Complex 3D Mesh Deformations</a></td>
-          <td>
-            Qingyang Tan, Zherong Pan, Breannan Smith, Takaaki Shiratori, Dinesh Manocha
-          </td>
-          <td>2021-10-08</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>95</td>
-        </tr>
-    
-        <tr id="Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term "Graph Network-based Simulators" (GNS)---represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c529f5b08675f787cdcc094ee495239592339f82" target='_blank'>Learning to Simulate Complex Physics with Graph Networks</a></td>
-          <td>
-            Alvaro Sanchez-Gonzalez, Jonathan Godwin, T. Pfaff, Rex Ying, J. Leskovec, P. Battaglia
-          </td>
-          <td>2020-02-21</td>
-          <td>ArXiv</td>
-          <td>849</td>
-          <td>134</td>
-        </tr>
-    
-        <tr id="Deep learning-based cloth simulation approaches have potential in achieving real-time simulation of complex cloth by directly learning a mapping from control input to resulting cloth movement, bypassing the need for time-consuming dynamic solving and collision processing. Recent advancements have demonstrated the effectiveness of Graph Neural Networks (GNN) in learning cloth dynamics. However, existing GNN-based models have limitations in predicting scenarios involving complex cloth movement. To overcome this limitation, we propose a novel GNN-based model that incorporates several components, including RNN-based state encoding and physics-informed features. Our model significantly improves the accuracy of cloth dynamics prediction in various scenarios, including those with complex cloth movement driven by control handles. Furthermore, our model demonstrates generalization capabilities for cloth mesh topology and control handle configurations. We validate the effectiveness of our approach through ablation studies and comparisons with a baseline model.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/947d571f5f4bb080a6453a593595373aca73642f" target='_blank'>MeshGraphNetRP: Improving Generalization of GNN-based Cloth Simulation</a></td>
-          <td>
-            Emmanuel Ian Libao, Myeongjin Lee, Sumin Kim, Sung-Hee Lee
-          </td>
-          <td>2023-11-15</td>
-          <td>Proceedings of the 16th ACM SIGGRAPH Conference on Motion, Interaction and Games</td>
-          <td>1</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="We present a novel mesh‐based learning approach (N‐Cloth) for plausible 3D cloth deformation prediction. Our approach is general and can handle cloth or obstacles represented by triangle meshes with arbitrary topologies. We use graph convolution to transform the cloth and object meshes into a latent space to reduce the non‐linearity in the mesh space. Our network can predict the target 3D cloth mesh deformation based on the initial state of the cloth mesh template and the target obstacle mesh. Our approach can handle complex cloth meshes with up to 100K triangles and scenes with various objects corresponding to SMPL humans, non‐SMPL humans or rigid bodies. In practice, our approach can be used to generate plausible cloth simulation at 30 – 45 fps on an NVIDIA GeForce RTX 3090 GPU. We highlight its benefits over prior learning‐based methods and physically‐based cloth simulators.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/654d109ce463e2e1d83187da22d12e7a184db508" target='_blank'>N‐Cloth: Predicting 3D Cloth Deformation with Mesh‐Based Networks</a></td>
-          <td>
-            Yudi Li, Min Tang, Yun-bo Yang, Zi Huang, Ruofeng Tong, Shuangcai Yang, Yao Li, Dinesh Manocha
-          </td>
-          <td>2021-12-13</td>
-          <td>Computer Graphics Forum</td>
-          <td>16</td>
-          <td>95</td>
-        </tr>
-    
-        <tr id="Physics-based simulation of mesh based domains remains a challenging task. State-of-the-art techniques can produce realistic results but require expert knowledge. A major bottleneck in many approaches is the step of integrating a potential energy in order to compute velocities or displacements. Recently, learning based method for physics-based simulation have sparked interest with graph based approaches being a promising research direction. One of the challenges for these methods is to generate models that are mesh independent and generalize to different material properties. Moreover, the model should also be able to react to unforeseen external forces like ubiquitous collisions. Our contribution is based on a simple observation: evaluating forces is computationally relatively cheap for traditional simulation methods and can be computed in parallel in contrast to their integration. If we learn how a system reacts to forces in general, irrespective of their origin, we can learn an integrator that can predict state changes due to the total forces with high generalization power. We effectively factor out the physical model behind resulting forces by relying on an opaque force module. We demonstrate that this idea leads to a learnable module that can be trained on basic internal forces of small mesh patches and generalizes to different mesh typologies, resolutions, material parameters and unseen forces like collisions at inference time. Our proposed paradigm is general and can be used to model a variety of physical phenomena. We focus our exposition on the detail enhancement of coarse clothing geometry which has many applications including computer games, virtual reality and virtual try-on.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/20c3503df4e7929dc25142ed2e45f0f759afeca7" target='_blank'>PhysGraph: Physics-Based Integration Using Graph Neural Networks</a></td>
-          <td>
-            Oshri Halimi, E.T Larionov, Zohar Barzelay, Philipp Herholz, Tuur Stuyck
-          </td>
-          <td>2023-01-27</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>12</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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diff --git a/docs/recommendations/d8d8e2c04ca47bd628bd2a499e03ad7cd29633da.md b/docs/recommendations/d8d8e2c04ca47bd628bd2a499e03ad7cd29633da.md
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-  <i class="footer">This page was last updated on 2024-07-22 06:06:36 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged covariate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of the variational autoencoder (VAE), which is able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/88a277bbc18ad0eed29ea02bef0219b1c1a111ab" target='_blank'>Variational encoding of complex dynamics.</a></td>
-          <td>
-            Carlos X. Hernández, H. Wayment-Steele, Mohammad M. Sultan, B. Husic, V. Pande
-          </td>
-          <td>2017-11-23</td>
-          <td>Physical review. E</td>
-          <td>135</td>
-          <td>103</td>
-        </tr>
-    
-        <tr id="Abstract Abstract The convergence of free-energy calculations based on importance sampling depends heavily on the choice of collective variables (CVs), which in principle, should include the slow degrees of freedom of the biological processes to be investigated. Autoencoders (AEs), as emerging data-driven dimension reduction tools, have been utilised for discovering CVs. AEs, however, are often treated as black boxes, and what AEs actually encode during training, and whether the latent variables from encoders are suitable as CVs for further free-energy calculations remains unknown. In this contribution, we review AEs and their time-series-based variants, including time-lagged AEs (TAEs) and modified TAEs, as well as the closely related model variational approach for Markov processes networks (VAMPnets). We then show through numerical examples that AEs learn the high-variance modes instead of the slow modes. In stark contrast, time series-based models are able to capture the slow modes. Moreover, both modified TAEs with extensions from slow feature analysis and the state-free reversible VAMPnets (SRVs) can yield orthogonal multidimensional CVs. As an illustration, we employ SRVs to discover the CVs of the isomerizations of N-acetyl-N′-methylalanylamide and trialanine by iterative learning with trajectories from biased simulations. Last, through numerical experiments with anisotropic diffusion, we investigate the potential relationship of time-series-based models and committor probabilities.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0ec461f9fd4b19b52508e85f3ffb7b7e70fc5d67" target='_blank'>Chasing collective variables using temporal data-driven strategies</a></td>
-          <td>
-            Haochuan Chen, C. Chipot
-          </td>
-          <td>2023-01-06</td>
-          <td>QRB Discovery</td>
-          <td>9</td>
-          <td>54</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f8a6341496701a0d7fdaa50e6a5aa157236a0ff8" target='_blank'>Author Correction: VAMPnets for deep learning of molecular kinetics</a></td>
-          <td>
-            Andreas Mardt, Luca Pasquali, Hao Wu, F. Noé
-          </td>
-          <td>2018-10-22</td>
-          <td>Nature Communications</td>
-          <td>24</td>
-          <td>61</td>
-        </tr>
-    
-        <tr id="High‐dimensional metastable molecular dynamics (MD) can often be characterised by a few features of the system, that is, collective variables (CVs). Thanks to the rapid advance in the area of machine learning and deep learning, various deep learning‐based CV identification techniques have been developed in recent years, allowing accurate modelling and efficient simulation of complex molecular systems. In this paper, we look at two different categories of deep learning‐based approaches for finding CVs, either by computing leading eigenfunctions of transfer operator associated to the underlying dynamics, or by learning an autoencoder via minimisation of reconstruction error. We present a concise overview of the mathematics behind these two approaches and conduct a comparative numerical study of these two approaches on illustrative examples.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0187ec0ad130049a72e9cfc50c6160437c3fb2aa" target='_blank'>Understanding recent deep‐learning techniques for identifying collective variables of molecular dynamics</a></td>
-          <td>
-            W. Zhang, Christof Schutte
-          </td>
-          <td>2023-07-01</td>
-          <td>PAMM</td>
-          <td>2</td>
-          <td>28</td>
-        </tr>
-    
-        <tr id="Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss the capabilities and limitations of TAEs through both theoretical and numerical analyses. Theoretically, we derive bounds for nonlinear TAE performance in slow mode discovery and show that in general TAEs learn a mixture of slow and maximum variance modes. Numerically, we illustrate cases where TAEs can and cannot correctly identify the leading slowest mode in two example systems: a 2D "Washington beltway" potential and the alanine dipeptide molecule in explicit water. We also compare the TAE results with those obtained using state-free reversible VAMPnets (SRVs) as a variational-based neural network approach for slow modes discovery, and show that SRVs can correctly discover slow modes where TAEs fail.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fe3850f70016ae3a31767166fb996ed0f0325fd4" target='_blank'>Capabilities and Limitations of Time-lagged Autoencoders for Slow Mode Discovery in Dynamical Systems</a></td>
-          <td>
-            Wei Chen, Hythem Sidky, Andrew L. Ferguson
-          </td>
-          <td>2019-06-02</td>
-          <td>ArXiv</td>
-          <td>31</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="The heat shock protein 90 (Hsp90) is a molecular chaperone that controls the folding and activation of client proteins using the free energy of ATP hydrolysis. The Hsp90 active site is in its N-terminal domain (NTD). Our goal is to characterize the dynamics of NTD using an autoencoder-learned collective variable (CV) in conjunction with adaptive biasing force Langevin dynamics. Using dihedral analysis, we cluster all available experimental Hsp90 NTD structures into distinct native states. We then perform unbiased molecular dynamics (MD) simulations to construct a dataset that represents each state and use this dataset to train an autoencoder. Two autoencoder architectures are considered, with one and two hidden layers, respectively, and bottlenecks of dimension k ranging from 1 to 10. We demonstrate that the addition of an extra hidden layer does not significantly improve the performance, while it leads to complicated CVs that increase the computational cost of biased MD calculations. In addition, a two-dimensional (2D) bottleneck can provide enough information of the different states, while the optimal bottleneck dimension is five. For the 2D bottleneck, the 2D CV is directly used in biased MD simulations. For the five-dimensional (5D) bottleneck, we perform an analysis of the latent CV space and identify the pair of CV coordinates that best separates the states of Hsp90. Interestingly, selecting a 2D CV out of the 5D CV space leads to better results than directly learning a 2D CV and allows observation of transitions between native states when running free energy biased dynamics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/510a041ffcc7dcccb23cf4a23f0992e5de6b8f9e" target='_blank'>Autoencoders for dimensionality reduction in molecular dynamics: Collective variable dimension, biasing, and transition states.</a></td>
-          <td>
-            Zineb Belkacemi, M. Bianciotto, H. Minoux, T. Lelièvre, G. Stoltz, P. Gkeka
-          </td>
-          <td>2023-06-05</td>
-          <td>The Journal of chemical physics</td>
-          <td>3</td>
-          <td>37</td>
-        </tr>
-    
-        <tr id="Molecular dynamics simulations produce data with complex nonlinear dynamics. If the timestep behavior of such a dynamic system can be represented by a linear operator, future states can be inferred directly without expensive simulations. The use of an autoencoder in combination with a physical timestep operator allows both the relevant structural characteristics of the molecular graphs and the underlying physics of the system to be isolated during the training process. In this work, we develop a pipeline for establishing graph-structured representations of time-series volumetric data from molecular dynamics simulations. We then train an autoencoder to find nonlinear mappings to a latent space where future timesteps can be predicted through application of a linear operator trained in tandem with the autoencoder. Increasing the dimensionality of the autoencoder output is shown to improve the accuracy of the physical timestep operator.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/446681b1a3b3cafc7522cffdc3550348480d4085" target='_blank'>Operator Autoencoders: Learning Physical Operations on Encoded Molecular Graphs</a></td>
-          <td>
-            Willis Hoke, D. Shea, S. Casey
-          </td>
-          <td>2021-05-26</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>8</td>
-        </tr>
-    
-        <tr id="The success of enhanced sampling molecular simulations that accelerate along collective variables (CVs) is predicated on the availability of variables coincident with the slow collective motions governing the long-time conformational dynamics of a system. It is challenging to intuit these slow CVs for all but the simplest molecular systems, and their data-driven discovery directly from molecular simulation trajectories has been a central focus of the molecular simulation community to both unveil the important physical mechanisms and drive enhanced sampling. In this work, we introduce state-free reversible VAMPnets (SRV) as a deep learning architecture that learns nonlinear CV approximants to the leading slow eigenfunctions of the spectral decomposition of the transfer operator that evolves equilibrium-scaled probability distributions through time. Orthogonality of the learned CVs is naturally imposed within network training without added regularization. The CVs are inherently explicit and differentiable functions of the input coordinates making them well-suited to use in enhanced sampling calculations. We demonstrate the utility of SRVs in capturing parsimonious nonlinear representations of complex system dynamics in applications to 1D and 2D toy systems where the true eigenfunctions are exactly calculable and to molecular dynamics simulations of alanine dipeptide and the WW domain protein.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2e7163e31e9b32cec11005678bae9e1dbeb6d573" target='_blank'>Nonlinear Discovery of Slow Molecular Modes using Hierarchical Dynamics Encoders</a></td>
-          <td>
-            Wei Chen, Hythem Sidky, Andrew L. Ferguson
-          </td>
-          <td>2019-02-09</td>
-          <td>The Journal of chemical physics</td>
-          <td>77</td>
-          <td>35</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/468bcdf36d129bce045af22d4ef6f2fd8e29c81a" target='_blank'>Using an Autoencoder for Dimensionality Reduction in Quantum Dynamics</a></td>
-          <td>
-            S. Reiter, T. Schnappinger, R. Vivie-Riedle
-          </td>
-          <td>2019-09-17</td>
-          <td>MAG, DBLP</td>
-          <td>2</td>
-          <td>27</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/58912e2c2aaa77d1448d51e9d9460e06a5b924b9" target='_blank'>VAMPnets for deep learning of molecular kinetics</a></td>
-          <td>
-            Andreas Mardt, Luca Pasquali, Hao Wu, F. Noé
-          </td>
-          <td>2017-10-16</td>
-          <td>Nature Communications</td>
-          <td>463</td>
-          <td>61</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
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diff --git a/docs/recommendations/e0ee02a573b3d83fec55ed5d7c80f1afa055a7b4.md b/docs/recommendations/e0ee02a573b3d83fec55ed5d7c80f1afa055a7b4.md
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-  <tbody>
-    
-        <tr id="We introduce an approach for imposing physically informed inductive biases in learned simulation models. We combine graph networks with a differentiable ordinary differential equation integrator as a mechanism for predicting future states, and a Hamiltonian as an internal representation. We find that our approach outperforms baselines without these biases in terms of predictive accuracy, energy accuracy, and zero-shot generalization to time-step sizes and integrator orders not experienced during training. This advances the state-of-the-art of learned simulation, and in principle is applicable beyond physical domains.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/57784e5db3504d549d16382de8f7f4ad222b3d71" target='_blank'>Hamiltonian Graph Networks with ODE Integrators</a></td>
-          <td>
-            Alvaro Sanchez-Gonzalez, V. Bapst, Kyle Cranmer, P. Battaglia
-          </td>
-          <td>2019-09-27</td>
-          <td>ArXiv</td>
-          <td>161</td>
-          <td>46</td>
-        </tr>
-    
-        <tr id="Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for physical systems with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. Finally, we demonstrate that our method also performs well when taking discontinuous effects into account such as collisions between individual rods. A video showing dynamic results of our graph learning assisted simulations of elastic rods can be found on the project website available at this http URL .">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0bf48ff5241fcf7116db676d87d98188dfcac175" target='_blank'>Accurately Solving Physical Systems with Graph Learning</a></td>
-          <td>
-            Han Shao, Tassilo Kugelstadt, Wojciech Palubicki, Jan Bender, S. Pirk, D. Michels
-          </td>
-          <td>2020-06-06</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>27</td>
-        </tr>
-    
-        <tr id="Here we present a machine learning framework and model implementation that can learn to simulate a wide variety of challenging physical domains, involving fluids, rigid solids, and deformable materials interacting with one another. Our framework---which we term "Graph Network-based Simulators" (GNS)---represents the state of a physical system with particles, expressed as nodes in a graph, and computes dynamics via learned message-passing. Our results show that our model can generalize from single-timestep predictions with thousands of particles during training, to different initial conditions, thousands of timesteps, and at least an order of magnitude more particles at test time. Our model was robust to hyperparameter choices across various evaluation metrics: the main determinants of long-term performance were the number of message-passing steps, and mitigating the accumulation of error by corrupting the training data with noise. Our GNS framework advances the state-of-the-art in learned physical simulation, and holds promise for solving a wide range of complex forward and inverse problems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c529f5b08675f787cdcc094ee495239592339f82" target='_blank'>Learning to Simulate Complex Physics with Graph Networks</a></td>
-          <td>
-            Alvaro Sanchez-Gonzalez, Jonathan Godwin, T. Pfaff, Rex Ying, J. Leskovec, P. Battaglia
-          </td>
-          <td>2020-02-21</td>
-          <td>ArXiv</td>
-          <td>849</td>
-          <td>134</td>
-        </tr>
-    
-        <tr id="Physical systems are commonly represented as a combination of particles, the individual dynamics of which govern the system dynamics. However, traditional approaches require the knowledge of several abstract quantities such as the energy or force to infer the dynamics of these particles. Here, we present a framework, namely, Lagrangian graph neural network (LGnn), that provides a strong inductive bias to learn the Lagrangian of a particle-based system directly from the trajectory. We test our approach on challenging systems with constraints and drag—LGnn outperforms baselines such as feed-forward Lagrangian neural network (Lnn) with improved performance. We also show the zero-shot generalizability of the system by simulating systems two orders of magnitude larger than the trained one and also hybrid systems that are unseen by the model, a unique feature. The graph architecture of LGnn significantly simplifies the learning in comparison to Lnn with ∼25 times better performance on ∼20 times smaller amounts of data. Finally, we show the interpretability of LGnn, which directly provides physical insights on drag and constraint forces learned by the model. LGnn can thus provide a fillip toward understanding the dynamics of physical systems purely from observable quantities.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b03df6544ff0eaf40b5ff8fc7434ce7c79cf367e" target='_blank'>Learning the dynamics of particle-based systems with Lagrangian graph neural networks</a></td>
-          <td>
-            Ravinder Bhattoo, Sayan Ranu, N. Krishnan
-          </td>
-          <td>2022-09-03</td>
-          <td>Machine Learning: Science and Technology</td>
-          <td>13</td>
-          <td>21</td>
-        </tr>
-    
-        <tr id="The great learning ability of deep learning models facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour. However, the complex laws of the physical world pose significant challenges to the learning based simulations, such as the varying spatial dependencies between interacting particles and varying temporal dependencies between particle system states in different time stamps, which dominate particles' interacting behaviour and the physical systems' evolution patterns. Existing learning based simulation methods fail to fully account for the complexities, making them unable to yield satisfactory simulations. To better comprehend the complex physical laws, this paper proposes a novel learning based simulation model- Graph Networks with Spatial-Temporal neural Ordinary Equations (GNSTODE)- that characterizes the varying spatial and temporal dependencies in particle systems using a united end-to-end framework. Through training with real-world particle-particle interaction observations, GNSTODE is able to simulate any possible particle systems with high precisions. We empirically evaluate GNSTODE's simulation performance on two real-world particle systems, Gravity and Coulomb, with varying levels of spatial and temporal dependencies. The results show that the proposed GNSTODE yields significantly better simulations than state-of-the-art learning based simulation methods, which proves that GNSTODE can serve as an effective solution to particle simulations in real-world application.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b8faa6683b9bea99f87387a6434eb064996007b2" target='_blank'>Towards Complex Dynamic Physics System Simulation with Graph Neural ODEs</a></td>
-          <td>
-            Guangsi Shi, Daokun Zhang, Ming Jin, Shirui Pan
-          </td>
-          <td>2023-05-21</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="We develop a PyTorch-based Graph Network Simulator (GNS) that learns physics and predicts the flow behavior of particulate and fluid systems. GNS discretizes the domain with nodes representing a collection of material points and the links connecting the nodes representing the local interaction between particles or clusters of particles. The GNS learns the interaction laws through message passing on the graph. GNS has three components: (a) Encoder, which embeds particle information to a latent graph, the edges are learned functions; (b) Processor, which allows data propagation and computes the nodal interactions across steps; and (c) Decoder, which extracts the relevant dynamics (e.g., particle acceleration) from the graph. We introduce physics-inspired simple inductive biases, such as an inertial frame that allows learning algorithms to prioritize one solution (constant gravitational acceleration) over another, reducing learning time. The GNS implementation uses semi-implicit Euler integration to update the next state based on the predicted accelerations. GNS trained on trajectory data is generalizable to predict particle kinematics in complex boundary conditions not seen during training. The trained model accurately predicts within a 5\% error of its associated material point method (MPM) simulation. The predictions are 5,000x faster than traditional MPM simulations (2.5 hours for MPM simulations versus 20 s for GNS simulation of granular flow). GNS surrogates are popular for solving optimization, control, critical-region prediction for in situ viz, and inverse-type problems. The GNS code is available under the open-source MIT license at https://github.com/geoelements/gns.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8d0ad8be491a5dad5af49f7c7f6c4dde40ee3f25" target='_blank'>GNS: A generalizable Graph Neural Network-based simulator for particulate and fluid modeling</a></td>
-          <td>
-            Krishna Kumar, J. Vantassel
-          </td>
-          <td>2022-11-18</td>
-          <td>J. Open Source Softw.</td>
-          <td>7</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9e20f6874feaaf7c9994f9875b1d9cab17a2fd59" target='_blank'>Learning Mesh-Based Simulation with Graph Networks</a></td>
-          <td>
-            T. Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, P. Battaglia
-          </td>
-          <td>2020-10-07</td>
-          <td>ArXiv</td>
-          <td>559</td>
-          <td>46</td>
-        </tr>
-    
-        <tr id="Differentiable physics simulation is a powerful family of new techniques that applies gradient-based methods to learning and control of physical systems. It enables optimization for control, and can also be integrated into neural network frameworks for performing complex tasks. We believe that differentiable physics simulation should be a key component for neural networks to bridge the gap between training performance and the generality to previously unseen real-world inputs. However, realizing a practical differentiable simulation is still challenging because of its high dimensionality and fragmented computation flow. In this paper, we motivate the importance of differentiable physics simulation, describe its current challenges, introduce state-of-the-art approaches, and discuss potential improvements and future directions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/543c6672b045081593aa27e045e853486e6c8967" target='_blank'>Differentiable Physics Simulation</a></td>
-          <td>
-            Junbang Liang, M. Lin
-          </td>
-          <td>2020-02-26</td>
-          <td></td>
-          <td>13</td>
-          <td>78</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/dbc6f9d83c021e9dc3cc6803d25e7189f3acdf4d" target='_blank'>Towards complex dynamic physics system simulation with graph neural ordinary equations</a></td>
-          <td>
-            Guangsi Shi, Daokun Zhang, Ming Jin, Shirui Pan, Phillp S. Yu
-          </td>
-          <td>2024-04-01</td>
-          <td>Neural networks : the official journal of the International Neural Network Society</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
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-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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-  <i class="footer">This page was last updated on 2024-08-08 13:16:39 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Taming Local Effects in Graph-based Spatiotemporal Forecasting</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Graph-based deep learning methods have become popular tools to process collections of correlated time series. Differently from traditional multivariate forecasting methods, neural graph-based predictors take advantage of pairwise relationships by conditioning forecasts on a (possibly dynamic) graph spanning the time series collection. The conditioning can take the form of an architectural inductive bias on the neural forecasting architecture, resulting in a family of deep learning models called spatiotemporal graph neural networks. Such relational inductive biases enable the training of global forecasting models on large time-series collections, while at the same time localizing predictions w.r.t. each element in the set (i.e., graph nodes) by accounting for local correlations among them (i.e., graph edges). Indeed, recent theoretical and practical advances in graph neural networks and deep learning for time series forecasting make the adoption of such processing frameworks appealing and timely. However, most of the studies in the literature focus on proposing variations of existing neural architectures by taking advantage of modern deep learning practices, while foundational and methodological aspects have not been subject to systematic investigation. To fill the gap, this paper aims to introduce a comprehensive methodological framework that formalizes the forecasting problem and provides design principles for graph-based predictive models and methods to assess their performance. At the same time, together with an overview of the field, we provide design guidelines, recommendations, and best practices, as well as an in-depth discussion of open challenges and future research directions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ccea298edb788edf821aef58f0952c3e8debc25a" target='_blank'>Graph Deep Learning for Time Series Forecasting</a></td>
-          <td>
-            Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi
-          </td>
-          <td>2023-10-24</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in most spatiotemporal GNNs, the computational complexity scales up to a quadratic factor with the length of the sequence times the number of links in the graph, hence hindering the application of these models to large graphs and long temporal sequences. While methods to improve scalability have been proposed in the context of static graphs, few research efforts have been devoted to the spatiotemporal case. To fill this gap, we propose a scalable architecture that exploits an efficient encoding of both temporal and spatial dynamics. In particular, we use a randomized recurrent neural network to embed the history of the input time series into high-dimensional state representations encompassing multi-scale temporal dynamics. Such representations are then propagated along the spatial dimension using different powers of the graph adjacency matrix to generate node embeddings characterized by a rich pool of spatiotemporal features. The resulting node embeddings can be efficiently pre-computed in an unsupervised manner, before being fed to a feed-forward decoder that learns to map the multi-scale spatiotemporal representations to predictions. The training procedure can then be parallelized node-wise by sampling the node embeddings without breaking any dependency, thus enabling scalability to large networks. Empirical results on relevant datasets show that our approach achieves results competitive with the state of the art, while dramatically reducing the computational burden.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5e60dc704e7933e2a3e83512f345bba0debfe3f3" target='_blank'>Scalable Spatiotemporal Graph Neural Networks</a></td>
-          <td>
-            Andrea Cini, Ivan Marisca, F. Bianchi, C. Alippi
-          </td>
-          <td>2022-09-14</td>
-          <td>ArXiv</td>
-          <td>28</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational information characterizing the underlying data-generating process is unavailable and the practitioner is left with the problem of inferring from data which relational graph to use in the subsequent processing stages. We propose novel, principled - yet practical - probabilistic score-based methods that learn the relational dependencies as distributions over graphs while maximizing end-to-end the performance at task. The proposed graph learning framework is based on consolidated variance reduction techniques for Monte Carlo score-based gradient estimation, is theoretically grounded, and, as we show, effective in practice. In this paper, we focus on the time series forecasting problem and show that, by tailoring the gradient estimators to the graph learning problem, we are able to achieve state-of-the-art performance while controlling the sparsity of the learned graph and the computational scalability. We empirically assess the effectiveness of the proposed method on synthetic and real-world benchmarks, showing that the proposed solution can be used as a stand-alone graph identification procedure as well as a graph learning component of an end-to-end forecasting architecture.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0d01d21137a5af9f04e4b16a55a0f732cb8a540b" target='_blank'>Sparse Graph Learning from Spatiotemporal Time Series</a></td>
-          <td>
-            Andrea Cini, Daniele Zambon, C. Alippi
-          </td>
-          <td>2022-05-26</td>
-          <td>J. Mach. Learn. Res.</td>
-          <td>11</td>
-          <td>49</td>
-        </tr>
-    
-        <tr id="Time series forecasting with additional spatial de-pendencies has attracted a tremendous amount of research interest in social sciences, due to its importance in modern real-world applications. The Graph Neural Networks (GNN) is one of the most exciting deep learning techniques among these spatio-temporal modeling approaches. Most existing spatio-temporal GNN frameworks are based on a two-step modeling process. In such scenario, spatial and temporal dependencies are modeled in separate steps, which lead to problems such as complex architecture design, hard to scale, etc. Targeting the shortcomings of existing studies, we take both spatial and temporal dependencies from another perspective, and consider them as two heterogeneous types of edges in the graph. We propose a unified spatio-temporal GNN framework that captures both dependencies in a single step. More specifically, for each node in the graph, a unified neural network component is designed to simultaneously extract information from its sur-rounding neighbors (spatial) and its past records (temporal), which enables much easier dependency aggregation with faster execution. Experiment results demonstrate the superiority of the proposed framework over state-of-the-art (SOTA) baselines on various applications, including modeling smart cities and data-driven political science research.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1fa11d10d7871cb7610f7e980fcf713979ce1c6e" target='_blank'>Unified Spatio-Temporal Graph Neural Networks: Data-Driven Modeling for Social Science</a></td>
-          <td>
-            Yifan Li, Yu Lin, Y. Gao, L. Khan
-          </td>
-          <td>2022-07-18</td>
-          <td>2022 International Joint Conference on Neural Networks (IJCNN)</td>
-          <td>0</td>
-          <td>11</td>
-        </tr>
-    
-        <tr id="The challenge of effectively learning inter-series correlations for multivariate time series forecasting remains a substantial and unresolved problem. Traditional deep learning models, which are largely dependent on the Transformer paradigm for modeling long sequences, often fail to integrate information from multiple time series into a coherent and universally applicable model. To bridge this gap, our paper presents ForecastGrapher, a framework reconceptualizes multivariate time series forecasting as a node regression task, providing a unique avenue for capturing the intricate temporal dynamics and inter-series correlations. Our approach is underpinned by three pivotal steps: firstly, generating custom node embeddings to reflect the temporal variations within each series; secondly, constructing an adaptive adjacency matrix to encode the inter-series correlations; and thirdly, augmenting the GNNs' expressive power by diversifying the node feature distribution. To enhance this expressive power, we introduce the Group Feature Convolution GNN (GFC-GNN). This model employs a learnable scaler to segment node features into multiple groups and applies one-dimensional convolutions with different kernel lengths to each group prior to the aggregation phase. Consequently, the GFC-GNN method enriches the diversity of node feature distribution in a fully end-to-end fashion. Through extensive experiments and ablation studies, we show that ForecastGrapher surpasses strong baselines and leading published techniques in the domain of multivariate time series forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/60560da7e2483d4f788c228ebd5e226ae1f40002" target='_blank'>ForecastGrapher: Redefining Multivariate Time Series Forecasting with Graph Neural Networks</a></td>
-          <td>
-            Wanlin Cai, Kun Wang, Hao Wu, Xiaoxu Chen, Yuankai Wu
-          </td>
-          <td>2024-05-28</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Multivariate time series (MTS) forecasting has shown great importance in numerous industries. Current state-of-the-art graph neural network (GNN)-based forecasting methods usually require both graph networks (e.g., GCN) and temporal networks (e.g., LSTM) to capture inter-series (spatial) dynamics and intra-series (temporal) dependencies, respectively. However, the uncertain compatibility of the two networks puts an extra burden on handcrafted model designs. Moreover, the separate spatial and temporal modeling naturally violates the unified spatiotemporal inter-dependencies in real world, which largely hinders the forecasting performance. To overcome these problems, we explore an interesting direction of directly applying graph networks and rethink MTS forecasting from a pure graph perspective. We first define a novel data structure, hypervariate graph, which regards each series value (regardless of variates or timestamps) as a graph node, and represents sliding windows as space-time fully-connected graphs. This perspective considers spatiotemporal dynamics unitedly and reformulates classic MTS forecasting into the predictions on hypervariate graphs. Then, we propose a novel architecture Fourier Graph Neural Network (FourierGNN) by stacking our proposed Fourier Graph Operator (FGO) to perform matrix multiplications in Fourier space. FourierGNN accommodates adequate expressiveness and achieves much lower complexity, which can effectively and efficiently accomplish the forecasting. Besides, our theoretical analysis reveals FGO's equivalence to graph convolutions in the time domain, which further verifies the validity of FourierGNN. Extensive experiments on seven datasets have demonstrated our superior performance with higher efficiency and fewer parameters compared with state-of-the-art methods.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9dbcb0893d05e6176353eee401afa4929b570cf6" target='_blank'>FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective</a></td>
-          <td>
-            Kun Yi, Qi Zhang, Wei Fan, Hui He, Liang Hu, Pengyang Wang, Ning An, Longbin Cao, Zhendong Niu
-          </td>
-          <td>2023-11-10</td>
-          <td>ArXiv</td>
-          <td>25</td>
-          <td>4</td>
-        </tr>
-    
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diff --git a/docs/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6.md b/docs/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6.md
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Tiny Time Mixers (TTMs): Fast Pre-trained Models for Enhanced Zero/Few-Shot Forecasting of Multivariate Time Series</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="We present General Time Transformer (GTT), an encoder-only style foundation model for zero-shot multivariate time series forecasting. GTT is pretrained on a large dataset of 200M high-quality time series samples spanning diverse domains. In our proposed framework, the task of multivariate time series forecasting is formulated as a channel-wise next curve shape prediction problem, where each time series sample is represented as a sequence of non-overlapping curve shapes with a unified numerical magnitude. GTT is trained to predict the next curve shape based on a window of past curve shapes in a channel-wise manner. Experimental results demonstrate that GTT exhibits superior zero-shot multivariate forecasting capabilities on unseen time series datasets, even surpassing state-of-the-art supervised baselines. Additionally, we investigate the impact of varying GTT model parameters and training dataset scales, observing that the scaling law also holds in the context of zero-shot multivariate time series forecasting.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/15ea0190593662402d0493958a53d5ca3b8e8406" target='_blank'>Only the Curve Shape Matters: Training Foundation Models for Zero-Shot Multivariate Time Series Forecasting through Next Curve Shape Prediction</a></td>
-          <td>
-            Cheng Feng, Long Huang, Denis Krompass
-          </td>
-          <td>2024-02-12</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="In recent years, generative pre-trained paradigms such as Large Language Models (LLMs) and Large Vision Models (LVMs) have achieved revolutionary advancements and widespread real-world applications. Particularly, the emergence of pre-trained LLMs-based temporal works, compared to previous deep model approaches, has demonstrated superior generalization and robustness, showcasing the potential of generative pre-trained paradigms as foundation models for time series. However, those LLMs-based works mainly focus on cross-modal research, i.e., leveraging the language capabilities of LLMs in time series contexts. Although they have achieved impressive performance, there still exist the issues of concept drift caused by differences in data distribution and inflexibility caused by misalignment of dimensions. To this end, inspired by recent work on LVMs, we reconsider the paradigm of time series modeling. In this paper, we comprehensively explore, for the first time, the effectiveness and superiority of the Generative Pre-trained Diffusion (GPD) paradigm in real-world multivariate time series forecasting (TSF). Specifically, to mitigate performance bias introduced by sophisticated networks, we propose a straightforward MLP diffusion network for unconditional modeling of time series. Then we employ a zero-shot and tuning-free method to predict (generate) future data using historical data as prompts. The GPD paradigm is established on the time series modality, effectively preventing the phenomenon of concept drift, and enabling flexible forecasting of arbitrary lengths. We demonstrate that the GPD paradigm achieves comprehensive performance and generalization comparable to current SOTA LLM-based and deep model paradigms on mainstream benchmarks and various TSF tasks. Extensive experiments validate the potential of the GPD paradigm and its assistance in future related research.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/818793961396bbe4c744932676f0ff9cc8385bed" target='_blank'>Generative Pre-Trained Diffusion Paradigm for Zero-Shot Time Series Forecasting</a></td>
-          <td>
-            Jiarui Yang, Tao Dai, Naiqi Li, Junxi Wu, Peiyuan Liu, Jinmin Li, Jigang Bao, Haigang Zhang, Shu-Tao Xia
-          </td>
-          <td>2024-06-04</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4fb78450650894091b0a55b5504a8b0a6f3dec37" target='_blank'>Chronos: Learning the Language of Time Series</a></td>
-          <td>
-            Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, Yuyang Wang
-          </td>
-          <td>2024-03-12</td>
-          <td>ArXiv</td>
-          <td>23</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="Over the past years, foundation models have caused a paradigm shift in machine learning due to their unprecedented capabilities for zero-shot and few-shot generalization. However, despite the success of foundation models in modalities such as natural language processing and computer vision, the development of foundation models for time series forecasting has lagged behind. We present Lag-Llama, a general-purpose foundation model for univariate probabilistic time series forecasting based on a decoder-only transformer architecture that uses lags as covariates. Lag-Llama is pretrained on a large corpus of diverse time series data from several domains, and demonstrates strong zero-shot generalization capabilities compared to a wide range of forecasting models on downstream datasets across domains. Moreover, when fine-tuned on relatively small fractions of such previously unseen datasets, Lag-Llama achieves state-of-the-art performance, outperforming prior deep learning approaches, emerging as the best general-purpose model on average. Lag-Llama serves as a strong contender to the current state-of-art in time series forecasting and paves the way for future advancements in foundation models tailored to time series data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7c9bb230946cf48a7b9de97fd0281f42fbc51d31" target='_blank'>Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting</a></td>
-          <td>
-            Kashif Rasul, Arjun Ashok, Andrew Robert Williams, Arian Khorasani, George Adamopoulos, Rishika Bhagwatkar, Marin Bilovs, Hena Ghonia, N. Hassen, Anderson Schneider, Sahil Garg, Alexandre Drouin, Nicolas Chapados, Yuriy Nevmyvaka, I. Rish
-          </td>
-          <td>2023-10-12</td>
-          <td>ArXiv</td>
-          <td>13</td>
-          <td>40</td>
-        </tr>
-    
-        <tr id="Time series data are ubiquitous across various domains, making time series analysis critically important. Traditional time series models are task-specific, featuring singular functionality and limited generalization capacity. Recently, large language foundation models have unveiled their remarkable capabilities for cross-task transferability, zero-shot/few-shot learning, and decision-making explainability. This success has sparked interest in the exploration of foundation models to solve multiple time series challenges simultaneously. There are two main research lines, namely pre-training foundation models from scratch for time series and adapting large language foundation models for time series. They both contribute to the development of a unified model that is highly generalizable, versatile, and comprehensible for time series analysis. This survey offers a 3E analytical framework for comprehensive examination of related research. Specifically, we examine existing works from three dimensions, namely Effectiveness, Efficiency and Explainability. In each dimension, we focus on discussing how related works devise tailored solution by considering unique challenges in the realm of time series. Furthermore, we provide a domain taxonomy to help followers keep up with the domain-specific advancements. In addition, we introduce extensive resources to facilitate the field's development, including datasets, open-source, time series libraries. A GitHub repository is also maintained for resource updates (https://github.com/start2020/Awesome-TimeSeries-LLM-FM).">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/522828823ff726598675971036fff01b57320578" target='_blank'>A Survey of Time Series Foundation Models: Generalizing Time Series Representation with Large Language Model</a></td>
-          <td>
-            Jiexia Ye, Weiqi Zhang, Ke Yi, Yongzi Yu, Ziyue Li, Jia Li, F. Tsung
-          </td>
-          <td>2024-05-03</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>47</td>
-        </tr>
-    
-        <tr id="In this study, we present aLLM4TS, an innovative framework that adapts Large Language Models (LLMs) for time-series representation learning. Central to our approach is that we reconceive time-series forecasting as a self-supervised, multi-patch prediction task, which, compared to traditional contrastive learning or mask-and-reconstruction methods, captures temporal dynamics in patch representations more effectively. Our strategy encompasses two-stage training: (i). a causal continual pre-training phase on various time-series datasets, anchored on next patch prediction, effectively syncing LLM capabilities with the intricacies of time-series data; (ii). fine-tuning for multi-patch prediction in the targeted time-series context. A distinctive element of our framework is the patch-wise decoding layer, which departs from previous methods reliant on sequence-level decoding. Such a design directly transposes individual patches into temporal sequences, thereby significantly bolstering the model's proficiency in mastering temporal patch-based representations. aLLM4TS demonstrates superior performance in several downstream tasks, proving its effectiveness in deriving temporal representations with enhanced transferability and marking a pivotal advancement in the adaptation of LLMs for time-series analysis.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c699624c3cdd5e2ac0d1f67de733bbad1b1c0e37" target='_blank'>Multi-Patch Prediction: Adapting LLMs for Time Series Representation Learning</a></td>
-          <td>
-            Yuxuan Bian, Xu Ju, Jiangtong Li, Zhijian Xu, Dawei Cheng, Qiang Xu
-          </td>
-          <td>2024-02-07</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>5</td>
-        </tr>
-    
-        <tr id="Time series has been left behind in the era of pre-training and transfer learning. While research in the fields of natural language processing and computer vision are enjoying progressively larger datasets to train massive models, the most popular time series datasets consist of only tens of thousands of time steps, limiting our ability to study the effectiveness of pre-training and scaling. Recent studies have also cast doubt on the need for expressive models and scale. To alleviate these issues, we introduce three large-scale time series forecasting datasets from the cloud operations (CloudOps) domain, the largest having billions of observations, enabling further study into pre-training and scaling of time series models. We build the empirical groundwork for studying pre-training and scaling of time series models and pave the way for future research by identifying a promising candidate architecture. We show that it is a strong zero-shot baseline and benefits from further scaling, both in model and dataset size. Accompanying these datasets and results is a suite of comprehensive benchmark results comparing classical and deep learning baselines to our pre-trained method - achieving a 27% reduction in error on the largest dataset. Code and datasets can be found https://github.com/SalesforceAIResearch/pretrain-time-series-cloudops.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/dbd6463cfff26861f6f3ea8e8d19eff4e6331904" target='_blank'>Pushing the Limits of Pre-training for Time Series Forecasting in the CloudOps Domain</a></td>
-          <td>
-            Gerald Woo, Chenghao Liu, Akshat Kumar, Doyen Sahoo
-          </td>
-          <td>2023-10-08</td>
-          <td>ArXiv</td>
-          <td>7</td>
-          <td>22</td>
-        </tr>
-    
-        <tr id="Despite the impressive achievements of pre-trained models in the fields of natural language processing (NLP) and computer vision (CV), progress in the domain of time series analysis has been limited. In contrast to NLP and CV, where a single model can handle various tasks, time series analysis still relies heavily on task-specific methods for activities such as classification, anomaly detection, forecasting, and few-shot learning. The primary obstacle to developing a pre-trained model for time series analysis is the scarcity of sufficient training data. In our research, we overcome this obstacle by utilizing pre-trained models from language or CV, which have been trained on billions of data points, and apply them to time series analysis. We assess the effectiveness of the pre-trained transformer model in two ways. Initially, we maintain the original structure of the self-attention and feedforward layers in the residual blocks of the pre-trained language or image model, using the Frozen Pre-trained Transformer (FPT) for time series analysis with the addition of projection matrices for input and output. Additionally, we introduce four unique adapters, designed specifically for downstream tasks based on the pre-trained model, including forecasting and anomaly detection. These adapters are further enhanced with efficient parameter tuning, resulting in superior performance compared to all state-of-the-art methods.Our comprehensive experimental studies reveal that (a) the simple FPT achieves top-tier performance across various time series analysis tasks; and (b) fine-tuning the FPT with the custom-designed adapters can further elevate its performance, outshining specialized task-specific models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/15bfe54223d28c74f9e39960f7ff1d03167e285f" target='_blank'>One Fits All: Universal Time Series Analysis by Pretrained LM and Specially Designed Adaptors</a></td>
-          <td>
-            Tian Zhou, Peisong Niu, Xue Wang, Liang Sun, Rong Jin
-          </td>
-          <td>2023-11-24</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="Predicting future values in multivariate time series is vital across various domains. This work explores the use of large language models (LLMs) for this task. However, LLMs typically handle one-dimensional data. We introduce MultiCast, a zero-shot LLM-based approach for multivariate time series forecasting. It allows LLMs to receive multivariate time series as input, through three novel token multiplexing solutions that effectively reduce dimensionality while preserving key repetitive patterns. Additionally, a quantization scheme helps LLMs to better learn these patterns, while significantly reducing token use for practical applications. We showcase the performance of our approach in terms of RMSE and execution time against state-of-the-art approaches on three real-world datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/695663f05473270744f228e9beeb7578ceee7c68" target='_blank'>MultiCast: Zero-Shot Multivariate Time Series Forecasting Using LLMs</a></td>
-          <td>
-            Georgios Chatzigeorgakidis, Konstantinos Lentzos, Dimitrios Skoutas
-          </td>
-          <td>2024-05-13</td>
-          <td>2024 IEEE 40th International Conference on Data Engineering Workshops (ICDEW)</td>
-          <td>0</td>
-          <td>7</td>
-        </tr>
-    
-  </tbody>
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-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Learning sparse nonlinear dynamics via mixed-integer optimization</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1f18c5206491626d36c2271aaf491dbc945f6247" target='_blank'>Automatically discovering ordinary differential equations from data with sparse regression</a></td>
-          <td>
-            Kevin Egan, Weizhen Li, Rui Carvalho
-          </td>
-          <td>2024-01-09</td>
-          <td>Communications Physics</td>
-          <td>7</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Significance Understanding dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled technology, including aircraft, combustion engines, satellites, and electrical power. This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. There are many critical data-driven problems, such as understanding cognition from neural recordings, inferring climate patterns, determining stability of financial markets, predicting and suppressing the spread of disease, and controlling turbulence for greener transportation and energy. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an important role in these efforts. Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5d150cec2775f9bc863760448f14104cc8f42368" target='_blank'>Discovering governing equations from data by sparse identification of nonlinear dynamical systems</a></td>
-          <td>
-            S. Brunton, J. Proctor, J. Kutz
-          </td>
-          <td>2015-09-11</td>
-          <td>Proceedings of the National Academy of Sciences</td>
-          <td>3168</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that violate basic physical laws. This work proposes a novel method for the Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI). SINDy-SI is an iterative method that uses Sum-of-Squares (SOS) programming to learn optimally fitted models while guaranteeing that the learned model satisfies side information, such as symmetry's and physical laws. Guided by the principle of Occam's razor, that the simplest or most regularized best fitted model is typically the superior choice, during each iteration SINDy-SI prunes the basis functions associated with small coefficients, yielding a sparse dynamical model upon termination. Through several numerical experiments we will show how the combination of side information constraints and sparse polynomial representation cultivates dynamical models that obey known physical laws while displaying impressive generalized performance beyond the training set.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/13a6b8f2d60ef8006dfe6e6bed42df96f773a323" target='_blank'>Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI)</a></td>
-          <td>
-            Gabriel F. Machado, Morgan Jones
-          </td>
-          <td>2023-10-06</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/433ba35ced5d3f47fa2688c81a60363a74193449" target='_blank'>PySINDy: A comprehensive Python package for robust sparse system identification</a></td>
-          <td>
-            A. Kaptanoglu, Brian M. de Silva, Urban Fasel, Kadierdan Kaheman, Jared L. Callaham, Charles B. Delahunt, Kathleen P. Champion, Jean-Christophe Loiseau, J. Kutz, S. Brunton
-          </td>
-          <td>2021-11-12</td>
-          <td>J. Open Source Softw.</td>
-          <td>109</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the uncertainty inherent in differential equations learned from data remains an open problem, thus we propose leveraging recent advances in statistical inference for sparse regression to address this issue. Focusing on systems of ordinary differential equations (ODEs), SINDy assumes that each equation is a parsimonious linear combination of a few candidate functions, such as polynomials, and uses methods such as sequentially-thresholded least squares or the Lasso to identify a small subset of these functions that govern the system's dynamics. We instead employ bias-corrected versions of the Lasso and ridge regression estimators, as well as an empirical Bayes variable selection technique known as SEMMS, to estimate each ODE as a linear combination of terms that are statistically significant. We demonstrate through simulations that this approach allows us to recover the functional terms that correctly describe the dynamics more often than existing methods that do not account for uncertainty.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/443f1abc41c983d0fd9fa79d3fbef0ef8125d892" target='_blank'>Sparse reconstruction of ordinary differential equations with inference</a></td>
-          <td>
-            S. Venkatraman, Sumanta Basu, M. Wells
-          </td>
-          <td>2023-08-17</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>40</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e596988b1df3a0bc78bf72c0bfdb21c85eaab6c9" target='_blank'>Physics-informed learning of governing equations from scarce data</a></td>
-          <td>
-            Zhao Chen, Yang Liu, Hao Sun
-          </td>
-          <td>2020-05-05</td>
-          <td>Nature Communications</td>
-          <td>234</td>
-          <td>12</td>
-        </tr>
-    
-        <tr id="PySINDy is a Python package for the discovery of governing dynamical systems models from data. In particular, PySINDy provides tools for applying the sparse identification of nonlinear dynamics (SINDy) (Brunton et al. 2016) approach to model discovery. In this work we provide a brief description of the mathematical underpinnings of SINDy, an overview and demonstration of the features implemented in PySINDy (with code examples), practical advice for users, and a list of potential extensions to PySINDy. Software is available at this https URL.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3e89a9f1301a46d011ff04d7c05ae5134f05961a" target='_blank'>PySINDy: A Python package for the Sparse Identification of Nonlinear Dynamics from Data.</a></td>
-          <td>
-            Brian M. de Silva, Kathleen P. Champion, M. Quade, Jean-Christophe Loiseau, J. Kutz, S. Brunton
-          </td>
-          <td>2020-04-17</td>
-          <td>arXiv: Dynamical Systems</td>
-          <td>46</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="Data-driven modeling frameworks that adopt sparse regression techniques, such as sparse identification of nonlinear dynamics (SINDy) and its modifications, are developed to resolve difficulties in extracting underlying dynamics from experimental data. In contrast to neural-network-based methods, these methods are designed to obtain white-box analytical models. In this work, we incorporate the concept of SINDy and knowledge in the field of classical mechanics to identify interpretable and sparse expressions of total energy and the Lagrangian that shelters the hidden dynamics. Moreover, our method (hereafter referred as Lagrangian-SINDy) is developed to use knowledge of simple systems that form the system being analyzed to ensure the likelihood of correct results and to improve the learning pace. Lagrangian-SINDy is highly accurate in discovering interpretable dynamics via energy-related physical quantities. Its performance is validated with three popular multi-DOF nonlinear dynamical systems, namely the spherical pendulum, double pendulum and cart-pendulum system. Comparisons with other SINDy-based methods are made and Lagrangian-SINDy is found to provide the most compact analytical models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7d7e107bcb40ed9596642ff12cc60f33f3eb47e2" target='_blank'>Discovering Interpretable Dynamics by Sparsity Promotion on Energy and the Lagrangian</a></td>
-          <td>
-            H. Chu, M. Hayashibe
-          </td>
-          <td>2020-01-31</td>
-          <td>IEEE Robotics and Automation Letters</td>
-          <td>23</td>
-          <td>23</td>
-        </tr>
-    
-        <tr id="Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based optimization technique that enables the control of such nonlinear systems with constraints. However, modern systems often lack computationally tractable models, motivating the use of system identification techniques to learn accurate and efficient models for real-time control. In this tutorial article, we review emerging data-driven methods for model discovery and how they are used for nonlinear MPC. In particular, we focus on the sparse identification of nonlinear dynamics (SINDy) algorithm and show how it may be used with MPC on an infectious disease control example. We compare the performance against MPC based on a linear dynamic mode decomposition (DMD) model. Code is provided to run the tutorial examples and may be modified to extend this data-driven control framework to arbitrary nonlinear systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/700552dde778bd1f6b76f7237e9b561597b859ba" target='_blank'>SINDy with Control: A Tutorial</a></td>
-          <td>
-            Urban Fasel, E. Kaiser, J. Kutz, Bingni W. Brunton, S. Brunton
-          </td>
-          <td>2021-08-30</td>
-          <td>2021 60th IEEE Conference on Decision and Control (CDC)</td>
-          <td>45</td>
-          <td>63</td>
-        </tr>
-    
-        <tr id="With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8787d66296c0337aeb54d87885d29a63af17711b" target='_blank'>Sparse learning of stochastic dynamical equations.</a></td>
-          <td>
-            L. Boninsegna, F. Nüske, C. Clementi
-          </td>
-          <td>2017-12-06</td>
-          <td>The Journal of chemical physics</td>
-          <td>190</td>
-          <td>44</td>
-        </tr>
-    
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-        <th>Abstract</th>
-        <th>Title</th>
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-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>A decoder-only foundation model for time-series forecasting</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Over the past years, foundation models have caused a paradigm shift in machine learning due to their unprecedented capabilities for zero-shot and few-shot generalization. However, despite the success of foundation models in modalities such as natural language processing and computer vision, the development of foundation models for time series forecasting has lagged behind. We present Lag-Llama, a general-purpose foundation model for univariate probabilistic time series forecasting based on a decoder-only transformer architecture that uses lags as covariates. Lag-Llama is pretrained on a large corpus of diverse time series data from several domains, and demonstrates strong zero-shot generalization capabilities compared to a wide range of forecasting models on downstream datasets across domains. Moreover, when fine-tuned on relatively small fractions of such previously unseen datasets, Lag-Llama achieves state-of-the-art performance, outperforming prior deep learning approaches, emerging as the best general-purpose model on average. Lag-Llama serves as a strong contender to the current state-of-art in time series forecasting and paves the way for future advancements in foundation models tailored to time series data.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7c9bb230946cf48a7b9de97fd0281f42fbc51d31" target='_blank'>Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting</a></td>
-          <td>
-            Kashif Rasul, Arjun Ashok, Andrew Robert Williams, Arian Khorasani, George Adamopoulos, Rishika Bhagwatkar, Marin Bilovs, Hena Ghonia, N. Hassen, Anderson Schneider, Sahil Garg, Alexandre Drouin, Nicolas Chapados, Yuriy Nevmyvaka, I. Rish
-          </td>
-          <td>2023-10-12</td>
-          <td>ArXiv</td>
-          <td>13</td>
-          <td>40</td>
-        </tr>
-    
-        <tr id="Large language models (LLMs) are being applied to time series tasks, particularly time series forecasting. However, are language models actually useful for time series? After a series of ablation studies on three recent and popular LLM-based time series forecasting methods, we find that removing the LLM component or replacing it with a basic attention layer does not degrade the forecasting results -- in most cases the results even improved. We also find that despite their significant computational cost, pretrained LLMs do no better than models trained from scratch, do not represent the sequential dependencies in time series, and do not assist in few-shot settings. Additionally, we explore time series encoders and reveal that patching and attention structures perform similarly to state-of-the-art LLM-based forecasters.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/df0d604b8e8e3b2947d9865d735f204c08635012" target='_blank'>Are Language Models Actually Useful for Time Series Forecasting?</a></td>
-          <td>
-            Mingtian Tan, Mike A. Merrill, Vinayak Gupta, Tim Althoff, Tom Hartvigsen
-          </td>
-          <td>2024-06-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Time series forecasting holds significant importance in many real-world dynamic systems and has been extensively studied. Unlike natural language process (NLP) and computer vision (CV), where a single large model can tackle multiple tasks, models for time series forecasting are often specialized, necessitating distinct designs for different tasks and applications. While pre-trained foundation models have made impressive strides in NLP and CV, their development in time series domains has been constrained by data sparsity. Recent studies have revealed that large language models (LLMs) possess robust pattern recognition and reasoning abilities over complex sequences of tokens. However, the challenge remains in effectively aligning the modalities of time series data and natural language to leverage these capabilities. In this work, we present Time-LLM, a reprogramming framework to repurpose LLMs for general time series forecasting with the backbone language models kept intact. We begin by reprogramming the input time series with text prototypes before feeding it into the frozen LLM to align the two modalities. To augment the LLM's ability to reason with time series data, we propose Prompt-as-Prefix (PaP), which enriches the input context and directs the transformation of reprogrammed input patches. The transformed time series patches from the LLM are finally projected to obtain the forecasts. Our comprehensive evaluations demonstrate that Time-LLM is a powerful time series learner that outperforms state-of-the-art, specialized forecasting models. Moreover, Time-LLM excels in both few-shot and zero-shot learning scenarios.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277" target='_blank'>Time-LLM: Time Series Forecasting by Reprogramming Large Language Models</a></td>
-          <td>
-            Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y. Zhang, X. Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, Qingsong Wen
-          </td>
-          <td>2023-10-03</td>
-          <td>ArXiv</td>
-          <td>111</td>
-          <td>9</td>
-        </tr>
-    
-        <tr id="Recent Transformer-based large language models (LLMs) demonstrate in-context learning ability to perform various functions based solely on the provided context, without updating model parameters. To fully utilize the in-context capabilities in time series forecasting (TSF) problems, unlike previous Transformer-based or LLM-based time series forecasting methods, we reformulate"time series forecasting tasks"as input tokens by constructing a series of (lookback, future) pairs within the tokens. This method aligns more closely with the inherent in-context mechanisms, and is more parameter-efficient without the need of using pre-trained LLM parameters. Furthermore, it addresses issues such as overfitting in existing Transformer-based TSF models, consistently achieving better performance across full-data, few-shot, and zero-shot settings compared to previous architectures.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3777e8d6cda553cbd9e3bbd6484e613386f3a59e" target='_blank'>In-context Time Series Predictor</a></td>
-          <td>
-            Jiecheng Lu, Yan Sun, Shihao Yang
-          </td>
-          <td>2024-05-23</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-    
-        <tr id="Multivariate time-series forecasting is vital in various domains, e.g., economic planning and weather prediction. Deep train-from-scratch models have exhibited effective performance yet require large amounts of data, which limits real-world applicability. Recently, researchers have leveraged the representation learning transferability of pre-trained Large Language Models (LLMs) to handle limited non-linguistic datasets effectively. However, incorporating LLMs with time-series data presents challenges of limited adaptation due to different compositions between time-series and linguistic data, and the inability to process multi-scale temporal information. To tackle these challenges, we propose LLM4TS, a framework for time-series forecasting with pre-trained LLMs. LLM4TS consists of a two-stage fine-tuning strategy: the \textit{time-series alignment} stage to align LLMs with the nuances of time-series data, and the \textit{forecasting fine-tuning} stage for downstream time-series forecasting tasks. Furthermore, our framework features a novel two-level aggregation method that integrates multi-scale temporal data within pre-trained LLMs, enhancing their ability to interpret time-specific information. In experiments across 7 time-series forecasting datasets, LLM4TS is superior to existing state-of-the-art methods compared with trained-from-scratch models in full-shot scenarios, and also achieves an average improvement of 6.84% in MSE in few-shot scenarios. In addition, evaluations compared with different self-supervised learning approaches highlight LLM4TS's effectiveness with representation learning in forecasting tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/663dc434fabc1cf1d3e85fff3f7ddcd313035d18" target='_blank'>LLM4TS: Aligning Pre-Trained LLMs as Data-Efficient Time-Series Forecasters</a></td>
-          <td>
-            Ching Chang, Wenjie Peng, Tien-Fu Chen
-          </td>
-          <td>2023-08-16</td>
-          <td>ArXiv</td>
-          <td>15</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Time series data are ubiquitous across various domains, making time series analysis critically important. Traditional time series models are task-specific, featuring singular functionality and limited generalization capacity. Recently, large language foundation models have unveiled their remarkable capabilities for cross-task transferability, zero-shot/few-shot learning, and decision-making explainability. This success has sparked interest in the exploration of foundation models to solve multiple time series challenges simultaneously. There are two main research lines, namely pre-training foundation models from scratch for time series and adapting large language foundation models for time series. They both contribute to the development of a unified model that is highly generalizable, versatile, and comprehensible for time series analysis. This survey offers a 3E analytical framework for comprehensive examination of related research. Specifically, we examine existing works from three dimensions, namely Effectiveness, Efficiency and Explainability. In each dimension, we focus on discussing how related works devise tailored solution by considering unique challenges in the realm of time series. Furthermore, we provide a domain taxonomy to help followers keep up with the domain-specific advancements. In addition, we introduce extensive resources to facilitate the field's development, including datasets, open-source, time series libraries. A GitHub repository is also maintained for resource updates (https://github.com/start2020/Awesome-TimeSeries-LLM-FM).">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/522828823ff726598675971036fff01b57320578" target='_blank'>A Survey of Time Series Foundation Models: Generalizing Time Series Representation with Large Language Model</a></td>
-          <td>
-            Jiexia Ye, Weiqi Zhang, Ke Yi, Yongzi Yu, Ziyue Li, Jia Li, F. Tsung
-          </td>
-          <td>2024-05-03</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>47</td>
-        </tr>
-    
-        <tr id="Time-series forecasting (TSF) finds broad applications in real-world scenarios. Prompting off-the-shelf Large Language Models (LLMs) demonstrates strong zero-shot TSF capabilities while preserving computational efficiency. However, existing prompting methods oversimplify TSF as language next-token predictions, overlooking its dynamic nature and lack of integration with state-of-the-art prompt strategies such as Chain-of-Thought. Thus, we propose LSTPrompt, a novel approach for prompting LLMs in zero-shot TSF tasks. LSTPrompt decomposes TSF into short-term and long-term forecasting sub-tasks, tailoring prompts to each. LSTPrompt guides LLMs to regularly reassess forecasting mechanisms to enhance adaptability. Extensive evaluations demonstrate consistently better performance of LSTPrompt than existing prompting methods, and competitive results compared to foundation TSF models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bbf272d92b76cc5f1e6f793dcfeb5edd4abed7ef" target='_blank'>LSTPrompt: Large Language Models as Zero-Shot Time Series Forecasters by Long-Short-Term Prompting</a></td>
-          <td>
-            Haoxin Liu, Zhiyuan Zhao, Jindong Wang, Harshavardhan Kamarthi, B. A. Prakash
-          </td>
-          <td>2024-02-25</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="Unlike natural language processing and computer vision, the development of Foundation Models (FMs) for time series forecasting is blocked due to data scarcity. While recent efforts are focused on building such FMs by unlocking the potential of language models (LMs) for time series analysis, dedicated parameters for various downstream forecasting tasks need training, which hinders the common knowledge sharing across domains. Moreover, data owners may hesitate to share the access to local data due to privacy concerns and copyright protection, which makes it impossible to simply construct a FM on cross-domain training instances. To address these issues, we propose Time-FFM, a Federated Foundation Model for Time series forecasting by leveraging pretrained LMs. Specifically, we begin by transforming time series into the modality of text tokens. To bootstrap LMs for time series reasoning, we propose a prompt adaption module to determine domain-customized prompts dynamically instead of artificially. Given the data heterogeneity across domains, we design a personalized federated training strategy by learning global encoders and local prediction heads. Our comprehensive experiments indicate that Time-FFM outperforms state-of-the-arts and promises effective few-shot and zero-shot forecaster.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68a65925ac6d270ca27a4fe99e58cf2ed0795821" target='_blank'>Time-FFM: Towards LM-Empowered Federated Foundation Model for Time Series Forecasting</a></td>
-          <td>
-            Qingxiang Liu, Xu Liu, Chenghao Liu, Qingsong Wen, Yuxuan Liang
-          </td>
-          <td>2024-05-23</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="Despite the impressive achievements of pre-trained models in the fields of natural language processing (NLP) and computer vision (CV), progress in the domain of time series analysis has been limited. In contrast to NLP and CV, where a single model can handle various tasks, time series analysis still relies heavily on task-specific methods for activities such as classification, anomaly detection, forecasting, and few-shot learning. The primary obstacle to developing a pre-trained model for time series analysis is the scarcity of sufficient training data. In our research, we overcome this obstacle by utilizing pre-trained models from language or CV, which have been trained on billions of data points, and apply them to time series analysis. We assess the effectiveness of the pre-trained transformer model in two ways. Initially, we maintain the original structure of the self-attention and feedforward layers in the residual blocks of the pre-trained language or image model, using the Frozen Pre-trained Transformer (FPT) for time series analysis with the addition of projection matrices for input and output. Additionally, we introduce four unique adapters, designed specifically for downstream tasks based on the pre-trained model, including forecasting and anomaly detection. These adapters are further enhanced with efficient parameter tuning, resulting in superior performance compared to all state-of-the-art methods.Our comprehensive experimental studies reveal that (a) the simple FPT achieves top-tier performance across various time series analysis tasks; and (b) fine-tuning the FPT with the custom-designed adapters can further elevate its performance, outshining specialized task-specific models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/15bfe54223d28c74f9e39960f7ff1d03167e285f" target='_blank'>One Fits All: Universal Time Series Analysis by Pretrained LM and Specially Designed Adaptors</a></td>
-          <td>
-            Tian Zhou, Peisong Niu, Xue Wang, Liang Sun, Rong Jin
-          </td>
-          <td>2023-11-24</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>7</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
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-  <i class="footer">This page was last updated on 2024-07-22 06:07:00 UTC</i>
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-  <h3 data-intro='Recommendations for the article'>
-    Recommendations for the article <i>Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations</i>
-  </h3>
-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
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-  <tbody>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d86084808994ac54ef4840ae65295f3c0ec4decd" target='_blank'>Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations</a></td>
-          <td>
-            M. Raissi, P. Perdikaris, G. Karniadakis
-          </td>
-          <td>2019-02-01</td>
-          <td>J. Comput. Phys.</td>
-          <td>7319</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/43bba6a3bb186e7370366e5c899c90ca9a573820" target='_blank'>Physics Informed Extreme Learning Machine (PIELM) - A rapid method for the numerical solution of partial differential equations</a></td>
-          <td>
-            Vikas Dwivedi, B. Srinivasan
-          </td>
-          <td>2019-07-08</td>
-          <td>ArXiv</td>
-          <td>130</td>
-          <td>14</td>
-        </tr>
-    
-        <tr id="This paper establishes a method for solving partial differential equations using a multi-step physics-informed deep operator neural network. The network is trained by embedding physics-informed constraints. Different from traditional neural networks for solving partial differential equations, the proposed method uses a deep neural operator network to indirectly construct the mapping relationship between the variable functions and solution functions. This approach makes full use of the hidden information between the variable functions and independent variables. The process whereby the model captures incredibly complex and highly nonlinear relationships is simplified, thereby making network learning easier and enhancing the extraction of information about the independent variables in partial differential systems. In terms of solving partial differential equations, we verify that the multi-step physics-informed deep operator neural network markedly improves the solution accuracy compared with a traditional physics-informed deep neural operator network, especially when the problem involves complex physical phenomena with large gradient changes.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ac5d801ec2ae339a109eb310769fe243cbff7025" target='_blank'>Multi-Step Physics-Informed Deep Operator Neural Network for Directly Solving Partial Differential Equations</a></td>
-          <td>
-            Jing Wang, Yubo Li, Anping Wu, Zheng Chen, Jun Huang, Qingfeng Wang, Feng Liu
-          </td>
-          <td>2024-06-25</td>
-          <td>Applied Sciences</td>
-          <td>0</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a Petrov-Galerkin version of PINNs based on the nonlinear approximation of deep neural networks (DNNs) by selecting the {\em trial space} to be the space of neural networks and the {\em test space} to be the space of Legendre polynomials. We formulate the \textit{variational residual} of the PDE using the DNN approximation by incorporating the variational form of the problem into the loss function of the network and construct a \textit{variational physics-informed neural network} (VPINN). By integrating by parts the integrand in the variational form, we lower the order of the differential operators represented by the neural networks, hence effectively reducing the training cost in VPINNs while increasing their accuracy compared to PINNs that essentially employ delta test functions. For shallow networks with one hidden layer, we analytically obtain explicit forms of the \textit{variational residual}. We demonstrate the performance of the new formulation for several examples that show clear advantages of VPINNs over PINNs in terms of both accuracy and speed.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d483f6ecc4685767344822d9e0f03c82b68531ba" target='_blank'>Variational Physics-Informed Neural Networks For Solving Partial Differential Equations</a></td>
-          <td>
-            E. Kharazmi, Z. Zhang, G. Karniadakis
-          </td>
-          <td>2019-11-27</td>
-          <td>ArXiv</td>
-          <td>185</td>
-          <td>127</td>
-        </tr>
-    
-        <tr id="A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical models of the physical world. In the current era of abundance of data and advanced machine learning capabilities, the natural question arises: How can we automatically uncover the underlying laws of physics from high-dimensional data generated from experiments? In this work, we put forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time. Specifically, we approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks. The first network acts as a prior on the unknown solution and essentially enables us to avoid numerical differentiations which are inherently ill-conditioned and unstable. The second network represents the nonlinear dynamics and helps us distill the mechanisms that govern the evolution of a given spatiotemporal data-set. We test the effectiveness of our approach for several benchmark problems spanning a number of scientific domains and demonstrate how the proposed framework can help us accurately learn the underlying dynamics and forecast future states of the system. In particular, we study the Burgers', Korteweg-de Vries (KdV), Kuramoto-Sivashinsky, nonlinear Schr\"{o}dinger, and Navier-Stokes equations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ebcc0e71ef6a77d05e7ab064435bc2da87c55e91" target='_blank'>Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations</a></td>
-          <td>
-            M. Raissi
-          </td>
-          <td>2018-01-20</td>
-          <td>J. Mach. Learn. Res.</td>
-          <td>658</td>
-          <td>24</td>
-        </tr>
-    
-        <tr id="We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization procedure in the training process. The so-called physics-informed neural networks (PINNs) are tested on a variety of academic ordinary differential equations in order to highlight the benefits and drawbacks of this approach with respect to standard integration methods. We focus on the possibility to use the least possible amount of data into the training process. The principles of PINNs for solving differential equations by enforcing physical laws via penalizing terms are reviewed. A tutorial on a simple equation model illustrates how to put into practice the method for ordinary differential equations. Benchmark tests show that a very small amount of training data is sufficient to predict the solution when the non linearity of the problem is weak. However, this is not the case in strongly non linear problems where a priori knowledge of training data over some partial or the whole time integration interval is necessary.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/10db5d6f57cf7f9b3fdedbd9c578d79dd2e863fa" target='_blank'>Solving differential equations using physics informed deep learning: a hand-on tutorial with benchmark tests</a></td>
-          <td>
-            H. Baty, L. Baty
-          </td>
-          <td>2023-02-23</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>14</td>
-        </tr>
-    
-        <tr id="Partial differential equations (PDEs) play a pivotal role in mathematical analysis and modeling of dynamic processes across various disciplines of science and engineering. Machine learning (ML) techniques have emerged as a promising new approach to solving PDEs. Among them, Physics-Informed Neural Networks (PINNs) have garnered significant attention in numerous scientific and engineering studies. PINNs employ a single deep neural network to assimilate observational data with PDEs across the entire space-time of a physical system, subsequently yielding rapid solutions. However, a PINN may entail intricate analyses or computations and can be cost-intensive, depending on initial or boundary conditions and other input parameters. To address the limitations of the PINN, especially concerning resolution for nonlinear problems, the Physical-Informed Deep Operator Network (DeepONet) is introduced in this paper. The Physics-Informed DeepONet is a deep learning framework crafted to discern solution operators for any given PDEs, even in scenarios lacking paired input/output training data. The proposed framework is able to predict solutions for various types of parameterized PDEs much faster than conventional PDE solvers. Several cases confirm that this approach is effective in establishing previously unexplored paradigms for modeling/simulating nonlinear and non-equilibrium processes in science and engineering.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/54aa8e27e0e1c52997a21502817afcb71d9e8ccb" target='_blank'>Understanding on Physics-Informed DeepONet</a></td>
-          <td>
-            Sang-Min Lee
-          </td>
-          <td>2024-01-31</td>
-          <td>Journal of the Korea Academia-Industrial cooperation Society</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-    
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3d6fd15fea21a3a5fff4bf294b67cb959b46008a" target='_blank'>Physics Informed RNN-DCT Networks for Time-Dependent Partial Differential Equations</a></td>
-          <td>
-            Benwei Wu, O. Hennigh, J. Kautz, S. Choudhry, Wonmin Byeon
-          </td>
-          <td>2022-02-24</td>
-          <td>ArXiv</td>
-          <td>4</td>
-          <td>91</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
-
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-  <table id="table1" class="display wrap" style="width:100%">
-  <thead>
-    <tr>
-        <th data-intro='Click to view the abstract (if available)'>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/ Conference</th>
-        <th>Citation count</th>
-        <th data-intro='Highest h-index among the authors'>Highest h-index</th>
-    </tr>
-  </thead>
-  <tbody>
-    
-        <tr id="Deep learning has contributed remarkably to the advancement of time series analysis. Still, deep models can encounter performance bottlenecks in real-world data-scarce scenarios, which can be concealed due to the performance saturation with small models on current benchmarks. Meanwhile, large models have demonstrated great powers in these scenarios through large-scale pre-training. Continuous progress has been achieved with the emergence of large language models, exhibiting unprecedented abilities such as few-shot generalization, scalability, and task generality, which are however absent in small deep models. To change the status quo of training scenario-specific small models from scratch, this paper aims at the early development of large time series models (LTSM). During pre-training, we curate large-scale datasets with up to 1 billion time points, unify heterogeneous time series into single-series sequence (S3) format, and develop the GPT-style architecture toward LTSMs. To meet diverse application needs, we convert forecasting, imputation, and anomaly detection of time series into a unified generative task. The outcome of this study is a Time Series Transformer (Timer), which is generative pre-trained by next token prediction and adapted to various downstream tasks with promising capabilities as an LTSM. Code and datasets are available at: https://github.com/thuml/Large-Time-Series-Model.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/73f58b90697f957832f5090946894480849dea3a" target='_blank'>Timer: Generative Pre-trained Transformers Are Large Time Series Models</a></td>
-          <td>
-            Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long
-          </td>
-          <td>2024-02-04</td>
-          <td>ArXiv</td>
-          <td>6</td>
-          <td>65</td>
-        </tr>
-    
-        <tr id="Large pre-trained models have been vital in recent advancements in domains like language and vision, making model training for individual downstream tasks more efficient and provide superior performance. However, tackling time-series analysis tasks usually involves designing and training a separate model from scratch leveraging training data and domain expertise specific to the task. We tackle a significant challenge for pre-training a foundational time-series model from multi-domain time-series datasets: extracting semantically useful tokenized inputs to the model across heterogenous time-series from different domains. We propose Large Pre-trained Time-series Models (LPTM) that introduces a novel method of \textit{adaptive segmentation} that automatically identifies optimal dataset-specific segmentation strategy during pre-training. This enables LPTM to perform similar to or better than domain-specific state-of-art model when fine-tuned to different downstream time-series analysis tasks and under zero-shot settings. LPTM achieves superior forecasting and time-series classification results taking up to 40% less data and 50% less training time compared to state-of-art baselines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d8140a17dfc21b1e3300158cb0676600136f14b1" target='_blank'>Large Pre-trained time series models for cross-domain Time series analysis tasks</a></td>
-          <td>
-            Harshavardhan Kamarthi, B. A. Prakash
-          </td>
-          <td>2023-11-19</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="The field of general time series analysis has recently begun to explore unified modeling, where a common architectural backbone can be retrained on a specific task for a specific dataset. In this work, we approach unification from a complementary vantage point: unification across tasks and domains. To this end, we explore the impact of discrete, learnt, time series data representations that enable generalist, cross-domain training. Our method, TOTEM, or TOkenized Time Series EMbeddings, proposes a simple tokenizer architecture that embeds time series data from varying domains using a discrete vectorized representation learned in a self-supervised manner. TOTEM works across multiple tasks and domains with minimal to no tuning. We study the efficacy of TOTEM with an extensive evaluation on 17 real world time series datasets across 3 tasks. We evaluate both the specialist (i.e., training a model on each domain) and generalist (i.e., training a single model on many domains) settings, and show that TOTEM matches or outperforms previous best methods on several popular benchmarks. The code can be found at: https://github.com/SaberaTalukder/TOTEM.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f9f09c782155ca4f2ae4b6ffcf28514b439226cd" target='_blank'>TOTEM: TOkenized Time Series EMbeddings for General Time Series Analysis</a></td>
-          <td>
-            Sabera Talukder, Yisong Yue, Georgia Gkioxari
-          </td>
-          <td>2024-02-26</td>
-          <td>ArXiv</td>
-          <td>3</td>
-          <td>3</td>
-        </tr>
-    
-        <tr id="Time-series data exists in every corner of real-world systems and services, ranging from satellites in the sky to wearable devices on human bodies. Learning representations by extracting and inferring valuable information from these time series is crucial for understanding the complex dynamics of particular phenomena and enabling informed decisions. With the learned representations, we can perform numerous downstream analyses more effectively. Among several approaches, deep learning has demonstrated remarkable performance in extracting hidden patterns and features from time-series data without manual feature engineering. This survey first presents a novel taxonomy based on three fundamental elements in designing state-of-the-art universal representation learning methods for time series. According to the proposed taxonomy, we comprehensively review existing studies and discuss their intuitions and insights into how these methods enhance the quality of learned representations. Finally, as a guideline for future studies, we summarize commonly used experimental setups and datasets and discuss several promising research directions. An up-to-date corresponding resource is available at https://github.com/itouchz/awesome-deep-time-series-representations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/72f38d513a8ab095a3d4f459958cbb31b1f7cdc4" target='_blank'>Universal Time-Series Representation Learning: A Survey</a></td>
-          <td>
-            Patara Trirat, Yooju Shin, Junhyeok Kang, Youngeun Nam, Jihye Na, Minyoung Bae, Joeun Kim, Byunghyun Kim, Jae-Gil Lee
-          </td>
-          <td>2024-01-08</td>
-          <td>ArXiv</td>
-          <td>5</td>
-          <td>6</td>
-        </tr>
-    
-        <tr id="Despite the impressive achievements of pre-trained models in the fields of natural language processing (NLP) and computer vision (CV), progress in the domain of time series analysis has been limited. In contrast to NLP and CV, where a single model can handle various tasks, time series analysis still relies heavily on task-specific methods for activities such as classification, anomaly detection, forecasting, and few-shot learning. The primary obstacle to developing a pre-trained model for time series analysis is the scarcity of sufficient training data. In our research, we overcome this obstacle by utilizing pre-trained models from language or CV, which have been trained on billions of data points, and apply them to time series analysis. We assess the effectiveness of the pre-trained transformer model in two ways. Initially, we maintain the original structure of the self-attention and feedforward layers in the residual blocks of the pre-trained language or image model, using the Frozen Pre-trained Transformer (FPT) for time series analysis with the addition of projection matrices for input and output. Additionally, we introduce four unique adapters, designed specifically for downstream tasks based on the pre-trained model, including forecasting and anomaly detection. These adapters are further enhanced with efficient parameter tuning, resulting in superior performance compared to all state-of-the-art methods.Our comprehensive experimental studies reveal that (a) the simple FPT achieves top-tier performance across various time series analysis tasks; and (b) fine-tuning the FPT with the custom-designed adapters can further elevate its performance, outshining specialized task-specific models.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/15bfe54223d28c74f9e39960f7ff1d03167e285f" target='_blank'>One Fits All: Universal Time Series Analysis by Pretrained LM and Specially Designed Adaptors</a></td>
-          <td>
-            Tian Zhou, Peisong Niu, Xue Wang, Liang Sun, Rong Jin
-          </td>
-          <td>2023-11-24</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>7</td>
-        </tr>
-    
-        <tr id="We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4fb78450650894091b0a55b5504a8b0a6f3dec37" target='_blank'>Chronos: Learning the Language of Time Series</a></td>
-          <td>
-            Abdul Fatir Ansari, Lorenzo Stella, Caner Turkmen, Xiyuan Zhang, Pedro Mercado, Huibin Shen, Oleksandr Shchur, Syama Sundar Rangapuram, Sebastian Pineda Arango, Shubham Kapoor, Jasper Zschiegner, Danielle C. Maddix, Michael W. Mahoney, Kari Torkkola, Andrew Gordon Wilson, Michael Bohlke-Schneider, Yuyang Wang
-          </td>
-          <td>2024-03-12</td>
-          <td>ArXiv</td>
-          <td>23</td>
-          <td>18</td>
-        </tr>
-    
-        <tr id="Deep learning for time series forecasting has traditionally operated within a one-model-per-dataset framework, limiting its potential to leverage the game-changing impact of large pre-trained models. The concept of universal forecasting, emerging from pre-training on a vast collection of time series datasets, envisions a single Large Time Series Model capable of addressing diverse downstream forecasting tasks. However, constructing such a model poses unique challenges specific to time series data: i) cross-frequency learning, ii) accommodating an arbitrary number of variates for multivariate time series, and iii) addressing the varying distributional properties inherent in large-scale data. To address these challenges, we present novel enhancements to the conventional time series Transformer architecture, resulting in our proposed Masked Encoder-based Universal Time Series Forecasting Transformer (Moirai). Trained on our newly introduced Large-scale Open Time Series Archive (LOTSA) featuring over 27B observations across nine domains, Moirai achieves competitive or superior performance as a zero-shot forecaster when compared to full-shot models. Code, data, and model weights can be found at https://github.com/SalesforceAIResearch/uni2ts.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4a111f7a3b56d0468f13104999844885157ef17d" target='_blank'>Unified Training of Universal Time Series Forecasting Transformers</a></td>
-          <td>
-            Gerald Woo, Chenghao Liu, Akshat Kumar, Caiming Xiong, Silvio Savarese, Doyen Sahoo
-          </td>
-          <td>2024-02-04</td>
-          <td>ArXiv</td>
-          <td>26</td>
-          <td>22</td>
-        </tr>
-    
-        <tr id="Learning time-series representations for discriminative tasks has been a long-standing challenge. Current pre-training methods are limited in either unidirectional next-token prediction or randomly masked token prediction. We propose a novel architecture called Bidirectional Timely Generative Pre-trained Transformer (BiTimelyGPT), which pre-trains on time-series data by both next-token and previous-token predictions in alternating transformer layers. This pre-training task preserves original distribution and data shapes of the time-series. Additionally, the full-rank forward and backward attention matrices exhibit more expressive representation capabilities. Using biosignal data, BiTimelyGPT demonstrates superior performance in predicting neurological functionality, disease diagnosis, and physiological signs. By visualizing the attention heatmap, we observe that the pre-trained BiTimelyGPT can identify discriminative segments from time-series sequences, even more so after fine-tuning on the task.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1d0328153f4136635b7df336fb958c92d066ac29" target='_blank'>Bidirectional Generative Pre-training for Improving Time Series Representation Learning</a></td>
-          <td>
-            Ziyang Song, Qincheng Lu, He Zhu, Yue Li
-          </td>
-          <td>2024-02-14</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>2</td>
-        </tr>
-    
-        <tr id="Time series data are ubiquitous across various domains, making time series analysis critically important. Traditional time series models are task-specific, featuring singular functionality and limited generalization capacity. Recently, large language foundation models have unveiled their remarkable capabilities for cross-task transferability, zero-shot/few-shot learning, and decision-making explainability. This success has sparked interest in the exploration of foundation models to solve multiple time series challenges simultaneously. There are two main research lines, namely pre-training foundation models from scratch for time series and adapting large language foundation models for time series. They both contribute to the development of a unified model that is highly generalizable, versatile, and comprehensible for time series analysis. This survey offers a 3E analytical framework for comprehensive examination of related research. Specifically, we examine existing works from three dimensions, namely Effectiveness, Efficiency and Explainability. In each dimension, we focus on discussing how related works devise tailored solution by considering unique challenges in the realm of time series. Furthermore, we provide a domain taxonomy to help followers keep up with the domain-specific advancements. In addition, we introduce extensive resources to facilitate the field's development, including datasets, open-source, time series libraries. A GitHub repository is also maintained for resource updates (https://github.com/start2020/Awesome-TimeSeries-LLM-FM).">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/522828823ff726598675971036fff01b57320578" target='_blank'>A Survey of Time Series Foundation Models: Generalizing Time Series Representation with Large Language Model</a></td>
-          <td>
-            Jiexia Ye, Weiqi Zhang, Ke Yi, Yongzi Yu, Ziyue Li, Jia Li, F. Tsung
-          </td>
-          <td>2024-05-03</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>47</td>
-        </tr>
-    
-  </tbody>
-  <tfoot>
-    <tr>
-        <th>Abstract</th>
-        <th>Title</th>
-        <th>Authors</th>
-        <th>Publication Date</th>
-        <th>Journal/Conference</th>
-        <th>Citation count</th>
-        <th>Highest h-index</th>
-    </tr>
-  </tfoot>
-  </table>
-  </p>
-
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diff --git a/requirements.txt b/requirements.txt
index 0021ef57..5006699b 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,6 +1,7 @@
 astroid==3.0.0
 Babel==2.14.0
 beautifulsoup4==4.12.3
+bibtexparser==1.4.1
 blinker==1.6.3
 certifi==2024.7.4
 charset-normalizer==3.3.2
@@ -56,6 +57,7 @@ python-dateutil==2.9.0.post0
 pytz==2024.1
 PyYAML==6.0.1
 pyyaml_env_tag==0.1
+pyzotero==1.5.20
 regex==2023.12.25
 requests==2.31.0
 seaborn==0.13.2
diff --git a/site/Symbolic regression/index.html b/site/Symbolic regression/index.html
index bc70b963..b29d0005 100644
--- a/site/Symbolic regression/index.html	
+++ b/site/Symbolic regression/index.html	
@@ -451,7 +451,7 @@ <h1>Symbolic regression</h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:19 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:48 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -515,9 +515,9 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
             S. Brunton, J. Proctor, J. Kutz
           </td>
           <td>2015-09-11</td>
-          <td>Proceedings of the National Academy of Sciences of the United States of America, Proceedings of the National Academy of Sciences</td>
-          <td>3159</td>
-          <td>63</td>
+          <td>Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences of the United States of America</td>
+          <td>3190</td>
+          <td>65</td>
 
             <td><a href='../recommendations/5d150cec2775f9bc863760448f14104cc8f42368' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -536,7 +536,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2021-02-24</td>
           <td>Nature Communications</td>
-          <td>84</td>
+          <td>85</td>
           <td>23</td>
 
             <td><a href='../recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c' target='_blank'>
@@ -556,8 +556,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2019-03-29</td>
           <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>595</td>
-          <td>63</td>
+          <td>603</td>
+          <td>65</td>
 
             <td><a href='../recommendations/3c9961153493370500020c81527b3548c96f81e0' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -576,8 +576,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2016-08-18</td>
           <td>Nature Communications</td>
-          <td>446</td>
-          <td>63</td>
+          <td>448</td>
+          <td>65</td>
 
             <td><a href='../recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -596,8 +596,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2017-11-15</td>
           <td>Proceedings of the Royal Society A, Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>425</td>
-          <td>63</td>
+          <td>428</td>
+          <td>65</td>
 
             <td><a href='../recommendations/b2eb064f432557c59ce99834d7dc7817e4687271' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -615,9 +615,9 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
             N. Mangan, S. Brunton, J. Proctor, J. Kutz
           </td>
           <td>2016-05-26</td>
-          <td>IEEE Transactions on Molecular Biological and Multi-Scale Communications, IEEE Transactions on Molecular, Biological and Multi-Scale Communications</td>
-          <td>314</td>
-          <td>63</td>
+          <td>IEEE Transactions on Molecular, Biological and Multi-Scale Communications, IEEE Transactions on Molecular Biological and Multi-Scale Communications</td>
+          <td>317</td>
+          <td>65</td>
 
             <td><a href='../recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -636,8 +636,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2020-04-05</td>
           <td>Proceedings of the Royal Society A, Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>190</td>
-          <td>63</td>
+          <td>194</td>
+          <td>65</td>
 
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@@ -675,9 +675,9 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
             Kadierdan Kaheman, E. Kaiser, B. Strom, J. Kutz, S. Brunton
           </td>
           <td>2019-09-18</td>
-          <td>ArXiv, arXiv.org</td>
-          <td>31</td>
-          <td>63</td>
+          <td>arXiv.org, ArXiv</td>
+          <td>32</td>
+          <td>65</td>
 
             <td><a href='../recommendations/73dd9c49f205280991826b2ea4b50344203916b4' target='_blank'>
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@@ -696,8 +696,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2019-06-19</td>
           <td>Frontiers in Artificial Intelligence</td>
-          <td>66</td>
-          <td>63</td>
+          <td>67</td>
+          <td>65</td>
 
             <td><a href='../recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -716,8 +716,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2016-09-21</td>
           <td>Science Advances</td>
-          <td>1164</td>
-          <td>63</td>
+          <td>1172</td>
+          <td>65</td>
 
             <td><a href='../recommendations/0acd117521ef5aafb09fed02ab415523b330b058' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -736,8 +736,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2021-11-22</td>
           <td>Proceedings of the Royal Society A, Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>154</td>
-          <td>63</td>
+          <td>158</td>
+          <td>65</td>
 
             <td><a href='../recommendations/883547fdbd88552328a6615ec620f96e39c57018' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -756,8 +756,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2022-06-01</td>
           <td>Nonlinear Dynamics</td>
-          <td>27</td>
-          <td>90</td>
+          <td>28</td>
+          <td>91</td>
 
             <td><a href='../recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -776,8 +776,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Symbolic regr
           </td>
           <td>2018-07-14</td>
           <td>IEEE Access</td>
-          <td>114</td>
-          <td>63</td>
+          <td>115</td>
+          <td>65</td>
 
             <td><a href='../recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -835,48 +835,33 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>0</td>
         </tr>
 
-        <tr id="This paper proposes a sparse regression strategy for discovery of ordinary and partial differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated likelihood function. Sparsity is enforced by a selection algorithm which iteratively removes terms and compares models using statistical information criteria. Large scale optimization is performed using a second-order variant of the Levenberg-Marquardt method, where the gradient and Hessian are computed via automatic differentiation. Illustrations involving canonical systems of ordinary and partial differential equations are used to demonstrate the flexibility and robustness of the approach. Accurate reconstruction of systems is found to be possible even in extreme cases of limited data and large observation noise.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3d4419932eaa736ba7230568e3503746b37957c5" target='_blank'>
-              Discovery of differential equations using sparse state and parameter regression
-              </a>
-            </td>
-          <td>
-            Teddy Meissner, Karl Glasner
-          </td>
-          <td>2024-06-10</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-
-        <tr id="Enhancing the sparsity of data-driven reduced-order models (ROMs) has gained increasing attention in recent years. In this work, we analyze an efficient approach to identifying skillful ROMs with a sparse structure using an information-theoretic indicator called causation entropy. The causation entropy quantifies in a statistical way the additional contribution of each term to the underlying dynamics beyond the information already captured by all the other terms in the ansatz. By doing so, the causation entropy assesses the importance of each term to the dynamics before a parameter estimation procedure is performed. Thus, the approach can be utilized to eliminate terms with little dynamic impact, leading to a parsimonious structure that retains the essential physics. To circumvent the difficulty of estimating high-dimensional probability density functions (PDFs) involved in the causation entropy computation, we leverage Gaussian approximations for such PDFs, which are demonstrated to be sufficient even in the presence of highly non-Gaussian dynamics. The effectiveness of the approach is illustrated by the Kuramoto-Sivashinsky equation by building sparse causation-based ROMs for various purposes, such as recovering long-term statistics and inferring unobserved dynamics via data assimilation with partial observations.">
+        <tr id="This paper focuses on the application of experimental data-based system identification of unknown systems utilising sparse identification of nonlinear dynamics (SINDy). SINDy is used to detect the system dynamics in the three well-known nonlinear systems. Analyzed are SINDy’s abilities to accurately represent transient/steady-state behaviour, noise effect, and model structure. A sparse set of basis functions can effectively capture the dynamics of a system, according to the data-driven approach known as SINDy. The coefficients of these basis functions are determined via methods of sparse regression, and the final model is made up of a number of sparse ordinary differential equations. The findings demonstrate that SINDy, with sufficient time-series data, can capture both transient and steady-state phenomena. According to the analysis of the noise effect, SINDy’s performance declines as the system’s noise level rises. The feature library must contain the appropriate model structure in order for SINDy to function effectively. SINDy has the potential to extract unknown system dynamics from experimental data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/51343d94516402e35ba4c9c52a62e0d4dd4986ba" target='_blank'>
-              Minimum Reduced-Order Models via Causal Inference
+          <td><a href="https://www.semanticscholar.org/paper/315b7c145c5a86b92e656ad174cede9f67bf3f34" target='_blank'>
+              Data-driven system identification of unknown systems utilising sparse identification of nonlinear dynamics (SINDy)
               </a>
             </td>
           <td>
-            Nan Chen, Honghu Liu
+            P. Pandey, H. Haddad Khodaparast, M. Friswell, T. Chatterjee, N. Jamia, T. Deighan
           </td>
-          <td>2024-06-29</td>
-          <td>ArXiv</td>
-          <td>0</td>
+          <td>2024-06-01</td>
+          <td>Journal of Physics: Conference Series</td>
           <td>0</td>
+          <td>2</td>
         </tr>
 
-        <tr id="This paper focuses on the application of experimental data-based system identification of unknown systems utilising sparse identification of nonlinear dynamics (SINDy). SINDy is used to detect the system dynamics in the three well-known nonlinear systems. Analyzed are SINDy’s abilities to accurately represent transient/steady-state behaviour, noise effect, and model structure. A sparse set of basis functions can effectively capture the dynamics of a system, according to the data-driven approach known as SINDy. The coefficients of these basis functions are determined via methods of sparse regression, and the final model is made up of a number of sparse ordinary differential equations. The findings demonstrate that SINDy, with sufficient time-series data, can capture both transient and steady-state phenomena. According to the analysis of the noise effect, SINDy’s performance declines as the system’s noise level rises. The feature library must contain the appropriate model structure in order for SINDy to function effectively. SINDy has the potential to extract unknown system dynamics from experimental data.">
+        <tr id="Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are first-principled, explainable, and sample-efficient. However, they often rely on strong modeling assumptions and expensive numerical integration, requiring significant computational resources and domain expertise. While deep learning (DL) provides efficient alternatives for modeling complex dynamics, they require a large amount of labeled training data. Furthermore, its predictions may disobey the governing physical laws and are difficult to interpret. Physics-guided DL aims to integrate first-principled physical knowledge into data-driven methods. It has the best of both worlds and is well equipped to better solve scientific problems. Recently, this field has gained great progress and has drawn considerable interest across discipline Here, we introduce the framework of physics-guided DL with a special emphasis on learning dynamical systems. We describe the learning pipeline and categorize state-of-the-art methods under this framework. We also offer our perspectives on the open challenges and emerging opportunities.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/315b7c145c5a86b92e656ad174cede9f67bf3f34" target='_blank'>
-              Data-driven system identification of unknown systems utilising sparse identification of nonlinear dynamics (SINDy)
+          <td><a href="https://www.semanticscholar.org/paper/60d721e89c2f9c549241a4982b77f9c752b34460" target='_blank'>
+              Learning dynamical systems from data: An introduction to physics-guided deep learning
               </a>
             </td>
           <td>
-            P. Pandey, H. Haddad Khodaparast, M. Friswell, T. Chatterjee, N. Jamia, T. Deighan
+            Rose Yu, Rui Wang
           </td>
-          <td>2024-06-01</td>
-          <td>Journal of Physics: Conference Series</td>
-          <td>0</td>
+          <td>2024-06-24</td>
+          <td>Proceedings of the National Academy of Sciences of the United States of America</td>
+          <td>1</td>
           <td>1</td>
         </tr>
 
@@ -891,38 +876,38 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           </td>
           <td>2024-07-29</td>
           <td>ArXiv</td>
-          <td>0</td>
+          <td>1</td>
           <td>49</td>
         </tr>
 
-        <tr id="Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are first-principled, explainable, and sample-efficient. However, they often rely on strong modeling assumptions and expensive numerical integration, requiring significant computational resources and domain expertise. While deep learning (DL) provides efficient alternatives for modeling complex dynamics, they require a large amount of labeled training data. Furthermore, its predictions may disobey the governing physical laws and are difficult to interpret. Physics-guided DL aims to integrate first-principled physical knowledge into data-driven methods. It has the best of both worlds and is well equipped to better solve scientific problems. Recently, this field has gained great progress and has drawn considerable interest across discipline Here, we introduce the framework of physics-guided DL with a special emphasis on learning dynamical systems. We describe the learning pipeline and categorize state-of-the-art methods under this framework. We also offer our perspectives on the open challenges and emerging opportunities.">
+        <tr id="We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional non-uniform grids. We address limitations of previous work on data-driven flow map learning in the sense that we focus on noisy and limited data to move toward data collection scenarios in real-world applications. Leveraging recent work on modeling PDEs in modal and nodal spaces, we present a neural network structure that is suitable for PDE modeling with noisy and limited data available only on a subset of the state variables or computational domain. In particular, spatial grid-point measurements are reduced using a learned linear transformation, after which the dynamics are learned in this reduced basis before being transformed back out to the nodal space. This approach yields a drastically reduced parameterization of the neural network compared with previous flow map models for nodal space learning. This primarily allows for smaller training data sets, but also enables reduced training times.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/60d721e89c2f9c549241a4982b77f9c752b34460" target='_blank'>
-              Learning dynamical systems from data: An introduction to physics-guided deep learning
+          <td><a href="https://www.semanticscholar.org/paper/33821b7c0acd5258ca0c60a09ffdc55439ac7ac2" target='_blank'>
+              Principal Component Flow Map Learning of PDEs from Incomplete, Limited, and Noisy Data
               </a>
             </td>
           <td>
-            Rose Yu, Rui Wang
+            Victor Churchill
           </td>
-          <td>2024-06-24</td>
-          <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>1</td>
-          <td>1</td>
+          <td>2024-07-15</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>0</td>
         </tr>
 
-        <tr id="We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional non-uniform grids. We address limitations of previous work on data-driven flow map learning in the sense that we focus on noisy and limited data to move toward data collection scenarios in real-world applications. Leveraging recent work on modeling PDEs in modal and nodal spaces, we present a neural network structure that is suitable for PDE modeling with noisy and limited data available only on a subset of the state variables or computational domain. In particular, spatial grid-point measurements are reduced using a learned linear transformation, after which the dynamics are learned in this reduced basis before being transformed back out to the nodal space. This approach yields a drastically reduced parameterization of the neural network compared with previous flow map models for nodal space learning. This primarily allows for smaller training data sets, but also enables reduced training times.">
+        <tr id="This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. We demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion-reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/33821b7c0acd5258ca0c60a09ffdc55439ac7ac2" target='_blank'>
-              Principal Component Flow Map Learning of PDEs from Incomplete, Limited, and Noisy Data
+          <td><a href="https://www.semanticscholar.org/paper/6c14dacd4e17965fe6d0db5f5cefb7cb8547dbb3" target='_blank'>
+              Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems
               </a>
             </td>
           <td>
-            Victor Churchill
+            Shane A. McQuarrie, Anirban Chaudhuri, Karen Willcox, Mengwu Guo
           </td>
-          <td>2024-07-15</td>
+          <td>2024-08-06</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>6</td>
         </tr>
 
         <tr id="The quasipotential function allows for comprehension and prediction of the escape mechanisms from metastable states in nonlinear dynamical systems. This function acts as a natural extension of the potential function for non-gradient systems and it unveils important properties such as the maximum likelihood transition paths, transition rates and expected exit times of the system. Here, we leverage on machine learning via the combination of two data-driven techniques, namely a neural network and a sparse regression algorithm, to obtain symbolic expressions of quasipotential functions. The key idea is first to determine an orthogonal decomposition of the vector field that governs the underlying dynamics using neural networks, then to interpret symbolically the downhill and circulatory components of the decomposition. These functions are regressed simultaneously with the addition of mathematical constraints. We show that our approach discovers a parsimonious quasipotential equation for an archetypal model with a known exact quasipotential and for the dynamics of a nanomechanical resonator. The analytical forms deliver direct access to the stability of the metastable states and predict rare events with significant computational advantages. Our data-driven approach is of interest for a wide range of applications in which to assess the fluctuating dynamics.">
@@ -951,38 +936,38 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           </td>
           <td>2024-07-05</td>
           <td>ArXiv</td>
-          <td>2</td>
+          <td>3</td>
           <td>22</td>
         </tr>
 
-        <tr id="The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. To enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared to the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5-10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1-7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1,779x speed-up.">
+        <tr id="Model parsimony is an important \emph{cognitive bias} in data-driven modelling that aids interpretability and helps to prevent over-fitting. Sparse identification of nonlinear dynamics (SINDy) methods are able to learn sparse representations of complex dynamics directly from data, given a basis of library functions. In this work, a novel Bayesian treatment of dictionary learning system identification, as an alternative to SINDy, is envisaged. The proposed method -- Bayesian identification of nonlinear dynamics (BINDy) -- is distinct from previous approaches in that it targets the full joint posterior distribution over both the terms in the library and their parameterisation in the model. This formulation confers the advantage that an arbitrary prior may be placed over the model structure to produce models that are sparse in the model space rather than in parameter space. Because this posterior is defined over parameter vectors that can change in dimension, the inference cannot be performed by standard techniques. Instead, a Gibbs sampler based on reversible-jump Markov-chain Monte-Carlo is proposed. BINDy is shown to compare favourably to ensemble SINDy in three benchmark case-studies. In particular, it is seen that the proposed method is better able to assign high probability to correct model terms.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/15fe2e82d4161103b69fe83f184552b9e9774633" target='_blank'>
-              Physics-informed active learning with simultaneous weak-form latent space dynamics identification
+          <td><a href="https://www.semanticscholar.org/paper/04666a9e47b5508a0c0f966265fe51da2b2c634a" target='_blank'>
+              BINDy -- Bayesian identification of nonlinear dynamics with reversible-jump Markov-chain Monte-Carlo
               </a>
             </td>
           <td>
-            Xiaolong He, April Tran, David M. Bortz, Youngsoo Choi
+            M.D. Champneys, T. J. Rogers
           </td>
-          <td>2024-06-29</td>
+          <td>2024-08-15</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly in others, a clarification of the assumptions under which DMD is applicable is desirable. Upon closer inspection, existing interpretations of DMD methods based on the Koopman operator are not quite satisfactory: they justify DMD under assumptions that hold only with probability zero for generic observables. Here, we give a justification for DMD as a local, leading-order reduced model for the dominant system dynamics under conditions that hold with probability one for generic observables and non-degenerate observational data. We achieve this for autonomous and for periodically forced systems of finite or infinite dimensions by constructing linearizing transformations for their dominant dynamics within attracting slow spectral submanifolds (SSMs). Our arguments also lead to a new algorithm, data-driven linearization (DDL), which is a higher-order, systematic linearization of the observable dynamics within slow SSMs. We show by examples how DDL outperforms DMD and EDMD on numerical and experimental data.">
+        <tr id="The parametric greedy latent space dynamics identification (gLaSDI) framework has demonstrated promising potential for accurate and efficient modeling of high-dimensional nonlinear physical systems. However, it remains challenging to handle noisy data. To enhance robustness against noise, we incorporate the weak-form estimation of nonlinear dynamics (WENDy) into gLaSDI. In the proposed weak-form gLaSDI (WgLaSDI) framework, an autoencoder and WENDy are trained simultaneously to discover intrinsic nonlinear latent-space dynamics of high-dimensional data. Compared to the standard sparse identification of nonlinear dynamics (SINDy) employed in gLaSDI, WENDy enables variance reduction and robust latent space discovery, therefore leading to more accurate and efficient reduced-order modeling. Furthermore, the greedy physics-informed active learning in WgLaSDI enables adaptive sampling of optimal training data on the fly for enhanced modeling accuracy. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including viscous and inviscid Burgers' equations, time-dependent radial advection, and the Vlasov equation for plasma physics. With data that contains 5-10% Gaussian white noise, WgLaSDI outperforms gLaSDI by orders of magnitude, achieving 1-7% relative errors. Compared with the high-fidelity models, WgLaSDI achieves 121 to 1,779x speed-up.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ce624ece7e2f2933c1731bee6e5b03bf7a57c90b" target='_blank'>
-              Data-Driven Linearization of Dynamical Systems
+          <td><a href="https://www.semanticscholar.org/paper/15fe2e82d4161103b69fe83f184552b9e9774633" target='_blank'>
+              Physics-informed active learning with simultaneous weak-form latent space dynamics identification
               </a>
             </td>
           <td>
-            George Haller, B. Kasz'as
+            Xiaolong He, April Tran, David M. Bortz, Youngsoo Choi
           </td>
-          <td>2024-07-11</td>
+          <td>2024-06-29</td>
           <td>ArXiv</td>
-          <td>1</td>
           <td>0</td>
+          <td>3</td>
         </tr>
 
         <tr id="This paper presents a sequence of two approaches for the data-driven control-oriented modeling of networked systems, i.e., the systems that involve many interacting dynamical components. First, a novel deep learning approach named the weak Latent Dynamics Model (wLDM) is developed for learning generic nonlinear dynamics with control. Leveraging the weak form, the wLDM enables more numerically stable and computationally efficient training as well as more accurate prediction, when compared to conventional methods such as neural ordinary differential equations. Building upon the wLDM framework, we propose the weak Graph Koopman Bilinear Form (wGKBF) model, which integrates geometric deep learning and Koopman theory to learn latent space dynamics for networked systems, especially for the challenging cases having multiple timescales. The effectiveness of the wLDM framework and wGKBF model are demonstrated on three example systems of increasing complexity - a controlled double pendulum, the stiff Brusselator dynamics, and an electrified aircraft energy system. These numerical examples show that the wLDM and wGKBF achieve superior predictive accuracy and training efficiency as compared to baseline models. Parametric studies provide insights into the effects of hyperparameters in the weak form. The proposed framework shows the capability to efficiently capture control-dependent dynamics in these systems, including stiff dynamics and multi-physics interactions, offering a promising direction for learning control-oriented models of complex networked systems.">
@@ -1000,79 +985,124 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>11</td>
         </tr>
 
-        <tr id="We introduce a method for constructing reduced-order models directly from videos of dynamical systems. The method uses a non-intrusive tracking to isolate the motion of a user-selected part in the video of an autonomous dynamical system. In the space of delayed observations of this motion, we reconstruct a low-dimensional attracting spectral submanifold (SSM) whose internal dynamics serves as a mathematically justified reduced-order model for nearby motions of the full system. We obtain this model in a simple polynomial form that allows explicit identification of important physical system parameters, such as natural frequencies, linear and nonlinear damping and nonlinear stiffness. Beyond faithfully reproducing attracting steady states and limit cycles, our SSM-reduced models can also uncover hidden motion not seen in the video, such as unstable fixed points and unstable limit cycles forming basin boundaries. We demonstrate all these features on experimental videos of five physical systems: a double pendulum, an inverted flag in counter-flow, water sloshing in tank, a wing exhibiting aeroelastic flutter and a shimmying wheel.">
+        <tr id="It has been found recently that more data can, counter-intuitively, hurt the performance of deep neural networks. Here, we show that a more extreme version of the phenomenon occurs in data-driven models of dynamical systems. To elucidate the underlying mechanism, we focus on next-generation reservoir computing (NGRC) -- a popular framework for learning dynamics from data. We find that, despite learning a better representation of the flow map with more training data, NGRC can adopt an ill-conditioned ``integrator'' and lose stability. We link this data-induced instability to the auxiliary dimensions created by the delayed states in NGRC. Based on these findings, we propose simple strategies to mitigate the instability, either by increasing regularization strength in tandem with data size, or by carefully introducing noise during training. Our results highlight the importance of proper regularization in data-driven modeling of dynamical systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7c0d9c3d71f8076148909574fb1589ce6d2d09d4" target='_blank'>
-              Modeling Nonlinear Dynamics from Videos
+          <td><a href="https://www.semanticscholar.org/paper/b882f72ec6688e53edbf612e32d2b97c2a4c8236" target='_blank'>
+              How more data can hurt: Instability and regularization in next-generation reservoir computing
               </a>
             </td>
           <td>
-            Antony Yang, Joar Axaas, Fanni K'ad'ar, G'abor St'ep'an, George Haller
+            Yuanzhao Zhang, Sean P. Cornelius
           </td>
-          <td>2024-06-13</td>
+          <td>2024-07-11</td>
           <td>ArXiv</td>
+          <td>0</td>
           <td>1</td>
+        </tr>
+
+        <tr id="Stochastic collocation (SC) is a well‐known non‐intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full‐field uncertainty propagation that characterizes the distributions of the high‐dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter‐to‐solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. This work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data‐driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC‐over‐dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full‐field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/dc0b58e254bb512300814c52b4a101046377d6e4" target='_blank'>
+              Accurate data‐driven surrogates of dynamical systems for forward propagation of uncertainty
+              </a>
+            </td>
+          <td>
+            Saibal De, Reese E. Jones, H. Kolla
+          </td>
+          <td>2024-08-03</td>
+          <td>International Journal for Numerical Methods in Engineering</td>
           <td>0</td>
+          <td>30</td>
         </tr>
 
-        <tr id="It has been found recently that more data can, counter-intuitively, hurt the performance of deep neural networks. Here, we show that a more extreme version of the phenomenon occurs in data-driven models of dynamical systems. To elucidate the underlying mechanism, we focus on next-generation reservoir computing (NGRC) -- a popular framework for learning dynamics from data. We find that, despite learning a better representation of the flow map with more training data, NGRC can adopt an ill-conditioned ``integrator'' and lose stability. We link this data-induced instability to the auxiliary dimensions created by the delayed states in NGRC. Based on these findings, we propose simple strategies to mitigate the instability, either by increasing regularization strength in tandem with data size, or by carefully introducing noise during training. Our results highlight the importance of proper regularization in data-driven modeling of dynamical systems.">
+        <tr id="We propose a novel learning framework for Koopman operator of nonlinear dynamical systems that is informed by the governing equation and guarantees long-time stability and robustness to noise. In contrast to existing frameworks where either ad-hoc observables or blackbox neural networks are used to construct observables in the extended dynamic mode decomposition (EDMD), our observables are informed by governing equations via Polyflow. To improve the noise robustness and guarantee long-term stability, we designed a stable parameterization of the Koopman operator together with a progressive learning strategy for roll-out recurrent loss. To further improve model performance in the phase space, a simple iterative strategy of data augmentation was developed. Numerical experiments of prediction and control of classic nonlinear systems with ablation study showed the effectiveness of the proposed techniques over several state-of-the-art practices.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b882f72ec6688e53edbf612e32d2b97c2a4c8236" target='_blank'>
-              How more data can hurt: Instability and regularization in next-generation reservoir computing
+          <td><a href="https://www.semanticscholar.org/paper/33d038a0e7775662768898c432284e433922c891" target='_blank'>
+              Learning Noise-Robust Stable Koopman Operator for Control with Physics-Informed Observables
               </a>
             </td>
           <td>
-            Yuanzhao Zhang, Sean P. Cornelius
+            Shahriar Akbar Sakib, Shaowu Pan
           </td>
-          <td>2024-07-11</td>
+          <td>2024-08-13</td>
           <td>ArXiv</td>
           <td>0</td>
+          <td>0</td>
+        </tr>
+
+        <tr id="Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly in others, a clarification of the assumptions under which DMD is applicable is desirable. Upon closer inspection, existing interpretations of DMD methods based on the Koopman operator are not quite satisfactory: they justify DMD under assumptions that hold only with probability zero for generic observables. Here, we give a justification for DMD as a local, leading-order reduced model for the dominant system dynamics under conditions that hold with probability one for generic observables and non-degenerate observational data. We achieve this for autonomous and for periodically forced systems of finite or infinite dimensions by constructing linearizing transformations for their dominant dynamics within attracting slow spectral submanifolds (SSMs). Our arguments also lead to a new algorithm, data-driven linearization (DDL), which is a higher-order, systematic linearization of the observable dynamics within slow SSMs. We show by examples how DDL outperforms DMD and EDMD on numerical and experimental data.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/ce624ece7e2f2933c1731bee6e5b03bf7a57c90b" target='_blank'>
+              Data-Driven Linearization of Dynamical Systems
+              </a>
+            </td>
+          <td>
+            George Haller, B. Kasz'as
+          </td>
+          <td>2024-07-11</td>
+          <td>ArXiv</td>
+          <td>1</td>
           <td>1</td>
         </tr>
 
         <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/cabb9ef9934cc450e8873d693c8dd8dfc73087ab" target='_blank'>
-              MBD-NODE: physics-informed data-driven modeling and simulation of constrained multibody systems
+              MBD-NODE: Physics-informed data-driven modeling and simulation of constrained multibody systems
               </a>
             </td>
           <td>
             Jingquan Wang, Shu Wang, H. Unjhawala, Jinlong Wu, D. Negrut
           </td>
           <td>2024-07-11</td>
-          <td>Multibody System Dynamics</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>28</td>
+          <td>29</td>
+        </tr>
+
+        <tr id="Data-driven discovery of partial differential equations (PDEs) has emerged as a promising approach for deriving governing physics when domain knowledge about observed data is limited. Despite recent progress, the identification of governing equations and their parametric dependencies using conventional information criteria remains challenging in noisy situations, as the criteria tend to select overly complex PDEs. In this paper, we introduce an extension of the uncertainty-penalized Bayesian information criterion (UBIC), which is adapted to solve parametric PDE discovery problems efficiently without requiring computationally expensive PDE simulations. This extended UBIC uses quantified PDE uncertainty over different temporal or spatial points to prevent overfitting in model selection. The UBIC is computed with data transformation based on power spectral densities to discover the governing parametric PDE that truly captures qualitative features in frequency space with a few significant terms and their parametric dependencies (i.e., the varying PDE coefficients), evaluated with confidence intervals. Numerical experiments on canonical PDEs demonstrate that our extended UBIC can identify the true number of terms and their varying coefficients accurately, even in the presence of noise. The code is available at \url{https://github.com/Pongpisit-Thanasutives/parametric-discovery}.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/d605721a21ed5e6e69cc14a1ab3eb9a559099ea9" target='_blank'>
+              Adaptation of uncertainty-penalized Bayesian information criterion for parametric partial differential equation discovery
+              </a>
+            </td>
+          <td>
+            Pongpisit Thanasutives, Ken-ichi Fukui
+          </td>
+          <td>2024-08-15</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>3</td>
         </tr>
 
-        <tr id="In a landscape where scientific discovery is increasingly driven by data, the integration of machine learning (ML) with traditional scientific methodologies has emerged as a transformative approach. This paper introduces a novel, data-driven framework that synergizes physics-based priors with advanced ML techniques to address the computational and practical limitations inherent in first-principle-based methods and brute-force machine learning methods. Our framework showcases four algorithms, each embedding a specific physics-based prior tailored to a particular class of nonlinear systems, including separable and nonseparable Hamiltonian systems, hyperbolic partial differential equations, and incompressible fluid dynamics. The intrinsic incorporation of physical laws preserves the system's intrinsic symmetries and conservation laws, ensuring solutions are physically plausible and computationally efficient. The integration of these priors also enhances the expressive power of neural networks, enabling them to capture complex patterns typical in physical phenomena that conventional methods often miss. As a result, our models outperform existing data-driven techniques in terms of prediction accuracy, robustness, and predictive capability, particularly in recognizing features absent from the training set, despite relying on small datasets, short training periods, and small sample sizes.">
+        <tr id="The identification of self-similarity is an indispensable tool for understanding and modelling physical phenomena. Unfortunately, this is not always possible to perform formally in highly complex problems. We propose a methodology to extract the similarity variables of a self-similar physical process directly from data, without prior knowledge of the governing equations or boundary conditions, based on an optimization problem and symbolic regression. We analyze the accuracy and robustness of our method in four problems which have been influential in fluid mechanics research: a laminar boundary layer, Burger's equation, a turbulent wake, and a collapsing cavity. Our analysis considers datasets acquired via both numerical and wind-tunnel experiments.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6ba424643899decf4b48792c380cc0c66abe63c7" target='_blank'>
-              Data-Driven Computing Methods for Nonlinear Physics Systems with Geometric Constraints
+          <td><a href="https://www.semanticscholar.org/paper/b4e59a9e878c505fc222908a8279de60c32a29db" target='_blank'>
+              Extracting self-similarity from data
               </a>
             </td>
           <td>
-            Yunjin Tong
+            Nikos Bempedelis, Luca Magri, Konstantinos Steiros
           </td>
-          <td>2024-06-20</td>
+          <td>2024-07-15</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Machine learning techniques have recently been of great interest for solving differential equations. Training these models is classically a data-fitting task, but knowledge of the expression of the differential equation can be used to supplement the training objective, leading to the development of physics-informed scientific machine learning. In this article, we focus on one class of models called nonlinear vector autoregression (NVAR) to solve ordinary differential equations (ODEs). Motivated by connections to numerical integration and physics-informed neural networks, we explicitly derive the physics-informed NVAR (piNVAR) which enforces the right-hand side of the underlying differential equation regardless of NVAR construction. Because NVAR and piNVAR completely share their learned parameters, we propose an augmented procedure to jointly train the two models. Then, using both data-driven and ODE-driven metrics, we evaluate the ability of the piNVAR model to predict solutions to various ODE systems, such as the undamped spring, a Lotka-Volterra predator-prey nonlinear model, and the chaotic Lorenz system.">
+        <tr id="While linear systems are well-understood, no explicit solution exists for general nonlinear systems. Thus, it is desirable to make the understanding of linear system available in the nonlinear setting. This motivates the search for linearization techniques which are able to represent the nonlinear system by an equivalent, linear system. While much progress has been made extending various linearization techniques to larger domains and more delicate attractor geometries, the limitations of such techniques for truly nonlinear dynamics, such as dynamics with coexisting attractors, have been pointed out recently. In this work, we show that genuinely nonlinear dynamics can be globally linearized. To this end, we investigate systems with a continuous spectrum, a limit cycle, and coexisting solutions and explicitly construct linear systems mimicking these nonlinear behaviors as close as possible. We approximate the transformations between linear and nonlinear system with deep neural networks. The obtained linearizations are finite dimensional exceeding the phase space dimension of the underlying linear system by one at most.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/59096640a40ed6b70acbbfdaca5a505cd1330bb4" target='_blank'>
-              Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systems
+          <td><a href="https://www.semanticscholar.org/paper/2196ed95f5d349e07c7af94fd99240eec34dfdb2" target='_blank'>
+              Learning Global Linear Representations of Truly Nonlinear Dynamics
               </a>
             </td>
           <td>
-            James H. Adler, Samuel Hocking, Xiaozhe Hu, Shafiqul Islam
+            Thomas Breunung, F. Kogelbauer
           </td>
-          <td>2024-07-25</td>
+          <td>2024-08-06</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>6</td>
         </tr>
 
         <tr id="The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that combine physical laws of different disciplines. In this paper, we present a new approach that allows identifying an ordinary differential equation by means of a physics-informed machine learning algorithm. Our method introduces a special neural network that allows exploiting prior human knowledge to a certain degree and extends it autonomously, so that the resulting differential equations describe the system as accurately as possible. We validate the method on a Duffing oscillator with simulation data and, additionally, on a cascaded tank example with real-world data. Subsequently, we use the developed algorithm in a model-based reinforcement learning framework by alternately identifying and controlling a system to a target state. We test the performance by swinging-up an inverted pendulum on a cart.">
@@ -1090,6 +1120,21 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2</td>
         </tr>
 
+        <tr id="Machine learning techniques have recently been of great interest for solving differential equations. Training these models is classically a data-fitting task, but knowledge of the expression of the differential equation can be used to supplement the training objective, leading to the development of physics-informed scientific machine learning. In this article, we focus on one class of models called nonlinear vector autoregression (NVAR) to solve ordinary differential equations (ODEs). Motivated by connections to numerical integration and physics-informed neural networks, we explicitly derive the physics-informed NVAR (piNVAR) which enforces the right-hand side of the underlying differential equation regardless of NVAR construction. Because NVAR and piNVAR completely share their learned parameters, we propose an augmented procedure to jointly train the two models. Then, using both data-driven and ODE-driven metrics, we evaluate the ability of the piNVAR model to predict solutions to various ODE systems, such as the undamped spring, a Lotka-Volterra predator-prey nonlinear model, and the chaotic Lorenz system.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/59096640a40ed6b70acbbfdaca5a505cd1330bb4" target='_blank'>
+              Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systems
+              </a>
+            </td>
+          <td>
+            James H. Adler, Samuel Hocking, Xiaozhe Hu, Shafiqul Islam
+          </td>
+          <td>2024-07-25</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>2</td>
+        </tr>
+
         <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/0d487b041502645ead57bcc0782fa0256ccec2fc" target='_blank'>
@@ -1105,34 +1150,49 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>0</td>
         </tr>
 
-        <tr id="This paper presents an identification method for the transient dynamics of microgrids that exploits the intrinsic geometric structure of the dynamics, i.e., the high-dimensional states reside on a relatively low-dimensional manifold. In terms of discrete-time dynamics, the increment in states is decomposed into the tangent and normal components using the local geometric information, inferred from the data set of dynamical responses. The sparse identification of nonlinear dynamical systems (SINDy) method and generalized moving least square (GMLS) algorithms are used to estimate the tangent and normal components of increments, respectively, at every time step to constrain the solution onto the manifold of dynamics; this reduces the sensitivity of the SINDy model to candidate function selection and improve the prediction performance. A ten-bus microgrid system with five loads is used to test and verify the effectiveness of the presented method in identifying the system’s nonlinear dynamics. Numerical tests show that the developed method can give a better estimation for the dynamic transients caused by load variation, when compared to the traditional SINDy model. The results imply that the proposed method is a useful tool to model the transient dynamics in power systems, especially when the state space lies on a low-dimensional manifold.">
+        <tr id="Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications or multi-query workflows. Hence, model reduction is needed. However, the mathematical operators of these models are often not available since, as is common in industry practice, the models are constructed using commercial simulation software. In this work, we propose an operator inference-based approach aimed at inferring, from data generated by the simulation model, reduced-order models (ROMs) of structural dynamics systems with stiffness terms represented by polynomials of arbitrary degree. To ensure physically meaningful models, we impose constraints on the inference such that the model is guaranteed to exhibit stability properties. Convexity of the optimization problem associated with the inference is maintained by applying a sum-of-squares relaxation to the polynomial term. To further reduce the size of the ROM and improve numerical conditioning of the inference, we also propose a novel clustering-based sparsification of the polynomial term. We validate the proposed method on several numerical examples, including a representative 3D Finite Element Model (FEM) of a steel piston rod.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/296994d8631fcb9aaf6f02f26a1fe8d5ec69ee66" target='_blank'>
-              Tangent and Normal Space-Based Method for Dynamics Identification in Microgrids
+          <td><a href="https://www.semanticscholar.org/paper/12474e97123f0f45095cbb219da196a32731873d" target='_blank'>
+              Stable Sparse Operator Inference for Nonlinear Structural Dynamics
               </a>
             </td>
           <td>
-            Hanyang He, John Harlim, Daning Huang, Yan Li
+            P. D. Boef, Diana Manvelyan, Jos Maubach, W. Schilders, N. Wouw
           </td>
-          <td>2024-06-19</td>
-          <td>2024 IEEE Transportation Electrification Conference and Expo (ITEC)</td>
+          <td>2024-07-31</td>
+          <td>ArXiv</td>
           <td>0</td>
+          <td>47</td>
+        </tr>
+
+        <tr id="Physics-Informed Neural Networks (PINNs) have revolutionized solving differential equations by integrating physical laws into neural network training. This paper explores PINNs for open-loop optimal control problems (OCPs) with incomplete information, such as unknown initial conditions and sparse boundary data. We derive optimality conditions from the Lagrangian multipliers and use a neural network to predict the state, adjoint, and control variables. In contrast with previous methods, our approach integrates these elements into a single neural network and addresses scenarios with consistently limited data. Specifically, we address the study of partially unknown equations identifying underlying parameters online by searching for the optimal solution. Numerical examples show the effectiveness of the proposed method even in scenarios characterized by a considerable lack of information.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/1de965a4fc10f47113e0b8b25e5ae6627f2c9cbb" target='_blank'>
+              A PINN approach for the online identification and control of unknown PDEs
+              </a>
+            </td>
+          <td>
+            Alessandro Alla, Giulia Bertaglia, Elisa Calzola
+          </td>
+          <td>2024-08-06</td>
+          <td>ArXiv</td>
           <td>0</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications or multi-query workflows. Hence, model reduction is needed. However, the mathematical operators of these models are often not available since, as is common in industry practice, the models are constructed using commercial simulation software. In this work, we propose an operator inference-based approach aimed at inferring, from data generated by the simulation model, reduced-order models (ROMs) of structural dynamics systems with stiffness terms represented by polynomials of arbitrary degree. To ensure physically meaningful models, we impose constraints on the inference such that the model is guaranteed to exhibit stability properties. Convexity of the optimization problem associated with the inference is maintained by applying a sum-of-squares relaxation to the polynomial term. To further reduce the size of the ROM and improve numerical conditioning of the inference, we also propose a novel clustering-based sparsification of the polynomial term. We validate the proposed method on several numerical examples, including a representative 3D Finite Element Model (FEM) of a steel piston rod.">
+        <tr id="We present a pragmatic approach to the sparse identification of nonlinear dynamics for systems with discrete delays. It relies on approximating the underlying delay model with a system of ordinary differential equations via pseudospectral collocation. To minimize the reconstruction error, the new strategy avoids optimizing all possible multiple unknown delays, identifying only the maximum one. The computational burden is thus greatly reduced, improving the performance of recent implementations that work directly on the delay system.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/12474e97123f0f45095cbb219da196a32731873d" target='_blank'>
-              Stable Sparse Operator Inference for Nonlinear Structural Dynamics
+          <td><a href="https://www.semanticscholar.org/paper/af6a7301b4680a556da5635cdd6aedbb64f047b0" target='_blank'>
+              Sparse identification of time delay systems via pseudospectral collocation
               </a>
             </td>
           <td>
-            P. D. Boef, Diana Manvelyan, Jos Maubach, W. Schilders, N. Wouw
+            Enrico Bozzo, Dimitri Breda, Muhammad Tanveer
           </td>
-          <td>2024-07-31</td>
+          <td>2024-08-04</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>47</td>
+          <td>0</td>
         </tr>
 
         <tr id="In order to accurately model the dynamics of non-linear electro-mechanical systems, it is imperative to consider the contributions of coupling terms and dissipation. The Lagrangian formulation alone is insufficient to fully capture the holistic behavior of the system. Coupling and dissipation mechanisms play a pivotal role in shaping the system's response. Consequently, to effectively capture the dynamics of inter-coupled electro-mechanical systems with dissipation, we propose an extended Lagrangian-informed deep neural network framework in this paper. Our approach leverages the underlying physics-based knowledge of the system, incorporating it into the neural network architecture. By employing the Euler-Lagrange equations as constraints in the training process, we ensure that the learned dynamics conform to the true behavior of the system. To validate the theoretical framework, we conduct simulation experiments on a DC motor with a cart system, which serves as a representative model of dissipative nonlinear electro-mechanical systems. The experimental results demonstrate the efficacy of our approach in accurately capturing and integrating the dynamics to solve the reference tracking model predictive control design.">
@@ -1142,7 +1202,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
               </a>
             </td>
           <td>
-            Nikhil Pagar, Pegah Ghaf-Ghanbari, Atul G. Kelkar, Javad Mohammadpour
+            Nikhil Pagar, Pegah Ghaf-Ghanbari, Atul Kelkar, Javad Mohammadpour
           </td>
           <td>2024-06-25</td>
           <td>2024 European Control Conference (ECC)</td>
@@ -1150,41 +1210,55 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>4</td>
         </tr>
 
-        <tr id="
- We present a tensor-based method for model selection which identifies the unknown partial differential equation that governs a dynamical system using only spatiotemporal measurements. The method circumvents a disadvantage of standard matrix-based methods which typically have large storage consumption. Using a recently developed multidimensional approximation of nonlinear dynamical systems, we collect the nonlinear and partial derivative terms of the measured data and construct a low-rank dictionary tensor in the tensor-train format. A tensor-based linear regression problem is then built, which balances the learning accuracy, model complexity, and computational efficiency. An algebraic expression of the unknown equations can be extracted. Numerical results are demonstrated on datasets generated by the wave equation, the Burgers' equation, and a few parametric partial differential equations.">
+        <tr id="Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven system identification framework that derives models in the port-Hamiltonian (pH) formulation. This formulation is suitable for multi-physical systems while guaranteeing the useful system theoretical properties of passivity and stability. Our framework combines linear and nonlinear reduction with structured, physics-motivated system identification. In this process, high-dimensional state data obtained from possibly nonlinear systems serves as input for an autoencoder, which then performs two tasks: (i) nonlinearly transforming and (ii) reducing this data onto a low-dimensional latent space. In this space, a linear pH system, that satisfies the pH properties per construction, is parameterized by the weights of a neural network. The mathematical requirements are met by defining the pH matrices through Cholesky factorizations. The neural networks that define the coordinate transformation and the pH system are identified in a joint optimization process to match the dynamics observed in the data while defining a linear pH system in the latent space. The learned, low-dimensional pH system can describe even nonlinear systems and is rapidly computable due to its small size. The method is exemplified by a parametric mass-spring-damper and a nonlinear pendulum example, as well as the high-dimensional model of a disc brake with linear thermoelastic behavior.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c7f12b781a01ed3dd9a5f51e745426539b84443b" target='_blank'>
-              Tensor-Based Data-Driven Identification of Partial Differential Equations
+          <td><a href="https://www.semanticscholar.org/paper/8c88f9ec4b5bd522ac8e312f90d2801489785951" target='_blank'>
+              Data-driven identification of latent port-Hamiltonian systems
               </a>
             </td>
           <td>
-            Wanting Lin, Xiaofan Lu, Linan Zhang
+            J. Rettberg, Jonas Kneifl, Julius Herb, Patrick Buchfink, J. Fehr, B. Haasdonk
           </td>
-          <td>2024-06-10</td>
-          <td>Journal of Computational and Nonlinear Dynamics</td>
+          <td>2024-08-15</td>
+          <td>ArXiv</td>
           <td>0</td>
+          <td>32</td>
+        </tr>
+
+        <tr id="Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and the earth system, for which direct numerical simulation that resolves all scales is often too expensive. For those systems without a clear scale separation, deterministic and local closure models often lack enough generalization capability, which limits their performance in many real-world applications. In this work, we propose a data-driven modeling framework for constructing stochastic and non-local closure models via conditional diffusion model and neural operator. Specifically, the Fourier neural operator is incorporated into a score-based diffusion model, which serves as a data-driven stochastic closure model for complex dynamical systems governed by partial differential equations (PDEs). We also demonstrate how accelerated sampling methods can improve the efficiency of the data-driven stochastic closure model. The results show that the proposed methodology provides a systematic approach via generative machine learning techniques to construct data-driven stochastic closure models for multiscale dynamical systems with continuous spatiotemporal fields.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/5b117384f237e71d202a61374a42d92e97b0c697" target='_blank'>
+              Data-Driven Stochastic Closure Modeling via Conditional Diffusion Model and Neural Operator
+              </a>
+            </td>
+          <td>
+            Xinghao Dong, Chuanqi Chen, Jin-Long Wu
+          </td>
+          <td>2024-08-06</td>
+          <td>ArXiv</td>
           <td>1</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Modeling the dynamics of flexible objects has become an emerging topic in the community as these objects become more present in many applications, e.g., soft robotics. Due to the properties of flexible materials, the movements of soft objects are often highly nonlinear and, thus, complex to predict. Data-driven approaches seem promising for modeling those complex dynamics but often neglect basic physical principles, which consequently makes them untrustworthy and limits generalization. To address this problem, we propose a physics-constrained learning method that combines powerful learning tools and reliable physical models. Our method leverages the data collected from observations by sending them into a Gaussian process that is physically constrained by a distributed Port-Hamiltonian model. Based on the Bayesian nature of the Gaussian process, we not only learn the dynamics of the system, but also enable uncertainty quantification. Furthermore, the proposed approach preserves the compositional nature of Port-Hamiltonian systems.">
+        <tr id="Forecasting dynamical systems is of importance to numerous real-world applications. When possible, dynamical systems forecasts are constructed based on first-principles-based models such as through the use of differential equations. When these equations are unknown, non-intrusive techniques must be utilized to build predictive models from data alone. Machine learning (ML) methods have recently been used for such tasks. Moreover, ML methods provide the added advantage of significant reductions in time-to-solution for predictions in contrast with first-principle based models. However, many state-of-the-art ML-based methods for forecasting rely on neural networks, which may be expensive to train and necessitate requirements for large amounts of memory. In this work, we propose a quantum mechanics inspired ML modeling strategy for learning nonlinear dynamical systems that provides data-driven forecasts for complex dynamical systems with reduced training time and memory costs. This approach, denoted the quantum reservoir computing technique (QRC), is a hybrid quantum-classical framework employing an ensemble of interconnected small quantum systems via classical linear feedback connections. By mapping the dynamical state to a suitable quantum representation amenable to unitary operations, QRC is able to predict complex nonlinear dynamical systems in a stable and accurate manner. We demonstrate the efficacy of this framework through benchmark forecasts of the NOAA Optimal Interpolation Sea Surface Temperature dataset and compare the performance of QRC to other ML methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/020e63b8b17cdec54c056d8a1edc98770c8fa7ab" target='_blank'>
-              Physics-constrained learning for PDE systems with uncertainty quantified port-Hamiltonian models
+          <td><a href="https://www.semanticscholar.org/paper/ff3c3b75e08bf25e53956e10e92ec03e5cda30f6" target='_blank'>
+              Higher order quantum reservoir computing for non-intrusive reduced-order models
               </a>
             </td>
           <td>
-            Kaiyuan Tan, Peilun Li, Thomas Beckers
+            Vinamr Jain, R. Maulik
           </td>
-          <td>2024-06-17</td>
-          <td>DBLP, ArXiv</td>
+          <td>2024-07-31</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>21</td>
         </tr>
 
         <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/8d69703a20ce4710f71900130dd935761bbf01fa" target='_blank'>
-              Promising directions of machine learning for partial differential equations.
+              Promising directions of machine learning for partial differential equations
               </a>
             </td>
           <td>
@@ -1193,7 +1267,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2024-06-28</td>
           <td>Nature computational science</td>
           <td>3</td>
-          <td>1</td>
+          <td>2</td>
         </tr>
 
         <tr id="Neural simulators for modeling complex dynamical systems have been extensively studied for various real-world applications, such as weather forecasting, ocean current prediction, and computational fluid dynamics simulation. Although they have demonstrated powerful fitting and predicting, most existing models are only built to learn single-system dynamics. Several advanced researches have considered learning dynamics across environments, which can exploit the potential commonalities among the dynamics across environments and adapt to new environments. However, these methods still are prone to scarcity problems where per-environment data is sparse or limited. Therefore, we propose a novel CoNDP (Context-Informed Neural ODE Processes) to achieve learning system dynamics from sparse observations across environments. It can fully use contextual information of each environment to better capture the intrinsic commonalities across environments and distinguishable differences among environments while modeling uncertainty of system evolution, producing more accurate predictions. Intensive experiments are conducted on five complex dynamical systems in various fields. Results show that the proposed CoNDP can achieve optimal results compared with common neural simulators and state-of-the-art cross-environmental models.">
@@ -1211,49 +1285,64 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>5</td>
         </tr>
 
-        <tr id="None">
+        <tr id="Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically employ closure models, which attempt to represent small-scale features in an unresolved manner. However, these methods often sacrifice accuracy and lose high-frequency/wavenumber information, especially in scenarios involving complex flow physics. In this paper, we introduce an innovative neural differentiable modeling framework designed to enhance the predictability and efficiency of spatiotemporal turbulence simulations. Our approach features differentiable hybrid modeling techniques that seamlessly integrate deep neural networks with numerical PDE solvers within a differentiable programming framework, synergizing deep learning with physics-based CFD modeling. Specifically, a hybrid differentiable neural solver is constructed on a coarser grid to capture large-scale turbulent phenomena, followed by the application of a Bayesian conditional diffusion model that generates small-scale turbulence conditioned on large-scale flow predictions. Two innovative hybrid architecture designs are studied, and their performance is evaluated through comparative analysis against conventional large eddy simulation techniques with physics-based subgrid-scale closures and purely data-driven neural solvers. The findings underscore the potential of the neural differentiable modeling framework to significantly enhance the accuracy and computational efficiency of turbulence simulations. This study not only demonstrates the efficacy of merging deep learning with physics-based numerical solvers but also sets a new precedent for advanced CFD modeling techniques, highlighting the transformative impact of differentiable programming in scientific computing.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1491d337e12daab70edf38ee62d8f8ee586b8e98" target='_blank'>
-              Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems
+          <td><a href="https://www.semanticscholar.org/paper/28636be802bd2c5ddbd07e3772c8b3a7822e64fa" target='_blank'>
+              Neural Differentiable Modeling with Diffusion-Based Super-resolution for Two-Dimensional Spatiotemporal Turbulence
               </a>
             </td>
           <td>
-            Katiana Kontolati, S. Goswami, G. Em Karniadakis, Michael D Shields
+            Xiantao Fan, Deepak Akhare, Jian-Xun Wang
           </td>
-          <td>2024-06-14</td>
-          <td>Nature Communications</td>
-          <td>5</td>
-          <td>19</td>
+          <td>2024-06-28</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>2</td>
         </tr>
 
-        <tr id="When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the long-time dynamics they produce are often unphysical or unstable. We analyze the origin of such instabilities when learning linear dynamical systems, focusing on the training dynamics. We make several analytical findings which empirical observations suggest extend to nonlinear dynamical systems. First, the rate of convergence of the training dynamics is uneven and depends on the distribution of energy in the data. As a special case, the dynamics in directions where the data have no energy cannot be learned. Second, in the unlearnable directions, the dynamics produced by the neural network depend on the weight initialization, and common weight initialization schemes can produce unstable dynamics. Third, injecting synthetic noise into the data during training adds damping to the training dynamics and can stabilize the learned simulator, though doing so undesirably biases the learned dynamics. For each contributor to instability, we suggest mitigative strategies. We also highlight important differences between learning discrete-time and continuous-time dynamics, and discuss extensions to nonlinear systems.">
+        <tr id="Understanding how the collective activity of neural populations relates to computation and ultimately behavior is a key goal in neuroscience. To this end, statistical methods which describe high-dimensional neural time series in terms of low-dimensional latent dynamics have played a fundamental role in characterizing neural systems. Yet, what constitutes a successful method involves two opposing criteria: (1) methods should be expressive enough to capture complex nonlinear dynamics, and (2) they should maintain a notion of interpretability often only warranted by simpler linear models. In this paper, we develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS). Our method builds on previous work modeling the latent state evolution via a stochastic differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs). We propose a novel kernel function which enforces smoothly interpolated locally linear dynamics, and therefore expresses flexible -- yet interpretable -- dynamics akin to those of recurrent switching linear dynamical systems (rSLDS). Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics. To fit our models, we leverage a modified learning objective which improves the estimation accuracy of kernel hyperparameters compared to previous GP-SDE fitting approaches. We apply our method to synthetic data and data recorded in two neuroscience experiments and demonstrate favorable performance in comparison to the rSLDS.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2a7fe97785b117217a2f1064f6983b137fe02e06" target='_blank'>
-              On instabilities in neural network-based physics simulators
+          <td><a href="https://www.semanticscholar.org/paper/b38dffa6030cac42cce7564c8fe38875646c5f4f" target='_blank'>
+              Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems
               </a>
             </td>
           <td>
-            Daniel Floryan
+            Amber Hu, D. Zoltowski, Aditya Nair, David Anderson, Lea Duncker, Scott W. Linderman
           </td>
-          <td>2024-06-18</td>
+          <td>2024-07-19</td>
           <td>ArXiv</td>
-          <td>1</td>
           <td>0</td>
+          <td>27</td>
         </tr>
 
-        <tr id="The identification of a nonlinear system model given only measurement data is a frequently encountered task. Uncovering the structure of differential equations as system model alongside with the determination of the optimal parameters is still problem under investigation. Assuming a differentially flat system under investigation, an algorithm for single input single output systems is proposed that faces this identification task. To find a proper state space model, an iterative strategy is presented expanding an initial solution in every step. Harnessing only the measurement data and not their time derivatives a criterion is proposed to select promising extensions to the model avoiding extensive simulation studies on possible model structures. Applying a subset selection reduces the complexity of the resulting models and avoids overfitting. To show the capability of the presented approach to identify a nonlinear state space model from data, a simulation example is presented.">
+        <tr id="Accurately predicting the long-term behavior of chaotic systems is crucial for various applications such as climate modeling. However, achieving such predictions typically requires iterative computations over a dense spatiotemporal grid to account for the unstable nature of chaotic systems, which is expensive and impractical in many real-world situations. An alternative approach to such a full-resolved simulation is using a coarse grid and then correcting its errors through a \textit{closure model}, which approximates the overall information from fine scales not captured in the coarse-grid simulation. Recently, ML approaches have been used for closure modeling, but they typically require a large number of training samples from expensive fully-resolved simulations (FRS). In this work, we prove an even more fundamental limitation, i.e., the standard approach to learning closure models suffers from a large approximation error for generic problems, no matter how large the model is, and it stems from the non-uniqueness of the mapping. We propose an alternative end-to-end learning approach using a physics-informed neural operator (PINO) that overcomes this limitation by not using a closure model or a coarse-grid solver. We first train the PINO model on data from a coarse-grid solver and then fine-tune it with (a small amount of) FRS and physics-based losses on a fine grid. The discretization-free nature of neural operators means that they do not suffer from the restriction of a coarse grid that closure models face, and they can provably approximate the long-term statistics of chaotic systems. In our experiments, our PINO model achieves a 120x speedup compared to FRS with a relative error $\sim 5\%$. In contrast, the closure model coupled with a coarse-grid solver is $58$x slower than PINO while having a much higher error $\sim205\%$ when the closure model is trained on the same FRS dataset.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2ff4fcc76f9849634c1a641bd0787cff2f7c9419" target='_blank'>
-              Flatness-Based Identification of Nonlinear Dynamics
+          <td><a href="https://www.semanticscholar.org/paper/ba56bfb99a735364b70e9f185e5b2a87b7ff7d3f" target='_blank'>
+              Beyond Closure Models: Learning Chaotic-Systems via Physics-Informed Neural Operators
               </a>
             </td>
           <td>
-            Alexander M. Kopp, Lisa Fuchs, Christoph Ament
+            Chuwei Wang, Julius Berner, Zong-Yi Li, Di Zhou, Jiayun Wang, Jane Bae, A. Anandkumar
           </td>
-          <td>2024-06-11</td>
-          <td>2024 32nd Mediterranean Conference on Control and Automation (MED)</td>
+          <td>2024-08-09</td>
+          <td>ArXiv</td>
           <td>0</td>
+          <td>18</td>
+        </tr>
+
+        <tr id="In this paper, we propose a physics-informed learning-based Koopman modeling approach and present a Koopman-based self-tuning moving horizon estimation design for a class of nonlinear systems. Specifically, we train Koopman operators and two neural networks - the state lifting network and the noise characterization network - using both data and available physical information. The two neural networks account for the nonlinear lifting functions for Koopman modeling and describing system noise distributions, respectively. Accordingly, a stochastic linear Koopman model is established in the lifted space to forecast the dynamic behavior of the nonlinear system. Based on the Koopman model, a self-tuning linear moving horizon estimation (MHE) scheme is developed. The weighting matrices of the MHE design are updated using the pre-trained noise characterization network at each sampling instant. The proposed estimation scheme is computationally efficient because only convex optimization is involved during online implementation, and updating the weighting matrices of the MHE scheme does not require re-training the neural networks. We verify the effectiveness and evaluate the performance of the proposed method via the application to a simulated chemical process.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/7f4e3675450b08e1344396a30181355d5565efe8" target='_blank'>
+              Self-tuning moving horizon estimation of nonlinear systems via physics-informed machine learning Koopman modeling
+              </a>
+            </td>
+          <td>
+            Mingxue Yan, Minghao Han, A. Law, Xunyuan Yin
+          </td>
+          <td>2024-08-07</td>
+          <td>ArXiv</td>
           <td>0</td>
+          <td>35</td>
         </tr>
 
         <tr id="Reconstructing a nonlinear dynamical system from empirical time series is a fundamental task in data-driven analysis. One of the main challenges is the existence of hidden variables; we only have records for some variables, and those for hidden variables are unavailable. In this work, the techniques for Carleman linearization, phase-space embedding, and dynamic mode decomposition are integrated to rebuild an optimal dynamical system from time series for one specific variable. Using the Takens theorem, the embedding dimension is determined, which is adopted as the dynamical system's dimension. The Carleman linearization is then used to transform this finite nonlinear system into an infinite linear system, which is further truncated into a finite linear system using the dynamic mode decomposition technique. We illustrate the performance of this integrated technique using data generated by the well-known Lorenz model, the Duffing oscillator, and empirical records of electrocardiogram, electroencephalogram, and measles outbreaks. The results show that this solution accurately estimates the operators of the nonlinear dynamical systems. This work provides a new data-driven method to estimate the Carleman operator of nonlinear dynamical systems.">
@@ -1268,7 +1357,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2024-08-01</td>
           <td>Chaos</td>
           <td>0</td>
-          <td>17</td>
+          <td>18</td>
         </tr>
 
         <tr id="Neural manifolds are an attractive theoretical framework for characterizing the complex behaviors of neural populations. However, many of the tools for identifying these low-dimensional subspaces are correlational and provide limited insight into the underlying dynamics. The ability to precisely control this latent activity would allow researchers to investigate the structure and function of neural manifolds. Employing techniques from the field of optimal control, we simulate controlling the latent dynamics of a neural population using closed-loop, dynamically generated sensory inputs. Using a spiking neural network (SNN) as a model of a neural circuit, we find low-dimensional representations of both the network activity (the neural manifold) and a set of salient visual stimuli. With a data-driven latent dynamics model, we apply model predictive control (MPC) to provide anticipatory, optimal control over the trajectory of the circuit in a latent space. We are able to control the latent dynamics of the SNN to follow several reference trajectories despite observing only a subset of neurons and with a substantial amount of unknown noise injected into the network. These results provide a framework to experimentally test for causal relationships between manifold dynamics and other variables of interest such as organismal behavior and BCI performance.">
@@ -1282,83 +1371,113 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           </td>
           <td>2024-06-21</td>
           <td>ArXiv</td>
-          <td>0</td>
+          <td>1</td>
           <td>6</td>
         </tr>
 
-        <tr id="System identification, as a rich and vital discipline, provides a practical and general methodology and tool for quantitatively modelling the input-output relationships of dynamical systems. Sparse nonlinear system identification (SNSI), especially parametric sparse nonlinear system identification (PSNSI), is an important and vital field of research with a wide range of applications. This work is concerned with PSNSI and particular attention is paid to the assessment of three well-known mainstream sparse learning methods, namely, orthogonal least squares (OLS), orthogonal matching pursuit (OMP) and least absolute shrinkage and selection operator (LASSO). The performances of these methods are tested and evaluated through three case studies relating to PSNSI problems. The research results and findings of this work provide practical useful information and guidance for researchers to better choose or adapt methods when solving PSNSI problems.">
+        <tr id="A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schr\"{o}dinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution of necklace patterns with integer, half-integer, and fractional reduced orbital angular momenta by means of PINN. The patterns exhibit phenomena similar to rotation of rigid bodies and centrifugal force. Even though the necklaces slowly expand (or shrink), they preserve their structure in the course of the quasi-stable propagation over several diffraction lengths, which is completely different from the ordinary fast diffraction-dominated dynamics. By comparing different ingredients, including the training time, loss value and $\mathbb{L}_{2}$ error, PINN accurately predicts specific nonlinear dynamical properties of the evolving necklace patterns. Furthermore, we perform the data-driven discovery of parameters for both clean and perturbed training data, adding $1\%$ random noise in the latter case. The results reveal that PINN not only effectively emulates the solution of partial differential equations, but also offers applications for predicting the nonlinear dynamics of physically relevant types of patterns.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5faed1c3a0e751abb45b7883e4c109282e696556" target='_blank'>
-              On Sparse Nonlinear System Identification Using Orthogonal Matching Pursuit, Orthogonal Least Squares and LASSO
+          <td><a href="https://www.semanticscholar.org/paper/27df54bec46e632334278c89b601027aa8a3cf9e" target='_blank'>
+              Physics-informed neural network for nonlinear dynamics of self-trapped necklace beams
               </a>
             </td>
           <td>
-            Hua‐Liang Wei
+            Dongshuai Liu, Wen Zhang, Yanxia Gao, Dianyuan Fan, B. Malomed, Lifu Zhang
           </td>
-          <td>2024-06-11</td>
-          <td>2024 32nd Mediterranean Conference on Control and Automation (MED)</td>
+          <td>2024-08-10</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>15</td>
+          <td>79</td>
         </tr>
 
-        <tr id="We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the stochastic system are unavailable. However, short bursts of input/output (I/O) data consisting of certain known excitation signals and their corresponding system responses are available. When a sufficient amount of such I/O data are available, our method is capable of learning the unknown dynamics and producing an accurate predictive model for the stochastic responses of the system subject to arbitrary excitation signals not in the training data. Our method has two key components: (1) a local approximation of the training I/O data to transfer the learning into a parameterized form; and (2) a generative model to approximate the underlying unknown stochastic flow map in distribution. After presenting the method in detail, we present a comprehensive set of numerical examples to demonstrate the performance of the proposed method, especially for long-term system predictions.">
+        <tr id="Lifted linear predictor (LLP) is an artificial linear dynamical system designed to predict trajectories of a generally nonlinear dynamical system based on the current state (or measurements) and the input. The main benefit of the LLP is its potential ability to capture the nonlinear system's dynamics with precision superior to other linearization techniques, such as local linearization about the operation point. The idea of lifting is supported by the theory of Koopman Operators. For LLP identification, we focus on the data-driven method based on the extended dynamic mode decomposition (EDMD) algorithm. However, while the EDMD algorithm presents an extremely simple and efficient way to obtain the LLP, it can also yield poor results. In this paper, we present some less intuitive practical guidelines for data-driven identification of the LLPs, aiming at improving usability of LLPs for designing control. We support the guidelines with two motivating examples. The implementation of the examples are shared on a public repository.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4edbecee7f2d1381939691be911b0026cab616bb" target='_blank'>
-              Modeling Unknown Stochastic Dynamical System Subject to External Excitation
+          <td><a href="https://www.semanticscholar.org/paper/bf1ce9a8c8346f1264e7cecb5aea44d98aa65af7" target='_blank'>
+              Practical Guidelines for Data-driven Identification of Lifted Linear Predictors for Control
               </a>
             </td>
           <td>
-            Yuan Chen, Dongbin Xiu
+            Loi Do, Adam Uchytil, Zdenvek Hur'ak
           </td>
-          <td>2024-06-22</td>
+          <td>2024-08-02</td>
           <td>ArXiv</td>
-          <td>0</td>
           <td>1</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach to solve physics-based initial value problems using unsupervised machine learning. We propose a deep learning framework that models the dynamics of a variety of mechanical systems through neural networks. Our framework is flexible, allowing us to solve non-linear, coupled, and chaotic dynamical systems. We demonstrate the effectiveness of our approach on systems including a free particle, a particle in a gravitational field, a classical pendulum, and the H\'enon--Heiles system (a pair of coupled harmonic oscillators with a non-linear perturbation, used in celestial mechanics). Our results show that deep neural networks can successfully approximate solutions to these problems, producing trajectories which conserve physical properties such as energy and those with stationary action. We note that probabilistic activation functions, as defined in this paper, are required to learn any solutions of initial value problems in their strictest sense, and we introduce coupled neural networks to learn solutions of coupled systems.">
+        <tr id="Modeling the non-linear dynamics of a system from measurement data accurately is an open challenge. Over the past few years, various tools such as SINDy and DySMHO have emerged as approaches to distill dynamics from data. However, challenges persist in accurately capturing dynamics of a system especially when the physical knowledge about the system is unknown. A promising solution is to use a hybrid paradigm, that combines mechanistic and black-box models to leverage their respective strengths. In this study, we combine a hybrid modeling paradigm with sparse regression, to develop and identify models simultaneously. Two methods are explored, considering varying complexities, data quality, and availability and by comparing different case studies. In the first approach, we integrate SINDy-discovered models with neural ODE structures, to model unknown physics. In the second approach, we employ Multifidelity Surrogate Models (MFSMs) to construct composite models comprised of SINDy-discovered models and error-correction models.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/71b2f475e6dd93def3f335fbbfac10259c5dba45" target='_blank'>
-              Solving physics-based initial value problems with unsupervised machine learning
+          <td><a href="https://www.semanticscholar.org/paper/4848ba60b88cc3dffed5030c77e9174131c7f918" target='_blank'>
+              Integrating Hybrid Modeling and Multifidelity Approaches for Data-Driven Process Model Discovery
               </a>
             </td>
           <td>
-            Jack Griffiths, S. A. Wrathmall, Simon A. Gardiner
+            Suryateja Ravutla, Fani Boukouvala
           </td>
-          <td>2024-07-25</td>
-          <td>ArXiv</td>
+          <td>2024-07-09</td>
+          <td>Systems and Control Transactions</td>
           <td>0</td>
-          <td>6</td>
+          <td>25</td>
         </tr>
 
-        <tr id="Nonlinear and non-stationary processes are prevalent in various natural and physical phenomena, where system dynamics can change qualitatively due to bifurcation phenomena. Traditional machine learning methods have advanced our ability to learn and predict such systems from observed time series data. However, predicting the behavior of systems with temporal parameter variations without knowledge of true parameter values remains a significant challenge. This study leverages the reservoir computing framework to address this problem by unsupervised extraction of slowly varying system parameters from time series data. We propose a model architecture consisting of a slow reservoir with long timescale internal dynamics and a fast reservoir with short timescale dynamics. The slow reservoir extracts the temporal variation of system parameters, which are then used to predict unknown bifurcations in the fast dynamics. Through experiments using data generated from chaotic dynamical systems, we demonstrate the ability to predict bifurcations not present in the training data. Our approach shows potential for applications in fields such as neuroscience, material science, and weather prediction, where slow dynamics influencing qualitative changes are often unobservable.">
+        <tr id="Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying neural ODEs in practical applications often encounters the challenge of stiffness, a condition where rapid variations in some components of the solution demand prohibitively small time steps for explicit solvers. This work addresses the stiffness issue when employing neural ODEs for model order reduction by introducing a suitable reparametrization in time. The considered map is data-driven and it is induced by the adaptive time-stepping of an implicit solver on a reference solution. We show the map produces a nonstiff system that can be cheaply solved with an explicit time integration scheme. The original, stiff, time dynamic is recovered by means of a map learnt by a neural network that connects the state space to the time reparametrization. We validate our method through extensive experiments, demonstrating improvements in efficiency for the neural ODE inference while maintaining robustness and accuracy. The neural network model also showcases good generalization properties for times beyond the training data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1f7ba13092aa22ef11ae95641fe8961d09c8fcd7" target='_blank'>
-              Prediction of Unobserved Bifurcation by Unsupervised Extraction of Slowly Time-Varying System Parameter Dynamics from Time Series Using Reservoir Computing
+          <td><a href="https://www.semanticscholar.org/paper/fc642cd2dc03d50f310399a91145bd5a14a7f646" target='_blank'>
+              Neural Ordinary Differential Equations for Model Order Reduction of Stiff Systems
               </a>
             </td>
           <td>
-            Keita Tokuda, Yuichi Katori
+            Matteo Caldana, J. Hesthaven
           </td>
-          <td>2024-06-20</td>
+          <td>2024-08-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>10</td>
+          <td>63</td>
         </tr>
 
-        <tr id="We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design. We provide a rigorous convergence statement of the method. The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus. Moreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory. This is illustrated on the example of the discrete wave equation and Schr\"odinger equation. The article constitutes an extension of our previous article arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.">
+        <tr id="We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the stochastic system are unavailable. However, short bursts of input/output (I/O) data consisting of certain known excitation signals and their corresponding system responses are available. When a sufficient amount of such I/O data are available, our method is capable of learning the unknown dynamics and producing an accurate predictive model for the stochastic responses of the system subject to arbitrary excitation signals not in the training data. Our method has two key components: (1) a local approximation of the training I/O data to transfer the learning into a parameterized form; and (2) a generative model to approximate the underlying unknown stochastic flow map in distribution. After presenting the method in detail, we present a comprehensive set of numerical examples to demonstrate the performance of the proposed method, especially for long-term system predictions.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e38b7de6c7022b28628627bbf045123b665619b4" target='_blank'>
-              Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification
+          <td><a href="https://www.semanticscholar.org/paper/4edbecee7f2d1381939691be911b0026cab616bb" target='_blank'>
+              Modeling Unknown Stochastic Dynamical System Subject to External Excitation
               </a>
             </td>
           <td>
-            Christian Offen
+            Yuan Chen, Dongbin Xiu
           </td>
-          <td>2024-07-10</td>
+          <td>2024-06-22</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>1</td>
+        </tr>
+
+        <tr id="Initial value problems -- a system of ordinary differential equations and corresponding initial conditions -- can be used to describe many physical phenomena including those arise in classical mechanics. We have developed a novel approach to solve physics-based initial value problems using unsupervised machine learning. We propose a deep learning framework that models the dynamics of a variety of mechanical systems through neural networks. Our framework is flexible, allowing us to solve non-linear, coupled, and chaotic dynamical systems. We demonstrate the effectiveness of our approach on systems including a free particle, a particle in a gravitational field, a classical pendulum, and the H\'enon--Heiles system (a pair of coupled harmonic oscillators with a non-linear perturbation, used in celestial mechanics). Our results show that deep neural networks can successfully approximate solutions to these problems, producing trajectories which conserve physical properties such as energy and those with stationary action. We note that probabilistic activation functions, as defined in this paper, are required to learn any solutions of initial value problems in their strictest sense, and we introduce coupled neural networks to learn solutions of coupled systems.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/71b2f475e6dd93def3f335fbbfac10259c5dba45" target='_blank'>
+              Solving physics-based initial value problems with unsupervised machine learning
+              </a>
+            </td>
+          <td>
+            Jack Griffiths, S. A. Wrathmall, Simon A. Gardiner
+          </td>
+          <td>2024-07-25</td>
           <td>ArXiv</td>
           <td>0</td>
+          <td>6</td>
+        </tr>
+
+        <tr id="None">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/4648ca55b2c3ba80a310409f8b48533ab6d4a66a" target='_blank'>
+              Learning interpretable dynamics of stochastic complex systems from experimental data
+              </a>
+            </td>
+          <td>
+            Tingting Gao, B. Barzel, Gang Yan
+          </td>
+          <td>2024-07-17</td>
+          <td>Nature Communications</td>
           <td>0</td>
+          <td>18</td>
         </tr>
 
         <tr id="
@@ -1377,19 +1496,34 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>0</td>
         </tr>
 
-        <tr id="Before we attempt to learn a function between two (sets of) observables of a physical process, we must first decide what the inputs and what the outputs of the desired function are going to be. Here we demonstrate two distinct, data-driven ways of initially deciding ``the right quantities'' to relate through such a function, and then proceed to learn it. This is accomplished by processing multiple simultaneous heterogeneous data streams (ensembles of time series) from observations of a physical system: multiple observation processes of the system. We thus determine (a) what subsets of observables are common between the observation processes (and therefore observable from each other, relatable through a function); and (b) what information is unrelated to these common observables, and therefore particular to each observation process, and not contributing to the desired function. Any data-driven function approximation technique can subsequently be used to learn the input-output relation, from k-nearest neighbors and Geometric Harmonics to Gaussian Processes and Neural Networks. Two particular ``twists'' of the approach are discussed. The first has to do with the identifiability of particular quantities of interest from the measurements. We now construct mappings from a single set of observations of one process to entire level sets of measurements of the process, consistent with this single set. The second attempts to relate our framework to a form of causality: if one of the observation processes measures ``now'', while the second observation process measures ``in the future'', the function to be learned among what is common across observation processes constitutes a dynamical model for the system evolution.">
+        <tr id="We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design. We provide a rigorous convergence statement of the method. The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus. Moreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory. This is illustrated on the example of the discrete wave equation and Schr\"odinger equation. The article constitutes an extension of our previous article arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/575c35910c98644dde823648246e69b413bae054" target='_blank'>
-              On Learning what to Learn: heterogeneous observations of dynamics and establishing (possibly causal) relations among them
+          <td><a href="https://www.semanticscholar.org/paper/e38b7de6c7022b28628627bbf045123b665619b4" target='_blank'>
+              Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification
               </a>
             </td>
           <td>
-            David W. Sroczynski, Felix Dietrich, E. D. Koronaki, R. Talmon, Ronald R. Coifman, Erik Bollt, Ioannis G. Kevrekidis
+            Christian Offen
           </td>
-          <td>2024-06-10</td>
+          <td>2024-07-10</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>28</td>
+          <td>1</td>
+        </tr>
+
+        <tr id="Machine learning presents opportunities to improve the scale-specific accuracy of mechanistic models in a data-driven manner. Here we demonstrate the use of a machine learning technique called Sparse Identification of Nonlinear Dynamics (SINDy) to improve a simple mechanistic model of algal growth. Time-series measurements of the microalga Chlorella Vulgaris were generated under controlled photobioreactor conditions at the University of Technology Sydney. A simple mechanistic growth model based on intensity of light and temperature was integrated over time and compared to the time-series data. While the mechanistic model broadly captured the overall growth trend, discrepancies remained between the model and data due to the model's simplicity and non-ideal behavior of real-world measurement. SINDy was applied to model the residual error by identifying an error derivative correction term. Addition of this SINDy-informed error dynamics term shows improvement to model accuracy while maintaining interpretability of the underlying mechanistic framework. This work demonstrates the potential for machine learning techniques like SINDy to aid simple mechanistic models in scale-specific predictive accuracy.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/0efd19b71be3ac13e47f098d9a6e63082477a540" target='_blank'>
+              Improving Mechanistic Model Accuracy with Machine Learning Informed Physics
+              </a>
+            </td>
+          <td>
+            Will Farlessyost, Shweta Singh
+          </td>
+          <td>2024-07-09</td>
+          <td>Systems and Control Transactions</td>
+          <td>0</td>
+          <td>1</td>
         </tr>
 
         <tr id="Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior physical knowledge. The size of the systems involved and the complexity of the underlying physical equations make it a challenging task from a computational point of view. Neural networks represent a promising method of emulating the physics at low cost, and therefore have the potential to considerably improve and accelerate data assimilation. In this work, we introduce a deep learning approach where the physical system is modeled as a sequence of coarse-to-fine Gaussian prior distributions parametrized by a neural network. This allows us to define an assimilation operator, which is trained in an end-to-end fashion to minimize the reconstruction error on a dataset with different observation processes. We illustrate our approach on chaotic dynamical physical systems with sparse observations, and compare it to traditional variational data assimilation methods.">
@@ -1407,6 +1541,21 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>16</td>
         </tr>
 
+        <tr id="Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods to analyze non-stationary processes, and yet most time-series analysis methods that are used in practice, on important problems across science and industry, make the simplifying assumption of stationarity. One important problem in the analysis of non-stationary systems is the problem class that we refer to as Parameter Inference from a Non-stationary Unknown Process (PINUP). Given an observed time series, this involves inferring the parameters that drive non-stationarity of the time series, without requiring knowledge or inference of a mathematical model of the underlying system. Here we review and unify a diverse literature of algorithms for PINUP. We formulate the problem, and categorize the various algorithmic contributions. This synthesis will allow researchers to identify gaps in the literature and will enable systematic comparisons of different methods. We also demonstrate that the most common systems that existing methods are tested on - notably the non-stationary Lorenz process and logistic map - are surprisingly easy to perform well on using simple statistical features like windowed mean and variance, undermining the practice of using good performance on these systems as evidence of algorithmic performance. We then identify more challenging problems that many existing methods perform poorly on and which can be used to drive methodological advances in the field. Our results unify disjoint scientific contributions to analyzing non-stationary systems and suggest new directions for progress on the PINUP problem and the broader study of non-stationary phenomena.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/585c3c4f3b30a814bc05e6f9e38a5a28b702ee79" target='_blank'>
+              Parameter inference from a non-stationary unknown process
+              </a>
+            </td>
+          <td>
+            Kieran S. Owens, Ben D. Fulcher
+          </td>
+          <td>2024-07-12</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>1</td>
+        </tr>
+
         <tr id="In this study, we investigate the effect of reservoir computing training data on the reconstruction of chaotic dynamics. Our findings indicate that a training time series comprising a few periodic orbits of low periods can successfully reconstruct the Lorenz attractor. We also demonstrate that biased training data does not negatively impact reconstruction success. Our method's ability to reconstruct a physical measure is much better than the so-called cycle expansion approach, which relies on weighted averaging. Additionally, we demonstrate that fixed point attractors and chaotic transients can be accurately reconstructed by a model trained from a few periodic orbits, even when using different parameters.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/f833e966a95961819f625f1095e380b4cf40eb4f" target='_blank'>
@@ -1444,42 +1593,12 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
               </a>
             </td>
           <td>
-            C. Ghnatios, Joel Mouterde, Jerome Tomezyk, Joaquim Da Silva, Francisco Chinesta
+            C. Ghnatios, Joel Mouterde, Jerome Tomezyk, Joaquim Da Silva, F. Chinesta
           </td>
           <td>2024-07-19</td>
           <td>Mathematics</td>
           <td>0</td>
-          <td>13</td>
-        </tr>
-
-        <tr id="Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods to analyze non-stationary processes, and yet most time-series analysis methods that are used in practice, on important problems across science and industry, make the simplifying assumption of stationarity. One important problem in the analysis of non-stationary systems is the problem class that we refer to as Parameter Inference from a Non-stationary Unknown Process (PINUP). Given an observed time series, this involves inferring the parameters that drive non-stationarity of the time series, without requiring knowledge or inference of a mathematical model of the underlying system. Here we review and unify a diverse literature of algorithms for PINUP. We formulate the problem, and categorize the various algorithmic contributions. This synthesis will allow researchers to identify gaps in the literature and will enable systematic comparisons of different methods. We also demonstrate that the most common systems that existing methods are tested on - notably the non-stationary Lorenz process and logistic map - are surprisingly easy to perform well on using simple statistical features like windowed mean and variance, undermining the practice of using good performance on these systems as evidence of algorithmic performance. We then identify more challenging problems that many existing methods perform poorly on and which can be used to drive methodological advances in the field. Our results unify disjoint scientific contributions to analyzing non-stationary systems and suggest new directions for progress on the PINUP problem and the broader study of non-stationary phenomena.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/585c3c4f3b30a814bc05e6f9e38a5a28b702ee79" target='_blank'>
-              Parameter inference from a non-stationary unknown process
-              </a>
-            </td>
-          <td>
-            Kieran S. Owens, Ben D. Fulcher
-          </td>
-          <td>2024-07-12</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-
-        <tr id="This study aims to discover the governing mathematical expressions of car-following dynamics from trajectory data directly using deep learning techniques. We propose an expression exploration framework based on deep symbolic regression (DSR) integrated with a variable intersection selection (VIS) method to find variable combinations that encourage interpretable and parsimonious mathematical expressions. In the exploration learning process, two penalty terms are added to improve the reward function: (i) a complexity penalty to regulate the complexity of the explored expressions to be parsimonious, and (ii) a variable interaction penalty to encourage the expression exploration to focus on variable combinations that can best describe the data. We show the performance of the proposed method to learn several car-following dynamics models and discuss its limitations and future research directions.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f9bb309310be4265ecdbe08b6a11baf260a21d96" target='_blank'>
-              Discovering Car-following Dynamics from Trajectory Data through Deep Learning
-              </a>
-            </td>
-          <td>
-            Ohay Angah, James Enouen, Xuegang (Jeff) Ban, Yan Liu
-          </td>
-          <td>2024-08-01</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>4</td>
+          <td>14</td>
         </tr>
 
         <tr id="Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in learning methods. Koopman operators have emerged as a dominant approach because they allow the study of nonlinear dynamics using linear techniques by solving an infinite-dimensional spectral problem. However, current algorithms face challenges such as lack of convergence, hindering practical progress. This paper addresses a fundamental open question: \textit{When can we robustly learn the spectral properties of Koopman operators from trajectory data of dynamical systems, and when can we not?} Understanding these boundaries is crucial for analysis, applications, and designing algorithms. We establish a foundational approach that combines computational analysis and ergodic theory, revealing the first fundamental barriers -- universal for any algorithm -- associated with system geometry and complexity, regardless of data quality and quantity. For instance, we demonstrate well-behaved smooth dynamical systems on tori where non-trivial eigenfunctions of the Koopman operator cannot be determined by any sequence of (even randomized) algorithms, even with unlimited training data. Additionally, we identify when learning is possible and introduce optimal algorithms with verification that overcome issues in standard methods. These results pave the way for a sharp classification theory of data-driven dynamical systems based on how many limits are needed to solve a problem. These limits characterize all previous methods, presenting a unified view. Our framework systematically determines when and how Koopman spectral properties can be learned.">
@@ -1493,7 +1612,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           </td>
           <td>2024-07-08</td>
           <td>ArXiv</td>
-          <td>0</td>
+          <td>2</td>
           <td>16</td>
         </tr>
 
@@ -1527,19 +1646,34 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>3</td>
         </tr>
 
-        <tr id="We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical solvers. Most existing forward or inverse PDE approaches perform poorly when the observations on the data or the underlying coefficients are incomplete, which is a common assumption for real-world measurements. In this work, we propose DiffusionPDE that can simultaneously fill in the missing information and solve a PDE by modeling the joint distribution of the solution and coefficient spaces. We show that the learned generative priors lead to a versatile framework for accurately solving a wide range of PDEs under partial observation, significantly outperforming the state-of-the-art methods for both forward and inverse directions.">
+        <tr id="Trained neural networks (NN) have attractive features for closing governing equations, but in the absence of additional constraints, they can stray from physical reality. A NN formulation is introduced to preclude spurious oscillations that violate solution boundedness or positivity. It is embedded in the discretized equations as a machine learning closure and strictly constrained, inspired by total variation diminishing (TVD) methods for hyperbolic conservation laws. The constraint is exactly enforced during gradient-descent training by rescaling the NN parameters, which maps them onto an explicit feasible set. Demonstrations show that the constrained NN closure model usefully recovers linear and nonlinear hyperbolic phenomena and anti-diffusion while enforcing the non-oscillatory property. Finally, the model is applied to subgrid-scale (SGS) modeling of a turbulent reacting flow, for which it suppresses spurious oscillations in scalar fields that otherwise violate the solution boundedness. It outperforms a simple penalization of oscillations in the loss function.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5c821763f76272b6deee95f9729107969ce0ae44" target='_blank'>
-              DiffusionPDE: Generative PDE-Solving Under Partial Observation
+          <td><a href="https://www.semanticscholar.org/paper/79145122aa7a9d0690a2cdf42f2290f96d562ae8" target='_blank'>
+              A TVD neural network closure and application to turbulent combustion
               </a>
             </td>
           <td>
-            Jiahe Huang, Guandao Yang, Zichen Wang, Jeong Joon Park
+            Seung Won Suh, J. MacArt, Luke N Olson, Jonathan B Freund
           </td>
-          <td>2024-06-25</td>
+          <td>2024-08-06</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>9</td>
+        </tr>
+
+        <tr id="Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM construction, schemes that allow to retain a portion of the physics tend to enhance the interpretability and generalization of ROMs. However, physics-based techniques can adversely scale when dealing with nonlinear systems that feature parametric dependencies. This study introduces a generative physics-based ROM that is suited for nonlinear systems with parametric dependencies and is additionally able to quantify the confidence associated with the respective estimates. A main contribution of this work is the conditioning of these parametric ROMs to features that can be derived from monitoring measurements, feasibly in an online fashion. This is contrary to most existing ROM schemes, which remain restricted to the prescription of the physics-based, and usually a priori unknown, system parameters. Our work utilizes conditional Variational Autoencoders to continuously map the required reduction bases to a feature vector extracted from limited output measurements, while additionally allowing for a probabilistic assessment of the ROM-estimated Quantities of Interest. An auxiliary task using a neural network-based parametrization of suitable probability distributions is introduced to re-establish the link with physical model parameters. We verify the proposed scheme on a series of simulated case studies incorporating effects of geometric and material nonlinearity under parametric dependencies related to system properties and input load characteristics.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/eb8cb80fb7c1708ef89c5e655f1cf2a1a98b8f0a" target='_blank'>
+              A Reduced Order Model conditioned on monitoring features for estimation and uncertainty quantification in engineered systems
+              </a>
+            </td>
+          <td>
+            Konstantinos Vlachas, Thomas Simpson, Anthony Garland, D. Quinn, Charbel Farhat, Eleni Chatzi
+          </td>
+          <td>2024-07-24</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>3</td>
         </tr>
 
         <tr id="The goal of this paper is to make a strong point for the usage of dynamical models when using reinforcement learning (RL) for feedback control of dynamical systems governed by partial differential equations (PDEs). To breach the gap between the immense promises we see in RL and the applicability in complex engineering systems, the main challenges are the massive requirements in terms of the training data, as well as the lack of performance guarantees. We present a solution for the first issue using a data-driven surrogate model in the form of a convolutional Long-Short Term Memory network with actuation. We demonstrate that learning an actuated model in parallel to training the RL agent significantly reduces the total amount of required data sampled from the real system. Furthermore, we show that iteratively updating the model is of major importance to avoid biases in the RL training. Detailed ablation studies reveal the most important ingredients of the modeling process. We use the chaotic Kuramoto-Sivashinsky equation do demonstrate our findings.">
@@ -1557,79 +1691,95 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>0</td>
         </tr>
 
-        <tr id="Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only as a state estimator and a prior estimator for the dynamics but also as a controller. This approach allows us to handle the nonlinearity of the dynamics and uncertainty of the latent state. We apply two distinct dynamics to verify the effectiveness of our proposed framework: a chaotic system defined by the Lorenz equation and a nonlinear neuronal system defined by the Morris–Lecar neuron model. The results indicate that our proposed framework can simultaneously estimate and control complex nonlinear dynamical systems.">
+        <tr id="
+ The time evolution of physical systems is described by differential equations, which depend on abstract quantities like energy and force. Traditionally, these quantities are derived as functionals based on observables such as positions and velocities. Discovering these governing symbolic laws is the key to comprehending the interactions in nature. Here, we present a Hamiltonian graph neural network (HGNN), a physics-enforced GNN that learns the dynamics of systems directly from their trajectory. We demonstrate the performance of HGNN on n-springs, n-pendulums, gravitational systems, and binary Lennard Jones systems; HGNN learns the dynamics in excellent agreement with the ground truth from small amounts of data. We also evaluate the ability of HGNN to generalize to larger system sizes, and to a hybrid spring-pendulum system that is a combination of two original systems (spring and pendulum) on which the models are trained independently. Finally, employing symbolic regression on the learned HGNN, we infer the underlying equations relating to the energy functionals, even for complex systems such as the binary Lennard-Jones liquid. Our framework facilitates the interpretable discovery of interaction laws directly from physical system trajectories. Furthermore, this approach can be extended to other systems with topology-dependent dynamics, such as cells, polydisperse gels, or deformable bodies.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/682bd11b89e6862f9721d25af1d528fadb6746f4" target='_blank'>
-              Probabilistic Estimation and Control of Dynamical Systems Using Particle Filter with Adaptive Backward Sampling
+          <td><a href="https://www.semanticscholar.org/paper/c632fd8fa34b6e12e92828eda9a171b587d0e51e" target='_blank'>
+              DISCOVERING SYMBOLIC LAWS DIRECTLY FROM TRAJECTORIES WITH HAMILTONIAN GRAPH NEURAL NETWORKS
               </a>
             </td>
           <td>
-            Taketo Omi, Toshiaki Omori
+            S. Bishnoi, Ravinder Bhattoo, Sayan Ranu, N. Krishnan
           </td>
-          <td>2024-07-30</td>
-          <td>Entropy</td>
-          <td>0</td>
-          <td>0</td>
+          <td>2024-08-06</td>
+          <td>Machine Learning: Science and Technology</td>
+          <td>1</td>
+          <td>10</td>
         </tr>
 
-        <tr id="Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation. Discovering these constitutive material laws remains a significant challenge, in particular when only material deformation data is available. To address this challenge, unsupervised machine learning methods have been proposed. However, existing approaches have several limitations: they either fail to ensure that the learned constitutive relations are consistent with physical principles, or they rely on a predefined library of constitutive relations or manually crafted input features. These dependencies require significant expertise and specialized domain knowledge. Here, we introduce a machine learning approach called uLED, which overcomes the limitations by using the input convex neural network (ICNN) as the surrogate constitutive model. We improve the optimization strategy for training ICNN, allowing it to be trained end-to-end using direct strain invariants as input across various materials. Furthermore, we utilize the nodal force equilibrium at the internal domain as the training objective, which enables us to learn the constitutive relation solely from temporal displacement recordings. We validate the effectiveness of the proposed method on a diverse range of material laws. We demonstrate that it is robust to a significant level of noise and that it converges to the ground truth with increasing data resolution. We also show that the model can be effectively trained using a displacement field from a subdomain of the test specimen and that the learned constitutive relation from one material sample is transferable to other samples with different geometries. The developed methodology provides an effective tool for discovering constitutive relations.">
+        <tr id="Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations, or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has advantages with respect to interpretability, transparency, data-efficiency, and extrapolation, the second approach is able to learn completely unknown functional relations from data and may result in models that can be evaluated more efficiently. To combine the complementary advantages, universal differential equations (UDE) have been suggested, which replace unknown terms in the differential equations with ANN. These hybrid models allow to both encode prior domain knowledge such as first principles and to learn unknown mechanisms from data. Often, data for the training of UDE can only be obtained via costly experiments. We consider optimal experimental design (OED) for the planning of experiments and generation of data needed to train UDE. The number of weights in the embedded ANN usually leads to an overfitting of the regression problem. To make the OED problem tractable for optimization, we propose and compare dimension reduction methods that are based on lumping of weights and singular value decomposition of the Fisher information matrix (FIM), respectively. They result in lower-dimensional variational differential equations which are easier to solve and which yield regular FIM. Our numerical results showcase the advantages of OED for UDE, such as an increased data-efficiency and better extrapolation properties.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/66917df8a8f69b2b557c7f74ef2c576d38a94797" target='_blank'>
-              Learning Physics-Consistent Material Behavior Without Prior Knowledge
+          <td><a href="https://www.semanticscholar.org/paper/2230fd0495ec13469526bd77cb385acbdb4bddfa" target='_blank'>
+              Optimal Experimental Design for Universal Differential Equations
               </a>
             </td>
           <td>
-            Zhichao Han, Mohit Pundir, Olga Fink, David S. Kammer
+            Christoph Plate, Carl Julius Martensen, Sebastian Sager
           </td>
-          <td>2024-07-25</td>
+          <td>2024-08-13</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems. However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes is yet to be fully established. This study introduces NeuroSEM, a hybrid framework integrating PINNs with the high-fidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into Nektar++. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where data are available. We applied NeuroSEM to the Rayleigh-B\'enard convection system, including cases with missing thermal boundary conditions. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework's plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for an efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.">
+        <tr id="Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only as a state estimator and a prior estimator for the dynamics but also as a controller. This approach allows us to handle the nonlinearity of the dynamics and uncertainty of the latent state. We apply two distinct dynamics to verify the effectiveness of our proposed framework: a chaotic system defined by the Lorenz equation and a nonlinear neuronal system defined by the Morris–Lecar neuron model. The results indicate that our proposed framework can simultaneously estimate and control complex nonlinear dynamical systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bf355890cfebb6682f601bfaea0ed245cda232dc" target='_blank'>
-              NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements
+          <td><a href="https://www.semanticscholar.org/paper/682bd11b89e6862f9721d25af1d528fadb6746f4" target='_blank'>
+              Probabilistic Estimation and Control of Dynamical Systems Using Particle Filter with Adaptive Backward Sampling
               </a>
             </td>
           <td>
-            K. Shukla, Zongren Zou, Chi Hin Chan, Additi Pandey, Zhicheng Wang, G. Karniadakis
+            Taketo Omi, Toshiaki Omori
           </td>
           <td>2024-07-30</td>
-          <td>ArXiv</td>
+          <td>Entropy</td>
           <td>0</td>
-          <td>127</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding of observed dynamic behavior, but also for designing efficient interventions. When the dynamical system at hand is complex, possibly noisy, and expensive to sample, standard (e.g. continuation based) numerical methods may become impractical. We propose an active learning framework, where Bayesian Optimization is leveraged to discover saddle-node or Hopf bifurcations, from a judiciously chosen small number of vector field observations. Such an approach becomes especially attractive in systems whose state x parameter space exploration is resource-limited. It also naturally provides a framework for uncertainty quantification (aleatoric and epistemic), useful in systems with inherent stochasticity.">
+        <tr id="We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory data points unlike traditional methods that require an averaging procedure, the exploration of phase transition graphs from regular periodic to chaotic dynamics to identify"almost integrable"trajectories where conserved quantities deviate from whole numbers, and the identification of"integrable regions"within chaotic trajectories. These methods are applied and tested on two dynamical systems:"Two objects moving on a rod"and the"Henon-Heiles"systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8580056dd0caf69a81d8730639e0828479823e8a" target='_blank'>
-              Active search for Bifurcations
+          <td><a href="https://www.semanticscholar.org/paper/8beba1025021fc988f71772e30840ce6845fdf65" target='_blank'>
+              Deciphering Complexity: Machine Learning Insights into Chaotic Dynamical Systems
               </a>
             </td>
           <td>
-            Y. M. Psarellis, T. Sapsis, I. G. Kevrekidis
+            Lazare Osmanov
           </td>
-          <td>2024-06-17</td>
+          <td>2024-08-04</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>37</td>
+          <td>0</td>
         </tr>
 
-        <tr id="We consider solving complex spatiotemporal dynamical systems governed by partial differential equations (PDEs) using frequency domain-based discrete learning approaches, such as Fourier neural operators. Despite their widespread use for approximating nonlinear PDEs, the majority of these methods neglect fundamental physical laws and lack interpretability. We address these shortcomings by introducing Physics-embedded Fourier Neural Networks (PeFNN) with flexible and explainable error control. PeFNN is designed to enforce momentum conservation and yields interpretable nonlinear expressions by utilizing unique multi-scale momentum-conserving Fourier (MC-Fourier) layers and an element-wise product operation. The MC-Fourier layer is by design translation- and rotation-invariant in the frequency domain, serving as a plug-and-play module that adheres to the laws of momentum conservation. PeFNN establishes a new state-of-the-art in solving widely employed spatiotemporal PDEs and generalizes well across input resolutions. Further, we demonstrate its outstanding performance for challenging real-world applications such as large-scale flood simulations.">
+        <tr id="Many physical systems exhibit translational invariance, meaning that the underlying physical laws are independent of the position in space. Data driven approximations of the infinite dimensional but linear Koopman operator of non-linear dynamical systems need to be physically informed in order to respect such physical symmetries. In the current work, we introduce a translation invariant extended dynamic mode decomposition (tieDMD) for coupled non-linear systems on periodic domains. This is achieved by exploiting a block-diagonal structure of the Koopman operator in Fourier space. Variants of tieDMD are applied to data obtained on one-dimensional periodic domains from the non-linear phase-diffusion equation, the Burgers equation, the Korteweg-de Vries equation, and a coupled FitzHugh-Nagumo system of partial differential equations. The reconstruction capability of tieDMD is compared to existing linear and non-linear variants of the dynamic mode decomposition applied to the same data. For the regarded data, tieDMD consistently shows superior capabilities in data reconstruction.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b1987fcbdf3f85b47d4df2efa239c0c5050a329a" target='_blank'>
-              Physics-embedded Fourier Neural Network for Partial Differential Equations
+          <td><a href="https://www.semanticscholar.org/paper/c3bb71d64de3bbe99545b75cc623bacfad3e1e76" target='_blank'>
+              Approximation of translation invariant Koopman operators for coupled non-linear systems.
               </a>
             </td>
           <td>
-            Qingsong Xu, Nils Thuerey, Yilei Shi, Jonathan Bamber, Chaojun Ouyang, Xiao Xiang Zhu
+            Thomas Hochrainer, Gurudas Kar
           </td>
-          <td>2024-07-15</td>
+          <td>2024-08-01</td>
+          <td>Chaos</td>
+          <td>0</td>
+          <td>3</td>
+        </tr>
+
+        <tr id="Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for supervised and unsupervised learning of nonlinear dynamical systems, and has received considerable interest in recent years. Here, we propose a data-driven technique for spectral approximation of Koopman operators of continuous-time, measure-preserving ergodic systems that is asymptotically consistent and makes direct use of known equations of motion (physics). Our approach is based on a bounded transformation of the Koopman generator (an operator implementing directional derivatives of observables along the dynamical flow), followed by smoothing by a Markov semigroup of kernel integral operators. This results in a skew-adjoint, compact operator whose eigendecomposition is expressible as a variational generalized eigenvalue problem. We develop Galerkin methods to solve this eigenvalue problem and study their asymptotic consistency in the large-data limit. A key aspect of these methods is that they are physics-informed, in the sense of making direct use of dynamical vector field information through automatic differentiation of kernel functions. Solutions of the eigenvalue problem reconstruct evolution operators that preserve unitarity of the underlying Koopman group while spectrally converging to it in a suitable limit. In addition, the computed eigenfunctions have representatives in a reproducing kernel Hilbert space, enabling out-of-sample evaluation of learned dynamical features. Numerical experiments performed with this method on integrable and chaotic low-dimensional systems demonstrate its efficacy in extracting dynamically coherent observables under complex dynamics.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/7bfdb15c2217fa4993fd812bd48a56f8b7c2df5e" target='_blank'>
+              Physics-informed spectral approximation of Koopman operators
+              </a>
+            </td>
+          <td>
+            C. Valva, Dimitrios Giannakis
+          </td>
+          <td>2024-08-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>19</td>
+          <td>3</td>
         </tr>
 
         <tr id="This proposed work introduces a data-assimilation-assisted approach to train neural networks, aimed at effectively reducing epistemic uncertainty in state estimates of separated flows. This method, referred to as model-consistent training, ensures that input features are derived directly from physics-based models, such as Reynolds Averaged Navier Stokes (RANS) turbulence models, to accurately represent the current state of the flow. Autoencoders have been selected for this task due to their capability to capture essential information from large datasets, making them particularly suitable for handling high-dimensional data with numerous discretization points in both spatial and temporal dimensions. This innovative approach integrates the ensemble Kalman method to enhance the training process, providing a robust framework for improving model accuracy and performance in turbulent flow predictions.">
@@ -1647,49 +1797,49 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>0</td>
         </tr>
 
-        <tr id="Physics informed neural networks have been gaining popularity due to their unique ability to incorporate physics laws into data-driven models, ensuring that the predictions are not only consistent with empirical data but also align with domain-specific knowledge in the form of physics equations. The integration of physics principles enables the method to require less data while maintaining the robustness of deep learning in modeling complex dynamical systems. However, current PINN frameworks are not sufficiently mature for real-world ODE systems, especially those with extreme multi-scale behavior such as mosquito population dynamical modelling. In this research, we propose a PINN framework with several improvements for forward and inverse problems for ODE systems with a case study application in modelling the dynamics of mosquito populations. The framework tackles the gradient imbalance and stiff problems posed by mosquito ordinary differential equations. The method offers a simple but effective way to resolve the time causality issue in PINNs by gradually expanding the training time domain until it covers entire domain of interest. As part of a robust evaluation, we conduct experiments using simulated data to evaluate the effectiveness of the approach. Preliminary results indicate that physics-informed machine learning holds significant potential for advancing the study of ecological systems.">
+        <tr id="This paper presents, for the first time, a framework for Kolmogorov-Arnold Networks (KANs) in power system applications. Inspired by the recently proposed KAN architecture, this paper proposes physics-informed Kolmogorov-Arnold Networks (PIKANs), a novel KAN-based physics-informed neural network (PINN) tailored to efficiently and accurately learn dynamics within power systems. The PIKANs present a promising alternative to conventional Multi-Layer Perceptrons (MLPs) based PINNs, achieving superior accuracy in predicting power system dynamics while employing a smaller network size. Simulation results on a single-machine infinite bus system and a 4-bus 2- generator system underscore the accuracy of the PIKANs in predicting rotor angle and frequency with fewer learnable parameters than conventional PINNs. Furthermore, the simulation results demonstrate PIKANs capability to accurately identify uncertain inertia and damping coefficients. This work opens up a range of opportunities for the application of KANs in power systems, enabling efficient determination of grid dynamics and precise parameter identification.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bf1c97b75409ff1ee6e5c4298dd05295c9b772df" target='_blank'>
-              Adapting Physics-Informed Neural Networks To Optimize ODEs in Mosquito Population Dynamics
+          <td><a href="https://www.semanticscholar.org/paper/ba0e7f4ba7daa48bc5af967eba3f7af6be45476e" target='_blank'>
+              Physics-Informed Kolmogorov-Arnold Networks for Power System Dynamics
               </a>
             </td>
           <td>
-            D. V. Cuong, Branislava Lali'c, Mina Petri'c, Binh Nguyen, M. Roantree
+            H. Shuai, Fangxing Li
           </td>
-          <td>2024-06-07</td>
+          <td>2024-08-13</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>17</td>
+          <td>3</td>
         </tr>
 
-        <tr id="We propose CoNSAL (Combining Neural networks and Symbolic regression for Analytical Lyapunov function) to construct analytical Lyapunov functions for nonlinear dynamic systems. This framework contains a neural Lyapunov function and a symbolic regression component, where symbolic regression is applied to distill the neural network to precise analytical forms. Our approach utilizes symbolic regression not only as a tool for translation but also as a means to uncover counterexamples. This procedure terminates when no counterexamples are found in the analytical formulation. Compared with previous results, CoNSAL directly produces an analytical form of the Lyapunov function with improved interpretability in both the learning process and the final results. We apply CoNSAL to 2-D inverted pendulum, path following, Van Der Pol Oscillator, 3-D trig dynamics, 4-D rotating wheel pendulum, 6-D 3-bus power system, and demonstrate that our algorithm successfully finds their valid Lyapunov functions. Code examples are available at https://github.com/HaohanZou/CoNSAL.">
+        <tr id="Reservoir computing (RC) is known as a powerful machine learning approach for learning complex dynamics from limited data. Here, we use RC to predict highly stochastic dynamics of cell shapes. We find that RC is able to predict the steady state climate from very limited data. Furthermore, the RC learns the timescale of transients from only four observations. We find that these capabilities of the RC to act as a dynamic twin allows us to also infer important statistics of cell shape dynamics of unobserved conditions.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6829a0516285c595b5e8d5fcbc9c4858827f5784" target='_blank'>
-              Combining Neural Networks and Symbolic Regression for Analytical Lyapunov Function Discovery
+          <td><a href="https://www.semanticscholar.org/paper/20f5cfa59cf3363d794a2715ae08d7e092121b0f" target='_blank'>
+              Machine learning from limited data: Predicting biological dynamics under a time-varying external input
               </a>
             </td>
           <td>
-            Jie Feng, Haohan Zou, Yuanyuan Shi
+            Hoony Kang, Keshav Srinivasan, Wolfgang Losert
           </td>
-          <td>2024-06-21</td>
+          <td>2024-08-15</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>2</td>
         </tr>
 
-        <tr id="The precise and efficient interpretation of Fisher's equation is paramount while comprehending different dynamics of biological population spread and colonization. In this context, Physics-informed neural networks (PINNs) are emerging as a promising alternative to conventional numerical methods. This paper highlights the distinct advantages of using PINN in solving Fisher's equations compared to traditional methods. This method involves numerically approximated partial differential equations through PINNs based on the sampling of Latin supermassives. The optimization was performed using Adam's optimization technique to minimize the root mean square loss function associated with the targeted partial differential equation. This study provides a powerful tool that not only accurately predicts population distribution, but also captures underlying dynamics of the system. The effectiveness of the mentioned method is highlighted with numerous numerical testing and comparative analysis with traditional numerical methods.">
+        <tr id="We propose CoNSAL (Combining Neural networks and Symbolic regression for Analytical Lyapunov function) to construct analytical Lyapunov functions for nonlinear dynamic systems. This framework contains a neural Lyapunov function and a symbolic regression component, where symbolic regression is applied to distill the neural network to precise analytical forms. Our approach utilizes symbolic regression not only as a tool for translation but also as a means to uncover counterexamples. This procedure terminates when no counterexamples are found in the analytical formulation. Compared with previous results, CoNSAL directly produces an analytical form of the Lyapunov function with improved interpretability in both the learning process and the final results. We apply CoNSAL to 2-D inverted pendulum, path following, Van Der Pol Oscillator, 3-D trig dynamics, 4-D rotating wheel pendulum, 6-D 3-bus power system, and demonstrate that our algorithm successfully finds their valid Lyapunov functions. Code examples are available at https://github.com/HaohanZou/CoNSAL.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d6732656e841a9a913263f302a06cb3a1fbe2653" target='_blank'>
-              A Novel Approach for Approximating the Dynamics of Fisher's Equation Based on Physics-Informed Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/6829a0516285c595b5e8d5fcbc9c4858827f5784" target='_blank'>
+              Combining Neural Networks and Symbolic Regression for Analytical Lyapunov Function Discovery
               </a>
             </td>
           <td>
-            Nimmagadda Greeshma, Soumyendra Singh
+            Jie Feng, Haohan Zou, Yuanyuan Shi
           </td>
-          <td>2024-06-08</td>
-          <td>2024 International Conference on Integrated Circuits, Communication, and Computing Systems (ICIC3S)</td>
-          <td>0</td>
+          <td>2024-06-21</td>
+          <td>ArXiv</td>
           <td>0</td>
+          <td>1</td>
         </tr>
 
         <tr id="Port-Hamiltonian systems (pHS) allow for a structure-preserving modeling of dynamical systems. Coupling pHS via linear relations between input and output defines an overall pHS, which is structure preserving. However, in multiphysics applications, some subsystems do not allow for a physical pHS description, as (a) this is not available or (b) too expensive. Here, data-driven approaches can be used to deliver a pHS for such subsystems, which can then be coupled to the other subsystems in a structure-preserving way. In this work, we derive a data-driven identification approach for port-Hamiltonian differential algebraic equation (DAE) systems. The approach uses input and state space data to estimate nonlinear effort functions of pH-DAEs. As underlying technique, we us (multi-task) Gaussian processes. This work thereby extends over the current state of the art, in which only port-Hamiltonian ordinary differential equation systems could be identified via Gaussian processes. We apply this approach successfully to two applications from network design and constrained multibody system dynamics, based on pH-DAE system of index one and three, respectively.">
@@ -1703,7 +1853,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           </td>
           <td>2024-06-26</td>
           <td>ArXiv</td>
-          <td>0</td>
+          <td>1</td>
           <td>2</td>
         </tr>
 
@@ -1734,22 +1884,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
-        </tr>
-
-        <tr id="In this paper, we present a generic physics-informed generative model called MPDM that integrates multi-fidelity physics simulations with diffusion models. MPDM categorizes multi-fidelity physics simulations into inexpensive and expensive simulations, depending on computational costs. The inexpensive simulations, which can be obtained with low latency, directly inject contextual information into DDMs. Furthermore, when results from expensive simulations are available, MPDM refines the quality of generated samples via a guided diffusion process. This design separates the training of a denoising diffusion model from physics-informed conditional probability models, thus lending flexibility to practitioners. MPDM builds on Bayesian probabilistic models and is equipped with a theoretical guarantee that provides upper bounds on the Wasserstein distance between the sample and underlying true distribution. The probabilistic nature of MPDM also provides a convenient approach for uncertainty quantification in prediction. Our models excel in cases where physics simulations are imperfect and sometimes inaccessible. We use a numerical simulation in fluid dynamics and a case study in heat dynamics within laser-based metal powder deposition additive manufacturing to demonstrate how MPDM seamlessly integrates multi-idelity physics simulations and observations to obtain surrogates with superior predictive performance.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4e5e531479fd961311f387fb904eca9e6d2466a0" target='_blank'>
-              Multi-physics Simulation Guided Generative Diffusion Models with Applications in Fluid and Heat Dynamics
-              </a>
-            </td>
-          <td>
-            Naichen Shi, Hao Yan, Shenghan Guo, R. Kontar
-          </td>
-          <td>2024-07-25</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>13</td>
+          <td>4</td>
         </tr>
 
         <tr id="The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.">
@@ -1767,19 +1902,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>3</td>
         </tr>
 
-        <tr id="In this paper, we explore the application of Machine Learning techniques, specifically Support Vector Machines (SVM), to unveil the chaotic and regular nature of trajectories in Hamiltonian systems using Lagrangian descriptors. Traditional chaos indicators, while effective, are computationally expensive and require an exhaustive study of the parameter space to establish the classification thresholds. By using SVMs trained on a dataset obtained from the analysis of the dynamics of the double pendulum Hamiltonian system, we aim at reducing the complexity of this process. Our trained SVM models demonstrate high accuracy when it comes to classifying trajectories in diverse Hamiltonian systems, such as for example in the four-well Hamiltonian, the H\'enon-Heiles system and the Chirikov Standard Map. The results indicate that SVMs, when combined with Lagrangian descriptors, offer a robust and efficient method for chaos classification across different dynamical systems. Our approach not only simplifies the classification process but also is highlighting the potential of Machine Learning algorithms in the study of nonlinear dynamics and chaos.">
+        <tr id="Kolmogorov-Arnold networks (KANs) have attracted attention recently as an alternative to multilayer perceptrons (MLPs) for scientific machine learning. However, KANs can be expensive to train, even for relatively small networks. Inspired by finite basis physics-informed neural networks (FBPINNs), in this work, we develop a domain decomposition method for KANs that allows for several small KANs to be trained in parallel to give accurate solutions for multiscale problems. We show that finite basis KANs (FBKANs) can provide accurate results with noisy data and for physics-informed training.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e3fc433a1690a469869c09f4b8c25ee5213c533c" target='_blank'>
-              Learning the Chaotic and Regular Nature of Trajectories in Hamiltonian Systems with Lagrangian descriptors
+          <td><a href="https://www.semanticscholar.org/paper/6be75a69bb14192a26be00ff51c9a2f086f26b41" target='_blank'>
+              Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems
               </a>
             </td>
           <td>
-            Javier Jim'enez L'opez, V'ictor Jos'e Garc'ia Garrido
+            Amanda Howard, Bruno Jacob, Sarah H. Murphy, Alexander Heinlein, P. Stinis
           </td>
-          <td>2024-07-26</td>
+          <td>2024-06-28</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
+          <td>3</td>
+          <td>12</td>
         </tr>
 
         <tr id="The continuously increasing amount of noisy data demands the development of accurate and efficient models for analysis, modeling, and control. In this article, we propose a novel data-driven moment matching method which employs Tikhonov regularization in the Reproducing Kernel Hilbert Spaces (RKHSs). Specifically, considering a realistic scenario in which the system's plant is unknown and only noisy measured data are available, we provide an estimation of the moment of the unknown plant by solving a regularized optimization problem on RKHS. For, we first demonstrate that the estimation of the moment can be improved via tuning the regularization term, and further, we show under which condition the effect of the transient improves the performance of the estimation. Then, we construct a parameterized model characterized by a kernel-based output mapping. Finally, the proposed data-driven approach is validated and discussed by means of a DC-to-DC Cuk converter driven by a Van der Pol oscillator.">
@@ -1797,64 +1932,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2</td>
         </tr>
 
-        <tr id="Recently, Conditional Neural Fields (NeFs) have emerged as a powerful modelling paradigm for PDEs, by learning solutions as flows in the latent space of the Conditional NeF. Although benefiting from favourable properties of NeFs such as grid-agnosticity and space-time-continuous dynamics modelling, this approach limits the ability to impose known constraints of the PDE on the solutions -- e.g. symmetries or boundary conditions -- in favour of modelling flexibility. Instead, we propose a space-time continuous NeF-based solving framework that - by preserving geometric information in the latent space - respects known symmetries of the PDE. We show that modelling solutions as flows of pointclouds over the group of interest $G$ improves generalization and data-efficiency. We validated that our framework readily generalizes to unseen spatial and temporal locations, as well as geometric transformations of the initial conditions - where other NeF-based PDE forecasting methods fail - and improve over baselines in a number of challenging geometries.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9c8295fdfb6de078027cabc7d49b319df8abb0ee" target='_blank'>
-              Space-Time Continuous PDE Forecasting using Equivariant Neural Fields
-              </a>
-            </td>
-          <td>
-            David M. Knigge, David R. Wessels, Riccardo Valperga, Samuele Papa, J. Sonke, E. Gavves, E. J. Bekkers
-          </td>
-          <td>2024-06-10</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>56</td>
-        </tr>
-
-        <tr id="We propose the Artificial Intelligence Velocimetry-Thermometry (AIVT) method to infer hidden temperature fields from experimental turbulent velocity data. This physics-informed machine learning method enables us to infer continuous temperature fields using only sparse velocity data, hence eliminating the need for direct temperature measurements. Specifically, AIVT is based on physics-informed Kolmogorov-Arnold Networks (not neural networks) and is trained by optimizing a combined loss function that minimizes the residuals of the velocity data, boundary conditions, and the governing equations. We apply AIVT to a unique set of experimental volumetric and simultaneous temperature and velocity data of Rayleigh-B\'enard convection (RBC) that we acquired by combining Particle Image Thermometry and Lagrangian Particle Tracking. This allows us to compare AIVT predictions and measurements directly. We demonstrate that we can reconstruct and infer continuous and instantaneous velocity and temperature fields from sparse experimental data at a fidelity comparable to direct numerical simulations (DNS) of turbulence. This, in turn, enables us to compute important quantities for quantifying turbulence, such as fluctuations, viscous and thermal dissipation, and QR distribution. This paradigm shift in processing experimental data using AIVT to infer turbulent fields at DNS-level fidelity is a promising avenue in breaking the current deadlock of quantitative understanding of turbulence at high Reynolds numbers, where DNS is computationally infeasible.">
+        <tr id="This paper presents an algorithm for developing sparse surrogate models that satisfy mass/energy conservation even when the training data are noisy and violate the conservation laws. In the first step, we employ the Bayesian Identification of Dynamic Sparse Algebraic Model (BIDSAM) algorithm proposed in our previous work to obtain a set of hierarchically ranked sparse models which approximate system behaviors with linear combinations of a set of well-defined basis functions. Although the model building algorithm was shown to be robust to noisy data, conservation laws may not be satisfied by the surrogate models. In this work we propose an algorithm that augments a data reconciliation step with the BIDSAM model for satisfaction of conservation laws. This method relies only on known boundary conditions and hence is generic for any chemical system. Two case studies are considered-one focused on mass conservation and another on energy conservation. Results show that models with minimum bias are built by using the developed algorithm while exactly satisfying the conservation laws for all data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eb6d8afffcc7bf5a551a6c5a5b9a454bde425d85" target='_blank'>
-              Inferring turbulent velocity and temperature fields and their statistics from Lagrangian velocity measurements using physics-informed Kolmogorov-Arnold Networks
+          <td><a href="https://www.semanticscholar.org/paper/a3b228eccbfc381c1bf8429fb1e6ed55fe3fb34c" target='_blank'>
+              Development of Mass/Energy Constrained Sparse Bayesian Surrogate Models from Noisy Data
               </a>
             </td>
           <td>
-            Juan Diego Toscano, Theo Kaufer, Zhibo Wang, Martin Maxey, Christian Cierpka, G. Karniadakis
+            Samuel Adeyemo, D. Bhattacharyya
           </td>
-          <td>2024-07-22</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>127</td>
-        </tr>
-
-        <tr id="Classical model reduction techniques project the governing equations onto a linear subspace of the original state space. More recent data-driven techniques use neural networks to enable nonlinear projections. Whilst those often enable stronger compression, they may have redundant parameters and lead to suboptimal latent dimensionality. To overcome these, we propose a multistep algorithm that induces sparsity in the encoder-decoder networks for effective reduction in the number of parameters and additional compression of the latent space. This algorithm starts with sparsely initialized a network and training it using linearized Bregman iterations. These iterations have been very successful in computer vision and compressed sensing tasks, but have not yet been used for reduced-order modelling. After the training, we further compress the latent space dimensionality by using a form of proper orthogonal decomposition. Last, we use a bias propagation technique to change the induced sparsity into an effective reduction of parameters. We apply this algorithm to three representative PDE models: 1D diffusion, 1D advection, and 2D reaction-diffusion. Compared to conventional training methods like Adam, the proposed method achieves similar accuracy with 30% less parameters and a significantly smaller latent space.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6d0716bb98b1bad42ed563160283dce3e8413da6" target='_blank'>
-              Sparsifying dimensionality reduction of PDE solution data with Bregman learning
-              </a>
-            </td>
-          <td>
-            T. J. Heeringa, Christoph Brune, Mengwu Guo
-          </td>
-          <td>2024-06-18</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-
-        <tr id="To improve the predictive capacity of system models in the input-output sense, this paper presents a framework for model updating via learning of modeling uncertainties in locally (and thus also in globally) Lipschitz nonlinear systems. First, we introduce a method to extend an existing known model with an uncertainty model so that stability of the extended model is guaranteed in the sense of set invariance and input-to-state stability. To achieve this, we provide two tractable semi-definite programs. These programs allow obtaining optimal uncertainty model parameters for both locally and globally Lipschitz nonlinear models, given uncertainty and state trajectories. Subsequently, in order to extract this data from the available input-output trajectories, we introduce a filter that incorporates an approximated internal model of the uncertainty and asymptotically estimates uncertainty and state realizations. This filter is also synthesized using semi-definite programs with guaranteed robustness with respect to uncertainty model mismatches, disturbances, and noise. Numerical simulations for a large data-set of a roll plane model of a vehicle illustrate the effectiveness and practicality of the proposed methodology in improving model accuracy, while guaranteeing stability.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e7ee6ed031b0068e5df250ad046941ba05393280" target='_blank'>
-              Model Updating for Nonlinear Systems with Stability Guarantees
-              </a>
-            </td>
-          <td>
-            Farhad Ghanipoor, C. Murguia, Peyman Mohajerin Esfahani, N. Wouw
-          </td>
-          <td>2024-06-10</td>
-          <td>ArXiv</td>
+          <td>2024-07-09</td>
+          <td>Systems and Control Transactions</td>
           <td>0</td>
-          <td>47</td>
+          <td>29</td>
         </tr>
 
         <tr id="
@@ -1903,64 +1993,79 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>6</td>
         </tr>
 
-        <tr id="Modern data-driven control applications call for flexible nonlinear models that are amenable to principled controller synthesis and realtime feedback. Many nonlinear dynamical systems of interest are control affine. We propose two novel classes of nonlinear feature representations which capture control affine structure while allowing for arbitrary complexity in the state dependence. Our methods make use of random features (RF) approximations, inheriting the expressiveness of kernel methods at a lower computational cost. We formalize the representational capabilities of our methods by showing their relationship to the Affine Dot Product (ADP) kernel proposed by Casta\~neda et al. (2021) and a novel Affine Dense (AD) kernel that we introduce. We further illustrate the utility by presenting a case study of data-driven optimization-based control using control certificate functions (CCF). Simulation experiments on a double pendulum empirically demonstrate the advantages of our methods.">
+        <tr id="Constraining a numerical weather prediction (NWP) model with observations via 4D variational (4D-Var) data assimilation is often difficult to implement in practice due to the need to develop and maintain a software-based tangent linear model and adjoint model. One of the most common 4D-Var algorithms uses an incremental update procedure, which has been shown to be an approximation of the Gauss-Newton method. Here we demonstrate that when using a forecast model that supports automatic differentiation, an efficient and in some cases more accurate alternative approximation of the Gauss-Newton method can be applied by combining backpropagation of errors with Hessian approximation. This approach can be used with either a conventional numerical model implemented within a software framework that supports automatic differentiation, or a machine learning (ML) based surrogate model. We test the new approach on a variety of Lorenz-96 and quasi-geostrophic models. The results indicate potential for a deeper integration of modeling, data assimilation, and new technologies in a next-generation of operational forecast systems that leverage weather models designed to support automatic differentiation.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/29cde075fe82ea752c015715f01f8a198477efc2" target='_blank'>
-              Random features approximation for control-affine systems
+          <td><a href="https://www.semanticscholar.org/paper/4b43d025345ba51dc1b8aa4bb1314e91f7a7174b" target='_blank'>
+              4D-Var using Hessian approximation and backpropagation applied to automatically-differentiable numerical and machine learning models
               </a>
             </td>
           <td>
-            Kimia Kazemian, Yahya Sattar, Sarah Dean
+            Kylen Solvik, Stephen G. Penny, Stephan Hoyer
           </td>
-          <td>2024-06-10</td>
+          <td>2024-08-05</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>10</td>
         </tr>
 
-        <tr id="We propose a randomized physics-informed neural network (PINN) or rPINN method for uncertainty quantification in inverse partial differential equation (PDE) problems with noisy data. This method is used to quantify uncertainty in the inverse PDE PINN solutions. Recently, the Bayesian PINN (BPINN) method was proposed, where the posterior distribution of the PINN parameters was formulated using the Bayes' theorem and sampled using approximate inference methods such as the Hamiltonian Monte Carlo (HMC) and variational inference (VI) methods. In this work, we demonstrate that HMC fails to converge for non-linear inverse PDE problems. As an alternative to HMC, we sample the distribution by solving the stochastic optimization problem obtained by randomizing the PINN loss function. The effectiveness of the rPINN method is tested for linear and non-linear Poisson equations, and the diffusion equation with a high-dimensional space-dependent diffusion coefficient. The rPINN method provides informative distributions for all considered problems. For the linear Poisson equation, HMC and rPINN produce similar distributions, but rPINN is on average 27 times faster than HMC. For the non-linear Poison and diffusion equations, the HMC method fails to converge because a single HMC chain cannot sample multiple modes of the posterior distribution of the PINN parameters in a reasonable amount of time.">
+        <tr id="For mathematical and experimental ease, models with time varying parameters are often simplified to assume constant parameters. However, this simplification can potentially lead to identifiability issues (lack of uniqueness of parameter estimates). Methods have been developed to algebraically and numerically determine the identifiability of a model, as well as resolve identifiability issues. This specific type of simplification presents an alternate opportunity to instead use this information to resolve the unidentifiability. Given that re-parameterizing, collecting more data, and adding inputs can be potentially costly or impractical, this could present new alternatives. We present a method for resolving unidentifiability in a system by introducing a new data stream correlated with a parameter of interest. First, we demonstrate how and when non-constant input data can be introduced into any rational function ODE system without worsening the model identifiability. Then, we prove when these input functions improve structural and potentially also practical identifiability for a given model and relevant data. By utilizing pre-existing data streams, these methods can potentially reduce experimental costs, while still answering key questions. By connecting mathematical proofs to application, our framework removes guesswork from when, where, and how researchers can best introduce new data to improve model outcomes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9a72f5071131521363e3f04ad6b40fd9347a43b5" target='_blank'>
-              Randomized Physics-Informed Neural Networks for Bayesian Data Assimilation
+          <td><a href="https://www.semanticscholar.org/paper/fbc38cc84b188d260525dcc553f64371eca970c3" target='_blank'>
+              Examining the impact of forcing function inputs on structural identifiability
               </a>
             </td>
           <td>
-            Yifei Zong, D. Barajas-Solano, A. Tartakovsky
+            Jessica R Conrad, Marisa C Eisenberg
           </td>
-          <td>2024-07-05</td>
+          <td>2024-07-03</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>41</td>
+          <td>0</td>
         </tr>
 
-        <tr id="For mathematical and experimental ease, models with time varying parameters are often simplified to assume constant parameters. However, this simplification can potentially lead to identifiability issues (lack of uniqueness of parameter estimates). Methods have been developed to algebraically and numerically determine the identifiability of a model, as well as resolve identifiability issues. This specific type of simplification presents an alternate opportunity to instead use this information to resolve the unidentifiability. Given that re-parameterizing, collecting more data, and adding inputs can be potentially costly or impractical, this could present new alternatives. We present a method for resolving unidentifiability in a system by introducing a new data stream correlated with a parameter of interest. First, we demonstrate how and when non-constant input data can be introduced into any rational function ODE system without worsening the model identifiability. Then, we prove when these input functions improve structural and potentially also practical identifiability for a given model and relevant data. By utilizing pre-existing data streams, these methods can potentially reduce experimental costs, while still answering key questions. By connecting mathematical proofs to application, our framework removes guesswork from when, where, and how researchers can best introduce new data to improve model outcomes.">
+        <tr id="This paper examines the application of the Kernel Sum of Squares (KSOS) method for enhancing kernel learning from data, particularly in the context of dynamical systems. Traditional kernel-based methods, despite their theoretical soundness and numerical efficiency, frequently struggle with selecting optimal base kernels and parameter tuning, especially with gradient-based methods prone to local optima. KSOS mitigates these issues by leveraging a global optimization framework with kernel-based surrogate functions, thereby achieving more reliable and precise learning of dynamical systems. Through comprehensive numerical experiments on the Logistic Map, Henon Map, and Lorentz System, KSOS is shown to consistently outperform gradient descent in minimizing the relative-$\rho$ metric and improving kernel accuracy. These results highlight KSOS's effectiveness in predicting the behavior of chaotic dynamical systems, demonstrating its capability to adapt kernels to underlying dynamics and enhance the robustness and predictive power of kernel-based approaches, making it a valuable asset for time series analysis in various scientific fields.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fbc38cc84b188d260525dcc553f64371eca970c3" target='_blank'>
-              Examining the impact of forcing function inputs on structural identifiability
+          <td><a href="https://www.semanticscholar.org/paper/be7befd5338268cfdfa3b26e66bece3caef3b91d" target='_blank'>
+              Kernel Sum of Squares for Data Adapted Kernel Learning of Dynamical Systems from Data: A global optimization approach
               </a>
             </td>
           <td>
-            Jessica R Conrad, Marisa C Eisenberg
+            Daniel Lengyel, P. Parpas, B. Hamzi, H. Owhadi
           </td>
-          <td>2024-07-03</td>
+          <td>2024-08-12</td>
           <td>ArXiv</td>
           <td>0</td>
+          <td>36</td>
+        </tr>
+
+        <tr id="Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently, research has introduced the concept of PDEs with Markov switching models, established their well-posedness and presented numerical methods. However, there has been limited discussion on parameter estimation for the jump coefficients in these models. This paper addresses this gap by focusing on parameter inference for the wave equation with Markovian switching. We propose a Bayesian statistical framework using discrete sparse Bayesian learning to establish its convergence and a uniform error bound. Our method requires fewer assumptions and enables independent parameter inference for each segment by allowing different underlying structures for the parameter estimation problem within each segmented time interval. The effectiveness of our approach is demonstrated through three numerical cases, which involve noisy spatiotemporal data from different wave equations with Markovian switching. The results show strong performance in parameter estimation for variable coefficient PDEs.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/5eda7824c0ecf7f45c2be3abef5f95f30fc1aafe" target='_blank'>
+              Parameters Inference for Nonlinear Wave Equations with Markovian Switching
+              </a>
+            </td>
+          <td>
+            Yi Zhang, Zhikun Zhang, Xiangjun Wang
+          </td>
+          <td>2024-08-12</td>
+          <td>ArXiv</td>
           <td>0</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural networks. However, for highly nonlinear real-world applications like aerospace composites processing, existing models often fail to capture underlying solutions accurately and are typically limited to single input functions, constraining rapid process design development. This paper introduces an advanced physics-informed DeepONet tailored for such complex systems with multiple input functions. Equipped with architectural enhancements like nonlinear decoders and effective training strategies such as curriculum learning and domain decomposition, the proposed model handles high-dimensional design spaces with significantly improved accuracy, outperforming the vanilla physics-informed DeepONet by two orders of magnitude. Its zero-shot prediction capability across a broad design space makes it a powerful tool for accelerating composites process design and optimization, with potential applications in other engineering fields characterized by strong nonlinearity.">
+        <tr id="Predicting the dynamics of turbulent fluid flows has long been a central goal of science and engineering. Yet, even with modern computing technology, accurate simulation of all but the simplest turbulent flow-fields remains impossible: the fields are too chaotic and multi-scaled to directly store them in memory and perform time-evolution. An alternative is to treat turbulence $\textit{probabilistically}$, viewing flow properties as random variables distributed according to joint probability density functions (PDFs). Turbulence PDFs are neither chaotic nor multi-scale, but are still challenging to simulate due to their high dimensionality. Here we show how to overcome the dimensionality problem by parameterising turbulence PDFs into an extremely compressed format known as a"tensor network"(TN). The TN paradigm enables simulations on single CPU cores that would otherwise be impractical even with supercomputers: for a $5+1$ dimensional PDF of a chemically reactive turbulent flow, we achieve reductions in memory and computational costs by factors of $\mathcal{O}(10^6)$ and $\mathcal{O}(10^3)$, respectively, compared to standard finite difference algorithms. A future path is opened towards something heretofore regarded as infeasible: directly simulating high-dimensional PDFs of both turbulent flows and other chaotic systems that are useful to describe probabilistically.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f126a96d65c71da6172a1c8961580b6248f14d65" target='_blank'>
-              An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Study
+          <td><a href="https://www.semanticscholar.org/paper/241b90969989bdb43a42587945b6b357630bfd72" target='_blank'>
+              Tensor networks enable the calculation of turbulence probability distributions
               </a>
             </td>
           <td>
-            Milad Ramezankhani, A. Deodhar, Rishi Parekh, Dagnachew Birru
+            Nikita Gourianov, P. Givi, Dieter Jaksch, Stephen B. Pope
           </td>
-          <td>2024-06-20</td>
+          <td>2024-07-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>31</td>
         </tr>
 
         <tr id="This paper presents the open-source stochastic model predictive control framework GRAMPC-S for nonlinear uncertain systems with chance constraints. It provides several uncertainty propagation methods to predict stochastic moments of the system state and can consider unknown parts of the system dynamics using Gaussian process regression. These methods are used to reformulate a stochastic MPC formulation as a deterministic one that is solved with GRAMPC. The performance of the presented framework is evaluated using examples from a wide range of technical areas. The experimental evaluation shows that GRAMPC-S can be used in practice for the control of nonlinear uncertain systems with sampling times in the millisecond range.">
@@ -1970,12 +2075,12 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
               </a>
             </td>
           <td>
-            D. Landgraf, Andreas Volz, Knut Graichen
+            D. Landgraf, Andreas Völz, Knut Graichen
           </td>
           <td>2024-07-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>9</td>
         </tr>
 
         <tr id="In this study, we present a novel non-intrusive reduced-order model (ROM) for solving time-dependent stochastic partial differential equations (SPDEs). Utilizing proper orthogonal decomposition (POD), we extract spatial modes from high-fidelity solutions. A dynamic mode decomposition (DMD) method is then applied to vertically stacked matrices of projection coefficients for future prediction of coefficient fields. Polynomial chaos expansion (PCE) is employed to construct a mapping from random parameter inputs to the DMD-predicted coefficient field. These lead to the POD-DMD-PCE method. The innovation lies in vertically stacking projection coefficients, ensuring time-dimensional consistency in the coefficient matrix for DMD and facilitating parameter integration for PCE analysis. This method combines the model reduction of POD with the time extrapolation strengths of DMD, effectively recovering field solutions both within and beyond the training time interval. The efficiency and time extrapolation capabilities of the proposed method are validated through various nonlinear SPDEs. These include a reaction-diffusion equation with 19 parameters, a two-dimensional heat equation with two parameters, and a one-dimensional Burgers equation with three parameters.">
@@ -1993,19 +2098,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>7</td>
         </tr>
 
-        <tr id="Data-enabled predictive control (DeePC) for linear systems utilizes data matrices of recorded trajectories to directly predict new system trajectories, which is very appealing for real-life applications. In this paper we leverage the universal approximation properties of neural networks (NNs) to develop neural DeePC algorithms for nonlinear systems. Firstly, we point out that the outputs of the last hidden layer of a deep NN implicitly construct a basis in a so-called neural (feature) space, while the output linear layer performs affine interpolation in the neural space. As such, we can train off-line a deep NN using large data sets of trajectories to learn the neural basis and compute on-line a suitable affine interpolation using DeePC. Secondly, methods for guaranteeing consistency of neural DeePC and for reducing computational complexity are developed. Several neural DeePC formulations are illustrated on a nonlinear pendulum example.">
+        <tr id="We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning (DL). The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple residual convolutional neural network, while assuming the dynamics to be known. Experiments are performed with the Lorenz 96 dynamics, which display spatiotemporal chaos and for which solid benchmarks for DA performance exist. The accuracy of the states obtained from the learned analysis approaches that of the best possibly tuned ensemble Kalman filter (EnKF), and is far better than that of variational DA alternatives. Critically, this can be achieved while propagating even just a single state in the forecast step. We investigate the reason for achieving ensemble filtering accuracy without an ensemble. We diagnose that the analysis scheme actually identifies key dynamical perturbations, mildly aligned with the unstable subspace, from the forecast state alone, without any ensemble-based covariances representation. This reveals that the analysis scheme has learned some multiplicative ergodic theorem associated to the DA process seen as a non-autonomous random dynamical system.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9e9290726d4b4f1bdd4194482dd006f7ef5fa49f" target='_blank'>
-              Neural Data-Enabled Predictive Control
+          <td><a href="https://www.semanticscholar.org/paper/049cb29c29c44d7bcd0b2872f2cc68742751159c" target='_blank'>
+              Deep learning-based sequential data assimilation for chaotic dynamics identifies local instabilities from single state forecasts
               </a>
             </td>
           <td>
-            Mircea Lazar
+            Marc Bocquet, A. Farchi, Tobias S. Finn, Charlotte Durand, Sibo Cheng, Yumeng Chen, I. Pasmans, A. Carrassi
           </td>
-          <td>2024-06-12</td>
+          <td>2024-08-08</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>28</td>
         </tr>
 
         <tr id="We provide an algorithm for the simultaneous system identification and model predictive control of nonlinear systems. The algorithm has finite-time near-optimality guarantees and asymptotically converges to the optimal (non-causal) controller. Particularly, the algorithm enjoys sublinear dynamic regret, defined herein as the suboptimality against an optimal clairvoyant controller that knows how the unknown disturbances and system dynamics will adapt to its actions. The algorithm is self-supervised and applies to control-affine systems with unknown dynamics and disturbances that can be expressed in reproducing kernel Hilbert spaces. Such spaces can model external disturbances and modeling errors that can even be adaptive to the system's state and control input. For example, they can model wind and wave disturbances to aerial and marine vehicles, or inaccurate model parameters such as inertia of mechanical systems. The algorithm first generates random Fourier features that are used to approximate the unknown dynamics or disturbances. Then, it employs model predictive control based on the current learned model of the unknown dynamics (or disturbances). The model of the unknown dynamics is updated online using least squares based on the data collected while controlling the system. We validate our algorithm in both hardware experiments and physics-based simulations. The simulations include (i) a cart-pole aiming to maintain the pole upright despite inaccurate model parameters, and (ii) a quadrotor aiming to track reference trajectories despite unmodeled aerodynamic drag effects. The hardware experiments include a quadrotor aiming to track a circular trajectory despite unmodeled aerodynamic drag effects, ground effects, and wind disturbances.">
@@ -2023,214 +2128,199 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>19</td>
         </tr>
 
-        <tr id="None">
+        <tr id="We consider the problem of data-driven stochastic optimal control of an unknown LTI dynamical system. Assuming the process noise is normally distributed, we pose the problem of steering the state's mean and covariance to a target normal distribution, under noisy data collected from the underlying system, a problem commonly referred to as covariance steering (CS). A novel framework for Data-driven Uncertainty quantification and density STeering (DUST) is presented that simultaneously characterizes the noise affecting the measured data and designs an optimal affine-feedback controller to steer the density of the state to a prescribed terminal value. We use both indirect and direct data-driven design approaches based on the notions of persistency of excitation and subspace predictors to exactly represent the mean and covariance dynamics of the state in terms of the data and noise realizations. Since both the mean and the covariance steering sub-problems are plagued with distributional uncertainty arising from noisy data collection, we first estimate the noise realization from this dataset and subsequently compute tractable upper bounds on the estimation errors. The moment steering problems are then solved to optimality using techniques from robust control and robust optimization. Lastly, we present an alternative control design approach based on the certainty equivalence principle and interpret the problem as one of CS under multiplicative uncertainties. We analyze the performance and efficacy of each of these data-driven approaches using a case study and compare them with their model-based counterparts.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/233d8ac0f20cf948548fc9238018c681a00d4cec" target='_blank'>
-              Structure-preserving formulations for data-driven analysis of coupled multi-physics systems
+          <td><a href="https://www.semanticscholar.org/paper/63a1f296701b24baf2d77272d401b9179d8d8312" target='_blank'>
+              DUST: A Framework for Data-Driven Density Steering
               </a>
             </td>
           <td>
-            Alba Muixí, David González, Francisco Chinesta, Elías Cueto
+            Joshua Pilipovsky, Panagiotis Tsiotras
           </td>
-          <td>2024-06-07</td>
-          <td>Computational Mechanics</td>
+          <td>2024-08-05</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>13</td>
+          <td>5</td>
         </tr>
 
-        <tr id="The contributions of this technical note are twofold. Firstly, we formulate an optimization problem to obtain a linear representation of a nonlinear vector field based on a system's trajectory. We also prove that its cost function is strictly convex, given the trajectory is persistently exciting. Under certain observability conditions, we provide results that guarantee the Hurwitz stability of the global minimizer. Secondly, we present a novel algorithm based on point-wise geometric flows to estimate the boundary of the region of attraction. We show that the algorithm converges to the exact boundary of the region of attraction under certain assumptions on the system dynamics. Finally, we validate the results using simulations on various nonlinear autonomous systems.">
+        <tr id="Pedestrian crowds encompass a complex interplay of intentional movements aimed at reaching specific destinations, fluctuations due to personal and interpersonal variability, and interactions with each other and the environment. Previous work showed the effectiveness of Langevin-like equations in capturing the statistical properties of pedestrian dynamics in simple settings, such as almost straight trajectories. However, modeling more complex dynamics, e.g. when multiple routes and origin-destinations are involved, remains a significant challenge. In this work, we introduce a novel and generic framework to describe the dynamics of pedestrians in any geometric setting, significantly extending previous works. Our model is based on Langevin dynamics with two timescales. The fast timescale corresponds to the stochastic fluctuations present when a pedestrian is walking. The slow timescale is associated with the dynamics that a pedestrian plans to follow, thus a smoother path. Employing a data-driven approach inspired by statistical field theories, we learn the complex potentials directly from the data, namely a high-statistics database of real-life pedestrian trajectories. This approach makes the model generic as the potentials can be read from any trajectory data set and the underlying Langevin structure enables physics-based insights. We validate our model through a comprehensive statistical analysis, comparing simulated trajectories with actual pedestrian measurements across five complementary settings, including a real-life train platform scenario, underscoring its practical societal relevance. We show that our model effectively captures fluctuation statistics in pedestrian motion. Beyond providing fundamental insights and predictive capabilities in pedestrian dynamics, our model could be used to investigate generic active dynamics such as vehicular traffic and collective animal behavior.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4f60368ae370b28f9ac8a52aafa0723b5154ed62" target='_blank'>
-              Analog Data-Driven Theory and Estimation of the Region of Attraction Using Sampled-Data
+          <td><a href="https://www.semanticscholar.org/paper/c76fb4ec34bb7b21a1b522e6fe51864181436102" target='_blank'>
+              Data-driven physics-based modeling of pedestrian dynamics
               </a>
             </td>
           <td>
-            Karthik Shenoy, Arvind Ragghav, V. Chellaboina
+            C. Pouw, Geert G.M. van der Vleuten, Alessandro Corbetta, Federico Toschi
           </td>
-          <td>2024-07-11</td>
+          <td>2024-07-30</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>30</td>
+          <td>18</td>
         </tr>
 
-        <tr id="This paper aims to construct a representation to approximate the behavior of linear time-invariant systems from a large data set whose input contains unmeasured uncertainty and output is subject to measurement noise. Using big data combined with the statistical properties of the input uncertainty and measurement noise, the covariance of the input uncertainty and the output can be approximated. This enables the construction of an approximate covariance of the trajectories in the data set, through which a representation for the approximation of system behavior is obtained. The behavior of this representation is shown to converge in probability to the true behavior. An illustrative example is provided to show that the proposed representation is able to predict the system trajectory to a satisfactory accuracy. The result of this paper provides a potential basis for the development of data-based trajectory estimation and predictive control algorithm when the system input uncertainty is unmeasured.">
+        <tr id="Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems. The nonequilibrium properties of many-body systems can be described by the dynamics of the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff-Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time simulations. In this paper, we develop an operator-learning framework based on Recurrent Neural Networks (RNNs) to address this challenge. The proposed framework utilizes RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. This new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$, where $N_t$ is the total time steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through different numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/963fe53a6065bfdb118e3128347e8c5bfc500a1d" target='_blank'>
-              Approximating the System Behavior with Input Uncertainty Using Big Data
+          <td><a href="https://www.semanticscholar.org/paper/526a9cb7b29055f6d28d2a654e064ac8a68bb587" target='_blank'>
+              Predicting nonequilibrium Green's function dynamics and photoemission spectra via nonlinear integral operator learning
               </a>
             </td>
           <td>
-            Yitao Yan, Jie Bao, Biao Huang
+            Yuanran Zhu, Jia Yin, Cian C. Reeves, Chao Yang, Vojtěch Vlček
           </td>
-          <td>2024-06-18</td>
-          <td>2024 IEEE 18th International Conference on Control & Automation (ICCA)</td>
-          <td>0</td>
-          <td>6</td>
+          <td>2024-07-13</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>4</td>
         </tr>
 
-        <tr id="In this paper, we introduce semi-autonomous neural ordinary differential equations (SA-NODEs), a variation of the vanilla NODEs, employing fewer parameters. We investigate the universal approximation properties of SA-NODEs for dynamical systems from both a theoretical and a numerical perspective. Within the assumption of a finite-time horizon, under general hypotheses we establish an asymptotic approximation result, demonstrating that the error vanishes as the number of parameters goes to infinity. Under additional regularity assumptions, we further specify this convergence rate in relation to the number of parameters, utilizing quantitative approximation results in the Barron space. Based on the previous result, we prove an approximation rate for transport equations by their neural counterparts. Our numerical experiments validate the effectiveness of SA-NODEs in capturing the dynamics of various ODE systems and transport equations. Additionally, we compare SA-NODEs with vanilla NODEs, highlighting the superior performance and reduced complexity of our approach.">
+        <tr id="Predicting chaotic systems is crucial for understanding complex behaviors, yet challenging due to their sensitivity to initial conditions and inherent unpredictability. Probabilistic Reservoir Computing (RC) is well-suited for long-term chaotic predictions by handling complex dynamic systems. Spin-Orbit Torque (SOT) devices in spintronics, with their nonlinear and probabilistic operations, can enhance performance in these tasks. This study proposes an RC system utilizing SOT devices for predicting chaotic dynamics. By simulating the reservoir in an RC network with SOT devices that achieve nonlinear resistance changes with random distribution, we enhance the robustness for the predictive capability of the model. The RC network predicted the behaviors of the Mackey-Glass and Lorenz chaotic systems, demonstrating that stochastic SOT devices significantly improve long-term prediction accuracy.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0c428906ea1c6ad6b5b45bc8a6ac5d654dad8749" target='_blank'>
-              Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications
+          <td><a href="https://www.semanticscholar.org/paper/c63d0c8c5a8e26832c065f07e28872c0828b13c7" target='_blank'>
+              Improved Long-Term Prediction of Chaos Using Reservoir Computing Based on Stochastic Spin-Orbit Torque Devices
               </a>
             </td>
           <td>
-            Ziqian Li, Kang Liu, Lorenzo Liverani, Enrique Zuazua
+            Cen Wang, Xinyao Lei, Kaiming Cai, Xiaofei Yang, Yue Zhang
           </td>
-          <td>2024-07-24</td>
+          <td>2024-07-02</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="Given the complexity and nonlinearity inherent in traffic dynamics within vehicular platoons, there exists a critical need for a modeling methodology with high accuracy while concurrently achieving physical analyzability. Currently, there are two predominant approaches: the physics model-based approach and the Artificial Intelligence (AI)--based approach. Knowing the facts that the physical-based model usually lacks sufficient modeling accuracy and potential function mismatches and the pure-AI-based method lacks analyzability, this paper innovatively proposes an AI-based Koopman approach to model the unknown nonlinear platoon dynamics harnessing the power of AI and simultaneously maintain physical analyzability, with a particular focus on periods of traffic oscillation. Specifically, this research first employs a deep learning framework to generate the embedding function that lifts the original space into the embedding space. Given the embedding space descriptiveness, the platoon dynamics can be expressed as a linear dynamical system founded by the Koopman theory. Based on that, the routine of linear dynamical system analysis can be conducted on the learned traffic linear dynamics in the embedding space. By that, the physical interpretability and analyzability of model-based methods with the heightened precision inherent in data-driven approaches can be synergized. Comparative experiments have been conducted with existing modeling approaches, which suggests our method's superiority in accuracy. Additionally, a phase plane analysis is performed, further evidencing our approach's effectiveness in replicating the complex dynamic patterns. Moreover, the proposed methodology is proven to feature the capability of analyzing the stability, attesting to the physical analyzability.">
+        <tr id="With the rapid development of articial intelligence, especially deep learning technology, scientic researchers have begun to explore its application in the eld of traditional scientic computing. Traditional scientic computing relies on mathematical equations to describe and predict the scientic laws of nature, while deep learning provides a new perspective to solve complex mathematical problems by learning patterns in data. The introduction of the Physical Information Neural Network (PINN) and the Ordinary Dierential Equation (ODENet) network layer enables deep learning technology to more accurately simulate and predict scientic phenomena. This study shows that by embedding an ODE-Net network layer in a physical information neural network (PINN), the tting accuracy and generalization performance of the model can be signicantly improved. Experimental results show that compared with traditional numerical methods and fully connected neural networks, this model combined with deep learning technology not only shows higher accuracy when solving partial dierential equations, but also exhibits faster convergence speed and stronger adaptability. These ndings not only promote the integration of scientic computing and deep learning, but also provide new research directions and practical strategies for using deep learning technology to solve complex scientic problems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/61de6c4570b16ba2cf34ebf49465dfa322f09fda" target='_blank'>
-              Physically Analyzable AI-Based Nonlinear Platoon Dynamics Modeling During Traffic Oscillation: A Koopman Approach
+          <td><a href="https://www.semanticscholar.org/paper/dedb6a263e8acff267028f948e0fbc5cc501e50c" target='_blank'>
+              A numerical method to solve PDE through PINN based on ODENet
               </a>
             </td>
           <td>
-            Kexin Tian, Haotian Shi, Yang Zhou, Sixu Li
+            Ziyi Wang
           </td>
-          <td>2024-06-20</td>
-          <td>ArXiv</td>
+          <td>2024-06-24</td>
+          <td>Applied and Computational Engineering</td>
+          <td>0</td>
           <td>0</td>
-          <td>6</td>
         </tr>
 
-        <tr id="We report synthesis of an open source test data set and work in progress to expand it. Sophisticated data mining and Machine Learning (ML) techniques can discover statistical associations among variables that may or may not reflect actual causal dependencies. In many applications, systems must discriminate between associations that are mere coincidences and those that are at least plausibly causal. Further, a graph of causal relationships may be complex, with fan-in, fan-out, transitive, and various combinations of, dependencies. To test a system’s power to filter out non-causal associations and untangle the causal web, suitable synthetic data is needed. We report the development, in Wolfram Mathematica, of code that synthesizes data with subtle, complex, causal dependencies among some but not all of the generated observable variables. We implement several simple dissipative chaotic flows. Four (4) are autonomous, six (6) are driven. Among the resulting ten (10) observable state vectors, there are forty-five (45) potential pairwise (1:1) relationships, of which four (4) are strong, five (5) are moderate, three (3) are weak, for a total of twelve (12) that are actually causal, and any others are mere statistical artifacts that a tool under test should reject. Each system’s observables are corrupted by additive Gaussian noise. Each system’s hidden dynamics are disturbed by a normal Wiener process. The levels of these stochastic components are parameterized to make problem difficulty tunable. A set of generated data and code for generating more will be released openly on-line.">
+        <tr id="Chaotic systems, such as turbulent flows, are ubiquitous in science and engineering. However, their study remains a challenge due to the large range scales, and the strong interaction with other, often not fully understood, physics. As a consequence, the spatiotemporal resolution required for accurate simulation of these systems is typically computationally infeasible, particularly for applications of long-term risk assessment, such as the quantification of extreme weather risk due to climate change. While data-driven modeling offers some promise of alleviating these obstacles, the scarcity of high-quality simulations results in limited available data to train such models, which is often compounded by the lack of stability for long-horizon simulations. As such, the computational, algorithmic, and data restrictions generally imply that the probability of rare extreme events is not accurately captured. In this work we present a general strategy for training neural network models to non-intrusively correct under-resolved long-time simulations of chaotic systems. The approach is based on training a post-processing correction operator on under-resolved simulations nudged towards a high-fidelity reference. This enables us to learn the dynamics of the underlying system directly, which allows us to use very little training data, even when the statistics thereof are far from converged. Additionally, through the use of probabilistic network architectures we are able to leverage the uncertainty due to the limited training data to further improve extrapolation capabilities. We apply our framework to severely under-resolved simulations of quasi-geostrophic flow and demonstrate its ability to accurately predict the anisotropic statistics over time horizons more than 30 times longer than the data seen in training.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8c21bbba8736b5afd19182b829dfd6049fad4e46" target='_blank'>
-              Coupled dynamical systems data for testing detection of subtle causal dependencies
+          <td><a href="https://www.semanticscholar.org/paper/04ef0e9cecd284e7e1805b26a448f7108f474e9b" target='_blank'>
+              A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training data
               </a>
             </td>
           <td>
-            Stuart W. Card
+            Benedikt Barthel Sorensen, Leonardo Zepeda-N'unez, Ignacio Lopez-Gomez, Zhong Yi Wan, Rob Carver, Fei Sha, T. Sapsis
           </td>
-          <td>2024-06-07</td>
-          <td>None</td>
-          <td>1</td>
-          <td>1</td>
+          <td>2024-08-02</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>39</td>
         </tr>
 
-        <tr id="The advancement of scientific machine learning (ML) techniques has led to the development of methods for approximating solutions to nonlinear partial differential equations (PDE) with increased efficiency and accuracy. Automatic differentiation has played a pivotal role in this progress, enabling the creation of physics-informed neural networks (PINN) that integrate relevant physics into machine learning models. PINN have shown promise in approximating the solutions to the Navier–Stokes equations, overcoming the limitations of traditional numerical discretization methods. However, challenges such as local minima and long training times persist, motivating the exploration of domain decomposition techniques to improve it. Previous domain decomposition models have introduced spatial and temporal domain decompositions but have yet to fully address issues of smoothness and regularity of global solutions. In this study, we present a novel domain decomposition approach for PINN, termed domain-discretized PINN (DD-PINN), which incorporates complementary loss functions, subdomain-specific transformer networks (TRF), and independent optimization within each subdomain. By enforcing continuity and differentiability through interface constraints and leveraging the Sobolev (H 1) norm of the mean squared error (MSE), rather than the Euclidean norm (L 2), DD-PINN enhances solution regularity and accuracy. The inclusion of TRF in each subdomain facilitates feature extraction and improves convergence rates, as demonstrated through simulations of threetest problems: steady-state flow in a two-dimensional lid-driven cavity, the time-dependent cylinder wake, and the viscous Burgers equation. Numerical comparisons highlight the effectiveness of DD-PINN in preserving global solution regularity and accurately approximating complex phenomena, marking a significant advancement over previous domain decomposition methods within the PINN framework.">
+        <tr id="There is overwhelming evidence that cognition, perception, and action rely on feedback control. However, if and how neural population dynamics are amenable to different control strategies is poorly understood, in large part because machine learning methods to directly assess controllability in neural population dynamics are lacking. To address this gap, we developed a novel dimensionality reduction method, Feedback Controllability Components Analysis (FCCA), that identifies subspaces of linear dynamical systems that are most feedback controllable based on a new measure of feedback controllability. We further show that PCA identifies subspaces of linear dynamical systems that maximize a measure of feedforward controllability. As such, FCCA and PCA are data-driven methods to identify subspaces of neural population data (approximated as linear dynamical systems) that are most feedback and feedforward controllable respectively, and are thus natural contrasts for hypothesis testing. We developed new theory that proves that non-normality of underlying dynamics determines the divergence between FCCA and PCA solutions, and confirmed this in numerical simulations. Applying FCCA to diverse neural population recordings, we find that feedback controllable dynamics are geometrically distinct from PCA subspaces and are better predictors of animal behavior. Our methods provide a novel approach towards analyzing neural population dynamics from a control theoretic perspective, and indicate that feedback controllable subspaces are important for behavior.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ea15c09f70a4fe243856a69a988cd4b37e7e4a11" target='_blank'>
-              A novel discretized physics-informed neural network model applied to the Navier–Stokes equations
+          <td><a href="https://www.semanticscholar.org/paper/b12cb2ef2eca3c8ee46436c8d7fddcc5787df892" target='_blank'>
+              Identifying Feedforward and Feedback Controllable Subspaces of Neural Population Dynamics
               </a>
             </td>
           <td>
-            Amirhossein Khademi, Steven Dufour
+            Ankit Kumar, Loren M. Frank, Kristofer E. Bouchard
           </td>
-          <td>2024-06-07</td>
-          <td>Physica Scripta</td>
+          <td>2024-08-11</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>5</td>
         </tr>
 
-        <tr id="This paper investigates the dynamics of cosmological models incorporating nonlinear electrodynamics (NLED), focusing on their stability and causality. We explore two specific NLED models: the Power-Law and Rational Lagrangians. We assess these models' viability in describing the universe's evolution using dynamical systems theory and Bayesian inference. We present the theoretical framework of NLED coupled with general relativity, followed by an analysis of the stability and causality through the squared sound speed of the NLED Lagrangians. We then conduct a detailed dynamical analysis to identify the universe's evolution with this matter content. Our results show that the Power-Law Lagrangian model transitions through various cosmological phases from a Maxwell radiation-dominated state to a matter-dominated state. For the Rational Lagrangian model, including the Maxwell term, stable and causal behavior is observed within specific parameter ranges, with critical points indicating the evolutionary pathways of the universe. To validate our theoretical findings, we perform Bayesian parameter estimation using a comprehensive set of observational data, including cosmic chronometers, Baryon Acoustic Oscillation (BAO) measurements, and Type Ia Supernovae (SNeIa). The estimated parameters for both models align with expected values for the current universe, particularly the matter density $\Omega_m$ and the Hubble parameter $h$. However, the parameters $\alpha$ and $b$ are not tightly constrained within the prior ranges. Our model comparison strongly favors the $\Lambda$CDM model over the NLED models for late-universe observations, as the NLED model does not exhibit a cosmological constant behavior. Our results highlight the need for further refinement and exploration of NLED-based cosmological models to fully integrate them into the standard cosmological framework.">
+        <tr id="Studies show that artificial intelligence (AI) with embedded physics solvers has improved the accuracy of predictions on various physics problems, especially those associated with fluid dynamics. The crucial element in optimizing weight training for estimating flow fields within the AI network lies in the choice of the loss function. In addressing regression-type problems, particularly those involving the temporal evolution of flow fields, the mean square error (MSE) loss function is commonly employed at the current and single time step. However, an issue arises in existing methodologies that utilize MSE-based loss functions with single-time step information for predicting unsteady flow. Most of these approaches overlook the significance of incorporating the temporal history of the flow, a factor that cannot be disregarded in the context of numerical solvers. Hence, in this work, a physics-based AI (PbAI) method with higher-order loss functions is applied to unsteady scenarios, in particular to two distinct turbulent flows where a multitude of fine structures is present, namely, forced and decaying turbulence. Direct numerical simulations on uniform Cartesian grids are conducted to simulate these scenarios, generating two distinct datasets for training and inference. Each dataset comprises 32 randomly initialized conditions spanning 4, 848 time steps for each turbulent flow type. Five distinct models are devised, incorporating features such as rollouts from coarse numerical solvers and temporal considerations in the loss function calculation. The constructed PbAI models demonstrate consistent improvements in predictive performance over the entire temporal domain. These findings are further corroborated through vorticity correlation analyses. The empirical result demonstrates that the accuracy of the baseline case improves by up to 48% and 30% for forced and decaying turbulence, respectively. These results significantly underscore the importance of the temporal histories of flow in the loss function in enhancing predictive capabilities for complex and unsteady turbulent flows.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/530617a7cd0b3388c0d7af097d46362991b5398b" target='_blank'>
-              Exploring the Evolution of Nonlinear Electrodynamics in the Universe: A Dynamical Systems Approach
+          <td><a href="https://www.semanticscholar.org/paper/e6a508269bfb08f5c8c66413efa4d444da72838f" target='_blank'>
+              Multi-Order Loss Functions For Accelerating Unsteady Flow Simulations with Physics-Based AI
               </a>
             </td>
           <td>
-            Ricardo Garc'ia-Salcedo, Isidro G'omez-Vargas, Tam'e Gonz'alez, Vicent Martinez-Badenes, Israel Quiros
+            Wei Xian Lim, Naheed Anjum Arafat, Wai Lee Chan, Adams Kong
           </td>
-          <td>2024-06-30</td>
-          <td>ArXiv</td>
+          <td>2024-06-25</td>
+          <td>2024 IEEE Conference on Artificial Intelligence (CAI)</td>
           <td>0</td>
-          <td>3</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or data assimilation. In many cases, their tightest stability condition is coming from a linear term. Exponential time differencing (ETD) is known to produce highly stable numerical schemes by treating the linear term in an exact fashion. In particular, for stiff problems, ETD methods are a method of choice. We propose an extension of the class of ETD algorithms to matrix-valued dynamical equations. This allows us to produce highly efficient and stable integration schemes. We show their efficiency and applicability for a variety of real-world problems, from geophysical applications to dynamical problems in machine learning.">
+        <tr id="There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the underlying chaotic systems is a notoriously difficult task. Building on prior theoretical studies that focus on the discontinuities at $q=1$ in the order-$q$ R\'enyi-entropy of the trajectory space, we measure the derivative of the spectrum. We derive within the general context of Markov processes a computationally efficient closed-form expression for this measure. We investigate its properties through well-known dynamical systems exploring its scope and limitations. The proposed mathematical instrument can serve as a predictor of dynamical phase transitions in time series.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f314941ad68915d7af43429006a76cffcf6ab2db" target='_blank'>
-              Exponential time differencing for matrix-valued dynamical systems
+          <td><a href="https://www.semanticscholar.org/paper/68dbc71449fe5142fd6c84de4af2b46f1f3412b9" target='_blank'>
+              Measuring dynamical phase transitions in time series
               </a>
             </td>
           <td>
-            Nayef Shkeir, Tobias Schäfer, T. Grafke
+            Bulcs'u S'andor, Andr'as Rusu, K'aroly D'enes, M'aria Ercsey-Ravasz, Zs.I. L'az'ar
           </td>
-          <td>2024-06-19</td>
+          <td>2024-07-18</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>14</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Predicting chaotic dynamical systems is critical in many scientific fields such as weather prediction, but challenging due to the characterizing sensitive dependence on initial conditions. Traditional modeling approaches require extensive domain knowledge, often leading to a shift towards data-driven methods using machine learning. However, existing research provides inconclusive results on which machine learning methods are best suited for predicting chaotic systems. In this paper, we compare different lightweight and heavyweight machine learning architectures using extensive existing databases, as well as a newly introduced one that allows for uncertainty quantification in the benchmark results. We perform hyperparameter tuning based on computational cost and introduce a novel error metric, the cumulative maximum error, which combines several desirable properties of traditional metrics, tailored for chaotic systems. Our results show that well-tuned simple methods, as well as untuned baseline methods, often outperform state-of-the-art deep learning models, but their performance can vary significantly with different experimental setups. These findings underscore the importance of matching prediction methods to data characteristics and available computational resources.">
+        <tr id=""AI for Science"aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a central component of scientific-ML. Physics-Informed Neural Networks (PINNs) is the general method that has evolved for this task but its training is well-known to be very unstable. In this work we explore the possibility of changing the model being trained from being just a neural network to being a non-linear transformation of it - one that algebraically includes the boundary/initial conditions. This reduces the number of terms in the loss function than the standard PINN losses. We demonstrate that our modification leads to significant performance gains across a range of benchmark tasks, in various dimensions and without having to tweak the training algorithm. Our conclusions are based on conducting hundreds of experiments, in the fully unsupervised setting, over multiple linear and non-linear PDEs set to exactly solvable scenarios, which lends to a concrete measurement of our performance gains in terms of order(s) of magnitude lower fractional errors being achieved, than by standard PINNs. The code accompanying this manuscript is publicly available at, https://github.com/MorganREN/Improving-PINNs-By-Algebraic-Inclusion-of-Boundary-and-Initial-Conditions">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5acbbc502b5f063b4661a749a95f9833ab9d11c1" target='_blank'>
-              Machine Learning for predicting chaotic systems
+          <td><a href="https://www.semanticscholar.org/paper/50ec057bbac038765a71bbcf35743418ac73a1d3" target='_blank'>
+              Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions
               </a>
             </td>
           <td>
-            Christof Schötz, Alistair White, Maximilian Gelbrecht, Niklas Boers
+            Mohan Ren, Zhihao Fang, Keren Li, Anirbit Mukherjee
           </td>
-          <td>2024-07-29</td>
+          <td>2024-07-30</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>5</td>
         </tr>
 
-        <tr id="With the rapid development of articial intelligence, especially deep learning technology, scientic researchers have begun to explore its application in the eld of traditional scientic computing. Traditional scientic computing relies on mathematical equations to describe and predict the scientic laws of nature, while deep learning provides a new perspective to solve complex mathematical problems by learning patterns in data. The introduction of the Physical Information Neural Network (PINN) and the Ordinary Dierential Equation (ODENet) network layer enables deep learning technology to more accurately simulate and predict scientic phenomena. This study shows that by embedding an ODE-Net network layer in a physical information neural network (PINN), the tting accuracy and generalization performance of the model can be signicantly improved. Experimental results show that compared with traditional numerical methods and fully connected neural networks, this model combined with deep learning technology not only shows higher accuracy when solving partial dierential equations, but also exhibits faster convergence speed and stronger adaptability. These ndings not only promote the integration of scientic computing and deep learning, but also provide new research directions and practical strategies for using deep learning technology to solve complex scientic problems.">
+        <tr id="Abstract The advent of machine learning has led to innovative approaches in dealing with clinical data. Among these, Neural Ordinary Differential Equations (Neural ODEs), hybrid models merging mechanistic with deep learning models have shown promise in accurately modeling continuous dynamical systems. Although initial applications of Neural ODEs in the field of model‐informed drug development and clinical pharmacology are becoming evident, applying these models to actual clinical trial datasets—characterized by sparse and irregularly timed measurements—poses several challenges. Traditional models often have limitations with sparse data, highlighting the urgent need to address this issue, potentially through the use of assumptions. This review examines the fundamentals of Neural ODEs, their ability to handle sparse and irregular data, and their applications in model‐informed drug development.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/dedb6a263e8acff267028f948e0fbc5cc501e50c" target='_blank'>
-              A numerical method to solve PDE through PINN based on ODENet
+          <td><a href="https://www.semanticscholar.org/paper/d55a1a4acc93d905399f2126e7beb524fd64ec38" target='_blank'>
+              Bridging pharmacology and neural networks: A deep dive into neural ordinary differential equations
               </a>
             </td>
           <td>
-            Ziyi Wang
+            Idris Bachali Losada, N. Terranova
           </td>
-          <td>2024-06-24</td>
-          <td>Applied and Computational Engineering</td>
-          <td>0</td>
+          <td>2024-07-11</td>
+          <td>CPT: Pharmacometrics & Systems Pharmacology</td>
           <td>0</td>
+          <td>12</td>
         </tr>
 
-        <tr id="We present ConDiff, a novel dataset for scientific machine learning. ConDiff focuses on the diffusion equation with varying coefficients, a fundamental problem in many applications of parametric partial differential equations (PDEs). The main novelty of the proposed dataset is that we consider discontinuous coefficients with high contrast. These coefficient functions are sampled from a selected set of distributions. This class of problems is not only of great academic interest, but is also the basis for describing various environmental and industrial problems. In this way, ConDiff shortens the gap with real-world problems while remaining fully synthetic and easy to use. ConDiff consists of a diverse set of diffusion equations with coefficients covering a wide range of contrast levels and heterogeneity with a measurable complexity metric for clearer comparison between different coefficient functions. We baseline ConDiff on standard deep learning models in the field of scientific machine learning. By providing a large number of problem instances, each with its own coefficient function and right-hand side, we hope to encourage the development of novel physics-based deep learning approaches, such as neural operators and physics-informed neural networks, ultimately driving progress towards more accurate and efficient solutions of complex PDE problems.">
+        <tr id="The treatment of Hall-effect thrusters as nonlinear, dynamical systems has emerged as a new perspective to understand and analyze data acquired from the thrusters. The acquisition of high-speed data that can resolve the characteristic high-frequency oscillations of these thruster enables additional levels of classification in these thrusters. Notably, these signals may serve as unique indicators for the full state of the system that can aid digital representations of thrusters and predictions of thruster dynamics. In this work, a Reservoir Computing framework is explored to build surrogate models from experimental time-series measurements of a Hall-effect thruster. Such a framework has shown immense promise for predicting the behavior of low-dimensional yet chaotic dynamical systems. In particular, the surrogates created by the Reservoir Computing framework are capable of both predicting the observed behavior of the thruster and estimating the values of certain measurements from others, known as inference.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5b93a26257c0ccfa34050385c31006a18b0c2538" target='_blank'>
-              ConDiff: A Challenging Dataset for Neural Solvers of Partial Differential Equations
+          <td><a href="https://www.semanticscholar.org/paper/408d323572dab3c6a6dc96e645703d0f78eee449" target='_blank'>
+              Time-Resolved Data-Driven Surrogates of Hall-effect Thrusters
               </a>
             </td>
           <td>
-            Vladislav Trifonov, Alexander Rudikov, Oleg Iliev, I. Oseledets, Ekaterina A. Muravleva
+            Adrian S. Wong, Christine M. Greve, Daniel Q. Eckhardt
           </td>
-          <td>2024-06-07</td>
+          <td>2024-08-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
-        </tr>
-
-        <tr id="Studies show that artificial intelligence (AI) with embedded physics solvers has improved the accuracy of predictions on various physics problems, especially those associated with fluid dynamics. The crucial element in optimizing weight training for estimating flow fields within the AI network lies in the choice of the loss function. In addressing regression-type problems, particularly those involving the temporal evolution of flow fields, the mean square error (MSE) loss function is commonly employed at the current and single time step. However, an issue arises in existing methodologies that utilize MSE-based loss functions with single-time step information for predicting unsteady flow. Most of these approaches overlook the significance of incorporating the temporal history of the flow, a factor that cannot be disregarded in the context of numerical solvers. Hence, in this work, a physics-based AI (PbAI) method with higher-order loss functions is applied to unsteady scenarios, in particular to two distinct turbulent flows where a multitude of fine structures is present, namely, forced and decaying turbulence. Direct numerical simulations on uniform Cartesian grids are conducted to simulate these scenarios, generating two distinct datasets for training and inference. Each dataset comprises 32 randomly initialized conditions spanning 4, 848 time steps for each turbulent flow type. Five distinct models are devised, incorporating features such as rollouts from coarse numerical solvers and temporal considerations in the loss function calculation. The constructed PbAI models demonstrate consistent improvements in predictive performance over the entire temporal domain. These findings are further corroborated through vorticity correlation analyses. The empirical result demonstrates that the accuracy of the baseline case improves by up to 48% and 30% for forced and decaying turbulence, respectively. These results significantly underscore the importance of the temporal histories of flow in the loss function in enhancing predictive capabilities for complex and unsteady turbulent flows.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e6a508269bfb08f5c8c66413efa4d444da72838f" target='_blank'>
-              Multi-Order Loss Functions For Accelerating Unsteady Flow Simulations with Physics-Based AI
-              </a>
-            </td>
-          <td>
-            Wei Xian Lim, Naheed Anjum Arafat, Wai Lee Chan, Adams Kong
-          </td>
-          <td>2024-06-25</td>
-          <td>2024 IEEE Conference on Artificial Intelligence (CAI)</td>
           <td>0</td>
-          <td>4</td>
         </tr>
 
-        <tr id=""AI for Science"aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a central component of scientific-ML. Physics-Informed Neural Networks (PINNs) is the general method that has evolved for this task but its training is well-known to be very unstable. In this work we explore the possibility of changing the model being trained from being just a neural network to being a non-linear transformation of it - one that algebraically includes the boundary/initial conditions. This reduces the number of terms in the loss function than the standard PINN losses. We demonstrate that our modification leads to significant performance gains across a range of benchmark tasks, in various dimensions and without having to tweak the training algorithm. Our conclusions are based on conducting hundreds of experiments, in the fully unsupervised setting, over multiple linear and non-linear PDEs set to exactly solvable scenarios, which lends to a concrete measurement of our performance gains in terms of order(s) of magnitude lower fractional errors being achieved, than by standard PINNs. The code accompanying this manuscript is publicly available at, https://github.com/MorganREN/Improving-PINNs-By-Algebraic-Inclusion-of-Boundary-and-Initial-Conditions">
+        <tr id="We introduce neural information field filter, a Bayesian state and parameter estimation method for high-dimensional nonlinear dynamical systems given large measurement datasets. Solving such a problem using traditional methods, such as Kalman and particle filters, is computationally expensive. Information field theory is a Bayesian approach that can efficiently reconstruct dynamical model state paths and calibrate model parameters from noisy measurement data. To apply the method, we parameterize the time evolution state path using the span of a finite linear basis. The existing method has to reparameterize the state path by initial states to satisfy the initial condition. Designing an expressive yet simple linear basis before knowing the true state path is crucial for inference accuracy but challenging. Moreover, reparameterizing the state path using the initial state is easy to perform for a linear basis, but is nontrivial for more complex and expressive function parameterizations, such as neural networks. The objective of this paper is to simplify and enrich the class of state path parameterizations using neural networks for the information field theory approach. To this end, we propose a generalized physics-informed conditional prior using an auxiliary initial state. We show the existing reparameterization is a special case. We parameterize the state path using a residual neural network that consists of a linear basis function and a Fourier encoding fully connected neural network residual function. The residual function aims to correct the error of the linear basis function. To sample from the intractable posterior distribution, we develop an optimization algorithm, nested stochastic variational inference, and a sampling algorithm, nested preconditioned stochastic gradient Langevin dynamics. A series of numerical and experimental examples verify and validate the proposed method.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/50ec057bbac038765a71bbcf35743418ac73a1d3" target='_blank'>
-              Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions
+          <td><a href="https://www.semanticscholar.org/paper/4f1f25c26be1528226a494d8e61aceb48b888ac8" target='_blank'>
+              Neural information field filter
               </a>
             </td>
           <td>
-            Mohan Ren, Zhihao Fang, Keren Li, Anirbit Mukherjee
+            Kairui Hao, Ilias Bilionis
           </td>
-          <td>2024-07-30</td>
+          <td>2024-07-23</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>5</td>
+          <td>1</td>
         </tr>
 
         <tr id="We previously presented a novel loss formulation for efficient learning of complex dynamics from governing physics, typically described by partial differential equations (PDEs), using physics-informed neural networks (PINNs). In these experiments, the incorporation of a Boundary Connectivity (BCXN) loss function was shown to greatly improve physics-informed learning across many problems, especially those with complex geometries. However, this imposition may not always be ideal, as the previously presented BCXN-loss strongly enforces a linear local structure at the boundary. While this assumption helps facilitate faster learning with an order of magnitude sparser training samples, this can adversely impact convergence in other situations. Hence, we propose a modification of this BCXN-loss that reduces the imposed structure to a soft constraint, allowing for more flexible learning and convergence. We further demonstrate the potential for this method to improve the convergence and performance of LSA-PINN across additional numerical experiments, with much smaller errors than existing methods in terms of the standard L2-norm metric. In particular, we have applied this method to the modelling of flow past complex geometries such as airfoils, which serve as the basic building block for various applications in fluid dynamics and renewable energy (e.g., in wind and tidal turbine design).">
@@ -2248,80 +2338,49 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>13</td>
         </tr>
 
-        <tr id="We present a neural operator architecture to simulate Lagrangian dynamics, such as fluid flow, granular flows, and elastoplasticity. Traditional numerical methods, such as the finite element method (FEM), suffer from long run times and large memory consumption. On the other hand, approaches based on graph neural networks are faster but still suffer from long computation times on dense graphs, which are often required for high-fidelity simulations. Our model, GIOROM or Graph Interaction Operator for Reduced-Order Modeling, learns temporal dynamics within a reduced-order setting, capturing spatial features from a highly sparse graph representation of the input and generalizing to arbitrary spatial locations during inference. The model is geometry-aware and discretization-agnostic and can generalize to different initial conditions, velocities, and geometries after training. We show that point clouds of the order of 100,000 points can be inferred from sparse graphs with $\sim$1000 points, with negligible change in computation time. We empirically evaluate our model on elastic solids, Newtonian fluids, Non-Newtonian fluids, Drucker-Prager granular flows, and von Mises elastoplasticity. On these benchmarks, our approach results in a 25$\times$ speedup compared to other neural network-based physics simulators while delivering high-fidelity predictions of complex physical systems and showing better performance on most benchmarks. The code and the demos are provided at https://github.com/HrishikeshVish/GIOROM.">
+        <tr id="Multi-fidelity machine learning methods address the accuracy-efficiency trade-off by integrating scarce, resource-intensive high-fidelity data with abundant but less accurate low-fidelity data. We propose a practical multi-fidelity strategy for problems spanning low- and high-dimensional domains, integrating a non-probabilistic regression model for the low-fidelity with a Bayesian model for the high-fidelity. The models are trained in a staggered scheme, where the low-fidelity model is transfer-learned to the high-fidelity data and a Bayesian model is trained for the residual. This three-model strategy -- deterministic low-fidelity, transfer learning, and Bayesian residual -- leads to a prediction that includes uncertainty quantification both for noisy and noiseless multi-fidelity data. The strategy is general and unifies the topic, highlighting the expressivity trade-off between the transfer-learning and Bayesian models (a complex transfer-learning model leads to a simpler Bayesian model, and vice versa). We propose modeling choices for two scenarios, and argue in favor of using a linear transfer-learning model that fuses 1) kernel ridge regression for low-fidelity with Gaussian processes for high-fidelity; or 2) deep neural network for low-fidelity with a Bayesian neural network for high-fidelity. We demonstrate the effectiveness and efficiency of the proposed strategies and contrast them with the state-of-the-art based on various numerical examples. The simplicity of these formulations makes them practical for a broad scope of future engineering applications.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b0931d26d7d6b637fece82e4653a754d6a28f5dc" target='_blank'>
-              Reduced-Order Neural Operators: Learning Lagrangian Dynamics on Highly Sparse Graphs
+          <td><a href="https://www.semanticscholar.org/paper/f0aac32171f95be4080bfb1caf4a77b613f4b14d" target='_blank'>
+              Practical multi-fidelity machine learning: fusion of deterministic and Bayesian models
               </a>
             </td>
           <td>
-            Hrishikesh Viswanath, Yue Chang, Julius Berner, Peter Yichen Chen, Aniket Bera
+            Jiaxiang Yi, Ji Cheng, Miguel A. Bessa
           </td>
-          <td>2024-07-04</td>
+          <td>2024-07-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>28</td>
-        </tr>
-
-        <tr id="We present a domain decomposition strategy for developing structure-preserving finite element discretizations from data when exact governing equations are unknown. On subdomains, trainable Whitney form elements are used to identify structure-preserving models from data, providing a Dirichlet-to-Neumann map which may be used to globally construct a mortar method. The reduced-order local elements may be trained offline to reproduce high-fidelity Dirichlet data in cases where first principles model derivation is either intractable, unknown, or computationally prohibitive. In such cases, particular care must be taken to preserve structure on both local and mortar levels without knowledge of the governing equations, as well as to ensure well-posedness and stability of the resulting monolithic data-driven system. This strategy provides a flexible means of both scaling to large systems and treating complex geometries, and is particularly attractive for multiscale problems with complex microstructure geometry. While consistency is traditionally obtained in finite element methods via quasi-optimality results and the Bramble-Hilbert lemma as the local element diameter $h\rightarrow0$, our analysis establishes notions of accuracy and stability for finite h with accuracy coming from matching data. Numerical experiments and analysis establish properties for $H(\operatorname{div})$ problems in small data limits ($\mathcal{O}(1)$ reference solutions).">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5e40b79cf0d6051174cb4015baf4f92afc84afb1" target='_blank'>
-              A Structure-Preserving Domain Decomposition Method for Data-Driven Modeling
-              </a>
-            </td>
-          <td>
-            Shuai Jiang, Jonas A. Actor, Scott A. Roberts, Nathaniel Trask
-          </td>
-          <td>2024-06-08</td>
-          <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
         </tr>
 
-        <tr id="In the context of proxy modeling for process systems, traditional data-driven deep learning approaches frequently encounter significant challenges, such as substantial training costs induced by large amounts of data, and limited generalization capabilities. As a promising alternative, physics-aware models incorporate partial physics knowledge to ameliorate these challenges. Although demonstrating efficacy, they fall short in terms of exploration depth and universality. To address these shortcomings, we introduce a physics-aware proxy model (PAPM) that fully incorporates partial prior physics of process systems, which includes multiple input conditions and the general form of conservation relations, resulting in better out-of-sample generalization. Additionally, PAPM contains a holistic temporal-spatial stepping module for flexible adaptation across various process systems. Through systematic comparisons with state-of-the-art pure data-driven and physics-aware models across five two-dimensional benchmarks in nine generalization tasks, PAPM notably achieves an average performance improvement of 6.7%, while requiring fewer FLOPs, and just 1% of the parameters compared to the prior leading method. The code is available at https://github.com/pengwei07/PAPM.">
+        <tr id="This paper proposes a generalized algorithmic approach for learning linear model representations for nonlinear systems within the Koopman framework. We focus on schemes that rely on learning the nonlinear transformation functions using deep neural networks. Beyond achieving dynamical accuracy, our primary objective is to develop models capable of simulating nonlinear systems across multiple time steps in the linear space. An algorithm that is based on recursive least squares is proposed to address the optimization complexities inherent in learning such models. In addition, we leverage the learned linear representation to design a linear quadratic regulator to control the original nonlinear system. The effectiveness of the proposed algorithm is demonstrated in two numerical examples.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/168b93840ae25e4ba1a3d7b19572fb125f6bb72a" target='_blank'>
-              PAPM: A Physics-aware Proxy Model for Process Systems
+          <td><a href="https://www.semanticscholar.org/paper/1dc9bf823159462d30a9a2199b18f6959ef1ccd3" target='_blank'>
+              Recursive Least Squares-Based Identification for Multi-Step Koopman Operators
               </a>
             </td>
           <td>
-            Pengwei Liu, Zhongkai Hao, Xingyu Ren, Hangjie Yuan, Jiayang Ren, Dong Ni
+            Omar Sayed, Sergio Lucia
           </td>
-          <td>2024-07-07</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>9</td>
+          <td>2024-06-25</td>
+          <td>2024 European Control Conference (ECC)</td>
+          <td>1</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. 
-
-However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical systems whose solutions exhibit multi-scale or turbulent behavior over time.
-
-The reason is that PINNs may violate the temporal causality property since all the temporal features in the PINNs loss are trained simultaneously. 
-
-This paper proposes to use implicit time differencing schemes to enforce temporal causality, and use transfer learning to sequentially update the PINNs in space as surrogates for PDE solutions in different time frames.
-
-The evolving PINNs are better able to capture the varying complexities of the evolutionary equations, while only requiring minor updates between adjacent time frames.
-
-Our method is theoretically proven to be convergent if the time step is small and each PINN in different time frames is well-trained.
-
-In addition, we provide state-of-the-art (SOTA) numerical results for a variety of benchmarks for which existing PINNs formulations may fail or be inefficient.
-
-We demonstrate that the proposed method improves the accuracy of PINNs approximation for evolutionary PDEs and improves efficiency by a factor of 4–40x.
-
-The code is available at https://github.com/SiqiChen9/TL-DPINNs.">
+        <tr id="Bayesian analysis enables combining prior knowledge with measurement data to learn model parameters. Commonly, one resorts to computing the maximum a posteriori (MAP) estimate, when only a point estimate of the parameters is of interest. We apply MAP estimation in the context of structural dynamic models, where the system response can be described by the frequency response function. To alleviate high computational demands from repeated expensive model calls, we utilize a rational polynomial chaos expansion (RPCE) surrogate model that expresses the system frequency response as a rational of two polynomials with complex coefficients. We propose an extension to an existing sparse Bayesian learning approach for RPCE based on Laplace's approximation for the posterior distribution of the denominator coefficients. Furthermore, we introduce a Bayesian optimization approach, which allows to adaptively enrich the experimental design throughout the optimization process of MAP estimation. Thereby, we utilize the expected improvement acquisition function as a means to identify sample points in the input space that are possibly associated with large objective function values. The acquisition function is estimated through Monte Carlo sampling based on the posterior distribution of the expansion coefficients identified in the sparse Bayesian learning process. By combining the sparsity-inducing learning procedure with the sequential experimental design, we effectively reduce the number of model evaluations in the MAP estimation problem. We demonstrate the applicability of the presented methods on the parameter updating problem of an algebraic two-degree-of-freedom system and the finite element model of a cross-laminated timber plate.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2baf92352b6cdc0a229e693600511b572a32085f" target='_blank'>
-              Causality-enhanced Discreted Physics-informed Neural Networks for Predicting Evolutionary Equations
+          <td><a href="https://www.semanticscholar.org/paper/9a03332f3ec82d4697eb9f8880eb0ae668a91b1a" target='_blank'>
+              Maximum a Posteriori Estimation for Linear Structural Dynamics Models Using Bayesian Optimization with Rational Polynomial Chaos Expansions
               </a>
             </td>
           <td>
-            Ye Li, Siqi Chen, Bin Shan, Sheng-Jun Huang
+            Felix Schneider, I. Papaioannou, Bruno Sudret, Gerhard Muller
           </td>
-          <td>2024-08-01</td>
-          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
+          <td>2024-08-07</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>25</td>
         </tr>
 
         <tr id="One of the most promising applications of machine learning (ML) in computational physics is to accelerate the solution of partial differential equations (PDEs). The key objective of ML-based PDE solvers is to output a sufficiently accurate solution faster than standard numerical methods, which are used as a baseline comparison. We first perform a systematic review of the ML-for-PDE solving literature. Of articles that use ML to solve a fluid-related PDE and claim to outperform a standard numerical method, we determine that 79% (60/76) compare to a weak baseline. Second, we find evidence that reporting biases, especially outcome reporting bias and publication bias, are widespread. We conclude that ML-for-PDE solving research is overoptimistic: weak baselines lead to overly positive results, while reporting biases lead to underreporting of negative results. To a large extent, these issues appear to be caused by factors similar to those of past reproducibility crises: researcher degrees of freedom and a bias towards positive results. We call for bottom-up cultural changes to minimize biased reporting as well as top-down structural reforms intended to reduce perverse incentives for doing so.">
@@ -2336,82 +2395,82 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2024-07-09</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>5</td>
         </tr>
 
-        <tr id="In this letter we investigate an information theoretic analogue of the classic two masses on spring system, arising from a physical interpretation of Friston's free energy principle in the theory of learning in a system of agents. Using methods from classical mechanics on manifolds, we define a kinetic energy term using the Fisher metric on distributions and a potential energy function defined in terms of stress on the agents' beliefs. The resulting Lagrangian (Hamiltonian) produces a variation of the classic DeGroot dynamics. In the two agent case, the potential function is defined using the Jeffrey's divergence and the resulting dynamics are characterized by a non-linear spring. These dynamics produce trajectories that resemble flows on tori but are shown numerically to produce chaos near the boundary of the space. We then investigate persuasion as an information theoretic control problem where analysis indicates that manipulating peer pressure with a fixed target is a more stable approach to altering an agent's belief than providing a slowly changing belief state that approaches the target.">
+        <tr id="Tipping points occur in many real-world systems, at which the system shifts suddenly from one state to another. The ability to predict the occurrence of tipping points from time series data remains an outstanding challenge and a major interest in a broad range of research fields. Particularly, the widely used methods based on bifurcation theory are neither reliable in prediction accuracy nor applicable for irregularly-sampled time series which are commonly observed from real-world systems. Here we address this challenge by developing a deep learning algorithm for predicting the occurrence of tipping points in untrained systems, by exploiting information about normal forms. Our algorithm not only outperforms traditional methods for regularly-sampled model time series but also achieves accurate predictions for irregularly-sampled model time series and empirical time series. Our ability to predict tipping points for complex systems paves the way for mitigation risks, prevention of catastrophic failures, and restoration of degraded systems, with broad applications in social science, engineering, and biology.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/52c8e6266ddf04fc931ce8e2677ea1562dda36dc" target='_blank'>
-              Dynamics of An Information Theoretic Analog of Two Masses on a Spring
+          <td><a href="https://www.semanticscholar.org/paper/6885f6f695d68eb9294efe8cb408c1d39a6fbe58" target='_blank'>
+              Deep learning for predicting the occurrence of tipping points
               </a>
             </td>
           <td>
-            Geoff Goehle, Christopher Griffin
+            Chengzuo Zhuge, Jiawei Li, Wei Chen
           </td>
-          <td>2024-07-03</td>
+          <td>2024-07-26</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>0</td>
         </tr>
 
-        <tr id="None">
+        <tr id="Most scientific machine learning (SciML) applications of neural networks involve hundreds to thousands of parameters, and hence, uncertainty quantification for such models is plagued by the curse of dimensionality. Using physical applications, we show that $L_0$ sparsification prior to Stein variational gradient descent ($L_0$+SVGD) is a more robust and efficient means of uncertainty quantification, in terms of computational cost and performance than the direct application of SGVD or projected SGVD methods. Specifically, $L_0$+SVGD demonstrates superior resilience to noise, the ability to perform well in extrapolated regions, and a faster convergence rate to an optimal solution.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c78e8674f4b4b137f15f996d2bc27957f1fe2af7" target='_blank'>
-              Optimal Reconstruction of Vector Fields from Data for Prediction and Uncertainty Quantification
+          <td><a href="https://www.semanticscholar.org/paper/2ef84e51598bc76cbb9e56bd3fdb600206e852c2" target='_blank'>
+              Improving the performance of Stein variational inference through extreme sparsification of physically-constrained neural network models
               </a>
             </td>
           <td>
-            Sean P. McGowan, William S. P. Robertson, Chantelle Blachut, Sanjeeva Balasuriya
+            G. A. Padmanabha, J. Fuhg, C. Safta, Reese E. Jones, N. Bouklas
           </td>
-          <td>2024-06-13</td>
-          <td>J. Nonlinear Sci.</td>
+          <td>2024-06-30</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>18</td>
+          <td>19</td>
         </tr>
 
-        <tr id="Deep neural networks (DNNs) have achieved exceptional performance across various fields by learning complex nonlinear mappings from large-scale datasets. However, they encounter challenges such as high computational costs and limited interpretability. To address these issues, hybrid approaches that integrate physics with AI are gaining interest. This paper introduces a novel physics-based AI model called the"Nonlinear Schr\"odinger Network", which treats the Nonlinear Schr\"odinger Equation (NLSE) as a general-purpose trainable model for learning complex patterns including nonlinear mappings and memory effects from data. Existing physics-informed machine learning methods use neural networks to approximate the solutions of partial differential equations (PDEs). In contrast, our approach directly treats the PDE as a trainable model to obtain general nonlinear mappings that would otherwise require neural networks. As a type of physics-AI symbiosis, it offers a more interpretable and parameter-efficient alternative to traditional black-box neural networks, achieving comparable or better accuracy in some time series classification tasks while significantly reducing the number of required parameters. Notably, the trained Nonlinear Schr\"odinger Network is interpretable, with all parameters having physical meanings as properties of a virtual physical system that transforms the data to a more separable space. This interpretability allows for insight into the underlying dynamics of the data transformation process. Applications to time series forecasting have also been explored. While our current implementation utilizes the NLSE, the proposed method of using physics equations as trainable models to learn nonlinear mappings from data is not limited to the NLSE and may be extended to other master equations of physics.">
+        <tr id="Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional regression or learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that applies both to classical regression approaches such as the LASSO as well as to neural networks. One of the most notable UQ techniques is the debiased LASSO, which modifies the LASSO to allow for the construction of asymptotic confidence intervals by decomposing the estimation error into a Gaussian and an asymptotically vanishing bias component. However, in real-world problems with finite-dimensional data, the bias term is often too significant to be neglected, resulting in overly narrow confidence intervals. Our work rigorously addresses this issue and derives a data-driven adjustment that corrects the confidence intervals for a large class of predictors by estimating the means and variances of the bias terms from training data, exploiting high-dimensional concentration phenomena. This gives rise to non-asymptotic confidence intervals, which can help avoid overestimating uncertainty in critical applications such as MRI diagnosis. Importantly, our analysis extends beyond sparse regression to data-driven predictors like neural networks, enhancing the reliability of model-based deep learning. Our findings bridge the gap between established theory and the practical applicability of such debiased methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/86e993b6260a5161e12c46644b62f8d53d34dba1" target='_blank'>
-              Nonlinear Schr\"odinger Network
+          <td><a href="https://www.semanticscholar.org/paper/6b74e7097e6bf5e51f1391656df98c0c04de0d93" target='_blank'>
+              Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning
               </a>
             </td>
           <td>
-            Yiming Zhou, Callen MacPhee, Tingyi Zhou, Bahram Jalali
+            Frederik Hoppe, C. M. Verdun, Hannah Laus, Felix Krahmer, Holger Rauhut
           </td>
-          <td>2024-07-19</td>
+          <td>2024-07-18</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>5</td>
         </tr>
 
-        <tr id="In dynamical systems reconstruction (DSR) we seek to infer from time series measurements a generative model of the underlying dynamical process. This is a prime objective in any scientific discipline, where we are particularly interested in parsimonious models with a low parameter load. A common strategy here is parameter pruning, removing all parameters with small weights. However, here we find this strategy does not work for DSR, where even low magnitude parameters can contribute considerably to the system dynamics. On the other hand, it is well known that many natural systems which generate complex dynamics, like the brain or ecological networks, have a sparse topology with comparatively few links. Inspired by this, we show that geometric pruning, where in contrast to magnitude-based pruning weights with a low contribution to an attractor's geometrical structure are removed, indeed manages to reduce parameter load substantially without significantly hampering DSR quality. We further find that the networks resulting from geometric pruning have a specific type of topology, and that this topology, and not the magnitude of weights, is what is most crucial to performance. We provide an algorithm that automatically generates such topologies which can be used as priors for generative modeling of dynamical systems by RNNs, and compare it to other well studied topologies like small-world or scale-free networks.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f7262300a7dc61b5b9020753dc9d2bbd63a06cc2" target='_blank'>
-              Optimal Recurrent Network Topologies for Dynamical Systems Reconstruction
+          <td><a href="https://www.semanticscholar.org/paper/dcaa44f8b49302272e5cab62125e644f57aefae1" target='_blank'>
+              Characterizing the dynamics of multi-scale global high impact weather events
               </a>
             </td>
           <td>
-            Christoph Jurgen Hemmer, Manuel Brenner, Florian Hess, Daniel Durstewitz
+            L. R. Frank, V. Galinsky, Zhenhai Zhang, F. M. Ralph
           </td>
-          <td>2024-06-07</td>
-          <td>ArXiv</td>
+          <td>2024-08-15</td>
+          <td>Scientific Reports</td>
           <td>0</td>
-          <td>3</td>
+          <td>13</td>
         </tr>
 
-        <tr id="This paper addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring flexible model behavior to incorporate non-data sample information. We introduce Bayesian Entropy Neural Networks (BENN), a framework grounded in Maximum Entropy (MaxEnt) principles, designed to impose constraints on Bayesian Neural Network (BNN) predictions. BENN is capable of constraining not only the predicted values but also their derivatives and variances, ensuring a more robust and reliable model output. To achieve simultaneous uncertainty quantification and constraint satisfaction, we employ the method of multipliers approach. This allows for the concurrent estimation of neural network parameters and the Lagrangian multipliers associated with the constraints. Our experiments, spanning diverse applications such as beam deflection modeling and microstructure generation, demonstrate the effectiveness of BENN. The results highlight significant improvements over traditional BNNs and showcase competitive performance relative to contemporary constrained deep learning methods.">
+        <tr id="In the field of machine learning, comprehending the intricate training dynamics of neural networks poses a significant challenge. This paper explores the training dynamics of neural networks, particularly whether these dynamics can be expressed in a general closed-form solution. We demonstrate that the dynamics of the gradient flow in two-layer narrow networks is not an integrable system. Integrable systems are characterized by trajectories confined to submanifolds defined by level sets of first integrals (invariants), facilitating predictable and reducible dynamics. In contrast, non-integrable systems exhibit complex behaviors that are difficult to predict. To establish the non-integrability, we employ differential Galois theory, which focuses on the solvability of linear differential equations. We demonstrate that under mild conditions, the identity component of the differential Galois group of the variational equations of the gradient flow is non-solvable. This result confirms the system's non-integrability and implies that the training dynamics cannot be represented by Liouvillian functions, precluding a closed-form solution for describing these dynamics. Our findings highlight the necessity of employing numerical methods to tackle optimization problems within neural networks. The results contribute to a deeper understanding of neural network training dynamics and their implications for machine learning optimization strategies.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4d74383a8ad720e106440e126defbad7231d316d" target='_blank'>
-              Bayesian Entropy Neural Networks for Physics-Aware Prediction
+          <td><a href="https://www.semanticscholar.org/paper/0ddef324ecc792db4cfe809ea02647e7e5e7d877" target='_blank'>
+              Absence of Closed-Form Descriptions for Gradient Flow in Two-Layer Narrow Networks
               </a>
             </td>
           <td>
-            R. Rathnakumar, Jiayu Huang, Hao Yan, Yongming Liu
+            Yeachan Park
           </td>
-          <td>2024-07-01</td>
+          <td>2024-08-15</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
+          <td>0</td>
         </tr>
 
         <tr id="Many dynamical systems are subjected to stochastic influences, such as random excitations, noise, and unmodeled behavior. Tracking the system's state and parameters based on a physical model is a common task for which filtering algorithms, such as Kalman filters and their non-linear extensions, are typically used. However, many of these filters use assumptions on the transition probabilities or the covariance model, which can lead to inaccuracies in non-linear systems. We will show the application of a stochastic coupling filter that can approximate arbitrary transition densities under non-Gaussian noise. The filter is based on transport maps, which couple the approximation densities to a user-chosen reference density, allowing for straightforward sampling and evaluation of probabilities.">
@@ -2429,49 +2488,49 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>21</td>
         </tr>
 
-        <tr id="Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning analogues. Any such numerical solution is subject to multiple sources of uncertainty, both from limited computational resources and limited data (including unknown parameters). Gaussian process analogues to classic PDE simulation methods have recently emerged as a framework to construct fully probabilistic estimates of all these types of uncertainty. So far, much of this work focused on theoretical foundations, and as such is not particularly data efficient or scalable. Here we propose a framework combining a discretization scheme based on the popular Finite Volume Method with complementary numerical linear algebra techniques. Practical experiments, including a spatiotemporal tsunami simulation, demonstrate substantially improved scaling behavior of this approach over previous collocation-based techniques.">
+        <tr id="Simulating Darcy flows in porous media is fundamental to understand the future flow behavior of fluids in hydrocarbon and carbon storage reservoirs. Geological models of reservoirs are often associated with high uncertainly leading to many numerical simulations for history matching and production optimization. Machine learning models trained with simulation data can provide a faster alternative to traditional simulators. In this paper we present a single Fourier Neural Operator (FNO) surrogate that outperforms traditional reservoir simulators by the ability to predict pressures and saturations on varying permeability fields, well locations, well controls, and number of wells. The maximum-mean relative error of 95\% of pressure and saturation predictions is less than 5\%. This is achieved by employing a simple yet very effective data augmentation technique that reduces the dataset size by 75\% and reduces overfitting. Also, constructing the input tensor in a binary fashion enables predictions on unseen well locations, well controls, and number of wells. Such model can accelerate history matching and reservoir characterization procedures by several orders of magnitude. The ability to predict on new well locations, well controls, and number of wells enables highly efficient reservoir management and optimization.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f405569ff0b7887d7f887ed428142bf13a634400" target='_blank'>
-              Scaling up Probabilistic PDE Simulators with Structured Volumetric Information
+          <td><a href="https://www.semanticscholar.org/paper/7d7a6b2e3b8fbcb3a223ec6dc61bbed982599799" target='_blank'>
+              Neural Operator-Based Proxy for Reservoir Simulations Considering Varying Well Settings, Locations, and Permeability Fields
               </a>
             </td>
           <td>
-            Tim Weiland, Marvin Pförtner, Philipp Hennig
+            Daniel Badawi, Eduardo Gildin
           </td>
-          <td>2024-06-07</td>
+          <td>2024-07-13</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="A dynamical system may be defined by a simple transition law - such as a map or a vector field. Most learning techniques primarily try to recreate the dynamic evolution law. This is a major shortcoming, as most dynamic properties of interest are asymptotic properties such as an attractor or invariant measure. One of the major theoretical challenges for numerical methods is that approximating the dynamical law may not be sufficient to approximate these asymptotic properties. This article presents a method of representing a discrete-time deterministic dynamical system as a Markov process. The procedure is completely data-driven. The technique is proved to be convergent -- the stationary density of the Markov process has a support that converges to the targeted invariant set. Thus invariant sets of arbitrary dynamical systems, even with complicated non-smooth topology, can be approximated by this technique. Under further assumptions of stochastic stability of the targeted system, the technique is also shown to provide a convergent statistical approximation.">
+        <tr id="We provide an approach enabling one to employ physics-informed neural networks (PINNs) for uncertainty quantification. Our approach is applicable to systems where observations are scarce (or even lacking), these being typical situations associated with subsurface water bodies. Our novel physics-informed neural network under uncertainty (PINN-UU) integrates the space-time domain across which processes take place and uncertain parameter spaces within a unique computational domain. PINN-UU is then trained to satisfy the relevant physical principles (e.g., mass conservation) in the defined input domain. We employ a stage training approach via transfer learning to accommodate high-dimensional solution spaces. We demonstrate the effectiveness of PINN-UU in a scenario associated with reactive transport in porous media, showcasing its reliability, efficiency, and applicability to sensitivity analysis. PINN-UU emerges as a promising tool for robust uncertainty quantification, with broad applicability to groundwater systems. As such, it can be considered as a valuable alternative to traditional methods such as multi-realization Monte Carlo simulations based on direct solvers or black-box surrogate models.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f7a9c8ed7750a7d4d14152ec7fe7c869a1655699" target='_blank'>
-              Reconstructing dynamical systems as zero-noise limits
+          <td><a href="https://www.semanticscholar.org/paper/9eb1778f55d55df5b6fa3d3b473be94da31915f8" target='_blank'>
+              Modelling parametric uncertainty in PDEs models via Physics-Informed Neural Networks
               </a>
             </td>
           <td>
-            Suddhasattwa Das
+            Milad Panahi, G. Porta, M. Riva, A. Guadagnini
           </td>
-          <td>2024-07-23</td>
+          <td>2024-08-08</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>43</td>
         </tr>
 
-        <tr id="In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by a set of randomly sampled data point clouds that are assumed to lie on or close to the manifold. When the loss function incorporates the physics, resulting in the so-called physics-informed DeepONets (PI-DeepONets), we approximate the differentiation terms in the PDE by an appropriate operator approximation scheme. For the second-order elliptic PDE with a nontrivial diffusion coefficient, we approximate the differentiation term with one of these methods: the Diffusion Maps (DM), the Radial Basis Functions (RBF), and the Generalized Moving Least Squares (GMLS) methods. For the GMLS approximation, which is more flexible for problems with boundary conditions, we derive the theoretical error bound induced by the approximate differentiation. Numerically, we found that DeepONet is accurate for various types of diffusion coefficients, including linear, exponential, piecewise linear, and quadratic functions, for linear and semi-linear PDEs with/without boundaries. When the number of observations is small, PI-DeepONet trained with sufficiently large samples of PDE constraints produces more accurate approximations than DeepONet. For the inverse problem, we incorporate PI-DeepONet in a Bayesian Markov Chain Monte Carlo (MCMC) framework to estimate the diffusion coefficient from noisy solutions of the PDEs measured at a finite number of point cloud data. Numerically, we found that PI-DeepONet provides accurate approximations comparable to those obtained by a more expensive method that directly solves the PDE on the proposed diffusion coefficient in each MCMC iteration.">
+        <tr id="A dynamical system may be defined by a simple transition law - such as a map or a vector field. Most learning techniques primarily try to recreate the dynamic evolution law. This is a major shortcoming, as most dynamic properties of interest are asymptotic properties such as an attractor or invariant measure. One of the major theoretical challenges for numerical methods is that approximating the dynamical law may not be sufficient to approximate these asymptotic properties. This article presents a method of representing a discrete-time deterministic dynamical system as a Markov process. The procedure is completely data-driven. The technique is proved to be convergent -- the stationary density of the Markov process has a support that converges to the targeted invariant set. Thus invariant sets of arbitrary dynamical systems, even with complicated non-smooth topology, can be approximated by this technique. Under further assumptions of stochastic stability of the targeted system, the technique is also shown to provide a convergent statistical approximation.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f1a2db1eb2d9fce75d3ec1e4b8ba8bfdab80a365" target='_blank'>
-              Solving forward and inverse PDE problems on unknown manifolds via physics-informed neural operators
+          <td><a href="https://www.semanticscholar.org/paper/f7a9c8ed7750a7d4d14152ec7fe7c869a1655699" target='_blank'>
+              Reconstructing dynamical systems as zero-noise limits
               </a>
             </td>
           <td>
-            Anran Jiao, Qile Yan, Jhn Harlim, Lu Lu
+            Suddhasattwa Das
           </td>
-          <td>2024-07-07</td>
+          <td>2024-07-23</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>0</td>
         </tr>
 
         <tr id="Echo state network (ESN) implements an alternative paradigm called reservoir computing to train recurrent neural networks (RNNs), where internal weights are randomly generated and kept fixed, and only readout weights need to be trained, which greatly reduces the training complexity of RNNs. ESN not only facilitates the practical implementation of RNNs but also shows superior performance over fully trained RNNs across a range of applications. However, the conventional ESN suffers from the drawbacks of stringent conditions for weight convergence and slow convergence speed. This paper proposes a memory regressor extended learning method to update the readout weights of ESNs. By constructing and incorporating a generalized prediction error based on regressor extension and filtering, the capacity of ESN to utilize historical data can be greatly improved. In the discrete-time domain, it is proven that exponential convergence of readout weights is achieved under a condition termed interval excitation that is strictly weaker than the classical condition of persistent excitation. Simulation results on modeling a 10th-order nonlinear autoregressive moving-average (NARMA) system have revealed that the proposed approach accelerates weight convergence speed almost ten times higher compared to the conventional ESN.">
@@ -2504,6 +2563,36 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>1</td>
         </tr>
 
+        <tr id="Accurate estimate of long-term risk is critical for safe decision-making, but sampling from rare risk events and long-term trajectories can be prohibitively costly. Risk gradient can be used in many first-order techniques for learning and control methods, but gradient estimate is difficult to obtain using Monte Carlo (MC) methods because the infinitesimal divisor may significantly amplify sampling noise. Motivated by this gap, we propose an efficient method to evaluate long-term risk probabilities and their gradients using short-term samples without sufficient risk events. We first derive that four types of long-term risk probability are solutions of certain partial differential equations (PDEs). Then, we propose a physics-informed learning technique that integrates data and physics information (aforementioned PDEs). The physics information helps propagate information beyond available data and obtain provable generalization beyond available data, which in turn enables long-term risk to be estimated using short-term samples of safe events. Finally, we demonstrate in simulation that the proposed technique has improved sample efficiency, generalizes well to unseen regions, and adapts to changing system parameters.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/b4b5d11c4861e28deddce08df1d92f4a1c23b924" target='_blank'>
+              Generalizable Physics-Informed Learning for Stochastic Safety-Critical Systems
+              </a>
+            </td>
+          <td>
+            Zhuoyuan Wang, Albert Chern, Yorie Nakahira
+          </td>
+          <td>2024-07-11</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>10</td>
+        </tr>
+
+        <tr id="Cyclostationary linear inverse models (CS-LIMs), generalized versions of the classical (stationary) LIM, are advanced data-driven techniques for extracting the first-order time-dependent dynamics and random forcing relevant information from complex non-linear stochastic processes. Though CS-LIMs lead to a breakthrough in climate sciences, their mathematical background and properties are worth further exploration. This study focuses on the mathematical perspective of CS-LIMs and introduces two variants: e-CS-LIM and l-CS-LIM. The former refines the original CS-LIM using the interval-wise linear Markov approximation, while the latter serves as an analytic inverse model for the linear periodic stochastic systems. Although relying on approximation, e-CS-LIM converges to l-CS-LIM under specific conditions and shows noise-robust performance. Numerical experiments demonstrate that each CS-LIM reveals the temporal structure of the system. The e-CS-LIM optimizes the original model for better dynamics performance, while l-CS-LIM excels in diffusion estimation due to reduced approximation reliance. Moreover, CS-LIMs are applied to real-world ENSO data, yielding a consistent result aligning with observations and current ENSO understanding.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/7f20f17be02b5ed8df3e9de809737832dc15d7e7" target='_blank'>
+              On the Cyclostationary Linear Inverse Models: A Mathematical Insight and Implication
+              </a>
+            </td>
+          <td>
+            Justin Lien, Yan-Ning Kuo, Hiroyasu Ando
+          </td>
+          <td>2024-07-15</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>1</td>
+        </tr>
+
         <tr id="The Koopman operator framework is a promising direction of analysis and synthesis of systems with nonlinear dynamics based on (linear) Koopman operators. In this paper, we address the resolvent of a Koopman operator for a nonlinear autonomous discrete-time system, which we call the Koopman resolvent, and its identification problem. First, we show that for the nonlinear system with a scalar-valued output, the $z$- transform of the output is represented by the action of Koop-man resolvent. Second, we describe an identification method of the Koopman resolvent directly from time-series data of the output, in which we estimate parameters of the resolvent as well as poles and residues of the z-transform of the output. By combining the so-called frequency-domain Prony method with the Vandermonde-Cauchy form in the Dynamic Mode Decomposition (DMD), we propose the method which we call the frequency-domain DMD, in which all the unknowns can be estimated in the frequency domain.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/df691892a89d4f0c1e7b43d373b04818f75bcc0b" target='_blank'>
@@ -2519,6 +2608,21 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>20</td>
         </tr>
 
+        <tr id="We propose an $\alpha$-separable graph Hamiltonian network ($\alpha$-SGHN) that reveals complex interaction patterns between particles in lattice systems. Utilizing trajectory data, $\alpha$-SGHN infers potential interactions without prior knowledge about particle coupling, overcoming the limitations of traditional graph neural networks that require predefined links. Furthermore, $\alpha$-SGHN preserves all conservation laws during trajectory prediction. Experimental results demonstrate that our model, incorporating structural information, outperforms baseline models based on conventional neural networks in predicting lattice systems. We anticipate that the results presented will be applicable beyond the specific onsite and inter-site interaction lattices studied, including the Frenkel-Kontorova model, the rotator lattice, and the Toda lattice.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/fa79f8d7dee50b48f0bb37e6b9aef968f5166f29" target='_blank'>
+              $\alpha$-SGHN: A Robust Model for Learning Particle Interactions in Lattice Systems
+              </a>
+            </td>
+          <td>
+            Yixian Gao, R. Geng, Panayotis Kevrekidis, Hong-Kun Zhang, Jian Zu
+          </td>
+          <td>2024-07-16</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>2</td>
+        </tr>
+
         <tr id="We propose a meta-learning method for modeling Hamiltonian dynamics from a limited number of data. Although Hamiltonian neural networks have been successfully used for modeling dynamics that obey the energy conservation law, they require many data to achieve high performance. The proposed method meta-learns our neural network-based model using datasets in various dynamical systems, such that our model can predict vector fields of unseen systems. In our model, a system representation is inferred from given small data using an encoder network. Then, the system-specific vector field is predicted by modeling the Hamiltonian using a Gaussian process (GP) with neural network-based mean and kernel functions that depend on the inferred system representation. This GP-based Hamiltonian allows us to analytically obtain predictions that are adapted to small data while imposing the constraint of the conservation law. The neural networks are shared across systems, which enables us to learn knowledge from multiple systems, and use it for unseen systems. In our experiments, we demonstrate that the proposed method outperforms existing methods for predicting dynamics from a small number of observations in target systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/37ac3a5b751bd136ecb4369b5f0c68f06bf4a91f" target='_blank'>
@@ -2531,37 +2635,52 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2024-08-01</td>
           <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>7</td>
+          <td>8</td>
         </tr>
 
-        <tr id="Within the context of machine learning-based closure mappings for RANS turbulence modelling, physical realizability is often enforced using ad-hoc postprocessing of the predicted anisotropy tensor. In this study, we address the realizability issue via a new physics-based loss function that penalizes non-realizable results during training, thereby embedding a preference for realizable predictions into the model. Additionally, we propose a new framework for data-driven turbulence modelling which retains the stability and conditioning of optimal eddy viscosity-based approaches while embedding equivariance. Several modifications to the tensor basis neural network to enhance training and testing stability are proposed. We demonstrate the conditioning, stability, and generalization of the new framework and model architecture on three flows: flow over a flat plate, flow over periodic hills, and flow through a square duct. The realizability-informed loss function is demonstrated to significantly increase the number of realizable predictions made by the model when generalizing to a new flow configuration. Altogether, the proposed framework enables the training of stable and equivariant anisotropy mappings, with more physically realizable predictions on new data. We make our code available for use and modification by others.">
+        <tr id="This paper is aimed at using the newly developing field of physics informed machine learning (PIML) to develop models for predicting the remaining useful lifetime (RUL) aircraft engines. We consider the well-known benchmark NASA Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) data as the main data for this paper, which consists of sensor outputs in a variety of different operating modes. C-MAPSS is a well-studied dataset with much existing work in the literature that address RUL prediction with classical and deep learning methods. In the absence of published empirical physical laws governing the C-MAPSS data, our approach first uses stochastic methods to estimate the governing physics models from the noisy time series data. In our approach, we model the various sensor readings as being governed by stochastic differential equations, and we estimate the corresponding transition density mean and variance functions of the underlying processes. We then augment LSTM (long-short term memory) models with the learned mean and variance functions during training and inferencing. Our PIML based approach is different from previous methods, and we use the data to first learn the physics. Our results indicate that PIML discovery and solutions methods are well suited for this problem and outperform previous data-only deep learning methods for this data set and task. Moreover, the framework developed herein is flexible, and can be adapted to other situations (other sensor modalities or combined multi-physics environments), including cases where the underlying physics is only partially observed or known.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d49d700d5797f8d7145ca83fa89f5c1491a5d703" target='_blank'>
-              Realizability-Informed Machine Learning for Turbulence Anisotropy Mappings
+          <td><a href="https://www.semanticscholar.org/paper/47c68f22e1c160e3cdac30be6f54af8a48a8eccd" target='_blank'>
+              Physics Informed Machine Learning (PIML) methods for estimating the remaining useful lifetime (RUL) of aircraft engines
               </a>
             </td>
           <td>
-            R. McConkey, Eugene Yee, F. Lien
+            Sriram Nagaraj, Truman Hickok
           </td>
-          <td>2024-06-17</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>36</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Nonlinear optimization (NOPT) is a meaningful tool for solving complex tasks in fields like engineering, economics, and operations research, among others. However, NOPT has problems when it comes to dealing with data variability and noisy input measurements that lead to incorrect solutions. Furthermore, nonlinear constraints may result in outcomes that are either infeasible or suboptimal, such as nonconvex optimization. This paper introduces a novel regularized physics-informed neural network (RPINN) framework as a new NOPT tool for both supervised and unsupervised data-driven scenarios. Our RPINN is threefold: By using custom activation functions and regularization penalties in an artificial neural network (ANN), RPINN can handle data variability and noisy inputs. Furthermore, it employs physics principles to construct the network architecture, computing the optimization variables based on network weights and learned features. In addition, it uses automatic differentiation training to make the system scalable and cut down on computation time through batch-based back-propagation. The test results for both supervised and unsupervised NOPT tasks show that our RPINN can provide solutions that are competitive compared to state-of-the-art solvers. In turn, the robustness of RPINN against noisy input measurements makes it particularly valuable in environments with fluctuating information. Specifically, we test a uniform mixture model and a gas-powered system as NOPT scenarios. Overall, with RPINN, its ANN-based foundation offers significant flexibility and scalability.">
+        <tr id="Physics informed neural networks (PINNs) have effectively demonstrated the ability to approximate the solutions of a system of partial differential equations (PDEs) by embedding the governing equations and auxiliary conditions directly into the loss function using automatic differentiation. Despite demonstrating potential across diverse applications, PINNs have encountered challenges in accurately predicting solutions for time-dependent problems. In response, this study presents a novel methodology aimed at enhancing the predictive capability of PINNs for time-dependent scenarios. Our approach involves dividing the temporal domain into multiple subdomains and employing an adaptive weighting strategy at the initial condition and at the interfaces between these subdomains. By employing such interfacial conditioning in physics informed neural networks (IcPINN), we have solved several unsteady PDEs (e.g., Allen–Cahn equation, advection equation, Korteweg–De Vries equation, Cahn–Hilliard equation, and Navier–Stokes equations) and conducted a comparative analysis with numerical results. The results have demonstrated that IcPINN was successful in obtaining highly accurate results in each case without the need for using any labeled data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/516f48e222fdad35b92113ecdbf8a459d37c95aa" target='_blank'>
-              A Regularized Physics-Informed Neural Network to Support Data-Driven Nonlinear Constrained Optimization
+          <td><a href="https://www.semanticscholar.org/paper/4c70375c9f4682ea136b267ae844b868bd46ae3c" target='_blank'>
+              Interfacial conditioning in physics informed neural networks
               </a>
             </td>
           <td>
-            Diego Armando Perez-Rosero, A. Álvarez-Meza, C. Castellanos-Dominguez
+            Saykat Kumar Biswas, N. K. Anand
           </td>
-          <td>2024-07-18</td>
-          <td>Computers</td>
+          <td>2024-07-01</td>
+          <td>Physics of Fluids</td>
           <td>0</td>
-          <td>15</td>
+          <td>1</td>
+        </tr>
+
+        <tr id="The objective of system identification is to derive models from input/output data. To extend advancements in regularization techniques for linear finite impulse response (FIR) models to the nonlinear domain, we employ local model networks (LMNs) with locally regularized FIR models to identify nonlinear processes. The training of the LMN is performed using the local linear model tree (LOLIMOT) algorithm, resulting in both the partitioning of the model space and the estimation of the corresponding linear local models for each region. One key advantage of this algorithm lies in its ability to create separate input spaces for the linear models (x-space) and the validity functions (z-space) comprising the partitioning. While the most straightforward choice (x-space = z-space) results in an extremely high-dimensional z-space for local FIR models, we ad-dress this drawback by proposing different z-spaces spanned by the input spaces of autoregressive with exogenous inputs (ARX) models or Laguerre filter models, respectively. The theoretical capabilities for the proposed z-spaces are characterized. The superiority in terms of computation time, as well as comparable performance for Laguerre z-spaces and FIR z-spaces, is demon-strated through numerical examples. Additionally, the limitations for the utilization of ARX z-spaces are highlighted. Finally, all z-spaces have been evaluated on real-world data of a Wiener-Hammerstein benchmark. The FIR and Laguerre z- space showed comparable performance, while the ARX z-space performed worse.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/9d7f2bb8d2c64f0e73154c706dc8921696b583cb" target='_blank'>
+              On the Choice of the Scheduling Variables for Dynamic Local Model Networks with Local Regularized FIR Models
+              </a>
+            </td>
+          <td>
+            Christopher Illg, T. Kösters, Oliver Nelles
+          </td>
+          <td>2024-06-30</td>
+          <td>2024 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)</td>
+          <td>0</td>
+          <td>2</td>
         </tr>
 
         <tr id="The task of sampling from a probability density can be approached as transporting a tractable density function to the target, known as dynamical measure transport. In this work, we tackle it through a principled unified framework using deterministic or stochastic evolutions described by partial differential equations (PDEs). This framework incorporates prior trajectory-based sampling methods, such as diffusion models or Schr\"odinger bridges, without relying on the concept of time-reversals. Moreover, it allows us to propose novel numerical methods for solving the transport task and thus sampling from complicated targets without the need for the normalization constant or data samples. We employ physics-informed neural networks (PINNs) to approximate the respective PDE solutions, implying both conceptional and computational advantages. In particular, PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently, leading to significantly better mode coverage in the sampling task compared to alternative methods. Moreover, they can readily be fine-tuned with Gauss-Newton methods to achieve high accuracy in sampling.">
@@ -2571,267 +2690,267 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
               </a>
             </td>
           <td>
-            Jingtong Sun, Julius Berner, Lorenz Richter, Marius Zeinhofer, Johannes Muller, K. Azizzadenesheli, A. Anandkumar
+            Jingtong Sun, Julius Berner, Lorenz Richter, Marius Zeinhofer, Johannes Müller, K. Azizzadenesheli, A. Anandkumar
           </td>
           <td>2024-07-10</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>31</td>
+          <td>32</td>
         </tr>
 
-        <tr id="Physics-Informed Neural Networks (PINNs) have emerged as a robust framework for solving Partial Differential Equations (PDEs) by approximating their solutions via neural networks and imposing physics-based constraints on the loss function. Traditionally, Multilayer Perceptrons (MLPs) are the neural network of choice, and significant progress has been made in optimizing their training. Recently, Kolmogorov-Arnold Networks (KANs) were introduced as a viable alternative, with the potential of offering better interpretability and efficiency while requiring fewer parameters. In this paper, we present a fast JAX-based implementation of grid-dependent Physics-Informed Kolmogorov-Arnold Networks (PIKANs) for solving PDEs. We propose an adaptive training scheme for PIKANs, incorporating known MLP-based PINN techniques, introducing an adaptive state transition scheme to avoid loss function peaks between grid updates, and proposing a methodology for designing PIKANs with alternative basis functions. Through comparative experiments we demonstrate that these adaptive features significantly enhance training efficiency and solution accuracy. Our results illustrate the effectiveness of PIKANs in improving performance for PDE solutions, highlighting their potential as a superior alternative in scientific and engineering applications.">
+        <tr id="Latent dynamical systems have been widely used to characterize the dynamics of neural population activity in the brain. However, these models typically ignore the fact that the brain contains multiple cell types. This limits their ability to capture the functional roles of distinct cell classes, or to accurately predict the effects of cell-specific optogenetic perturbations on neural activity or behavior. To overcome these limitations, we introduce the “cell-type dynamical systems” (CTDS) model. This model extends latent linear dynamical systems to contain distinct latent variables for each cell class, with biologically inspired constraints on both dynamics and emissions. To illustrate our approach, we consider neural recordings with distinct excitatory (E) and inhibitory (I) populations. The CTDS model defines separate latents for E and I cells, and constrains the dynamics so that E (I) latents have a strictly positive (negative) effects on other latents. We applied CTDS to recordings from rat frontal orienting fields (FOF) and anterior dorsal striatum (ADS) during an auditory decision-making task. The model achieved higher accuracy than a standard linear dynamical system (LDS), and revealed that both E and I latents could be used to decode the animal’s choice, showing that choice-related information is not restricted to a single cell class. We also performed in-silico optogenetic perturbation experiments in the FOF and ADS, and found that CTDS was able to replicate the causal effects of different perturbations on behavior, whereas a standard LDS model—which lacks the ability to capture cell-specific perturbations—did not. Crucially, our model allowed us to understand the effects of these perturbations by revealing the dynamics of different cell-specific latents. Finally, CTDS can also be used to identify cell types for neurons whose class labels are unknown in electrophysiological recordings. These results illustrate the power of the CTDS model to provide more accurate and more biologically interpretable descriptions of neural population dynamics and their relationship to behavior.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c1aaa25c69658448f0abd4e2430cf6925f39fdd5" target='_blank'>
-              Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks
+          <td><a href="https://www.semanticscholar.org/paper/31c1cd3d2f0ffab7d6fe212ee7ca7fdd655d8dfa" target='_blank'>
+              Disentangling the Roles of Distinct Cell Classes with Cell-Type Dynamical Systems
               </a>
             </td>
           <td>
-            Spyros Rigas, M. Papachristou, Theofilos Papadopoulos, Fotios Anagnostopoulos, Georgios Alexandridis
+            Aditi Jha, Diksha Gupta, C. Brody, Jonathan W. Pillow
           </td>
-          <td>2024-07-24</td>
-          <td>ArXiv</td>
+          <td>2024-07-11</td>
+          <td>bioRxiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>45</td>
         </tr>
 
-        <tr id="We introduce data to predictive control, D2PC, a framework to facilitate the design of robust and predictive controllers from data. The proposed framework is designed for discrete-time stochastic linear systems with output measurements and provides a principled design of a predictive controller based on data. The framework starts with a parameter identification method based on the Expectation-Maximization algorithm, which incorporates pre-defined structural constraints. Additionally, we provide an asymptotically correct method to quantify uncertainty in parameter estimates. Next, we develop a strategy to synthesize robust dynamic output-feedback controllers tailored to the derived uncertainty characterization. Finally, we introduce a predictive control scheme that guarantees recursive feasibility and satisfaction of chance constraints. This framework marks a significant advancement in integrating data into robust and predictive control schemes. We demonstrate the efficacy of D2PC through a numerical example involving a $10$-dimensional spring-mass-damper system.">
+        <tr id="Due to their flexibility and ease of use, Dynamical Movement Primitives (DMPs) are widely used in robotics applications and research. DMPs combine linear dynamical systems to achieve robustness to perturbations and adaptation to moving targets with non-linear function approximators to fit a wide range of demonstrated trajectories.We propose a novel DMP formulation with a generalized logistic function as a delayed goal system. This formulation inherently has low initial jerk, and generates the bell-shaped velocity profiles that are typical of human movement. As the novel formulation is more expressive, it is able to fit a wide range of human demonstrations well, also without a non-linear forcing term. We exploit this increased expressiveness by automating the fitting of the dynamical system parameters through opti-mization. Our experimental evaluation demonstrates that this optimization regularizes the forcing term, and improves the interpolation accuracy of parametric DMPs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2ea52a361e1eddc6fae9770357307a43f124b006" target='_blank'>
-              From Data to Predictive Control: A Framework for Stochastic Linear Systems with Output Measurements
+          <td><a href="https://www.semanticscholar.org/paper/904213d0ea3643d20cba8b38f58690176de07076" target='_blank'>
+              Fitting Parameters of Linear Dynamical Systems to Regularize Forcing Terms in Dynamical Movement Primitives
               </a>
             </td>
           <td>
-            Haldun Balim, Andrea Carron, M. Zeilinger, Johannes Kohler
+            F. Stulp, Adrià Colomé, Carme Torras
           </td>
-          <td>2024-07-24</td>
-          <td>ArXiv</td>
+          <td>2024-05-13</td>
+          <td>2024 IEEE International Conference on Robotics and Automation (ICRA)</td>
           <td>0</td>
-          <td>35</td>
+          <td>32</td>
         </tr>
 
-        <tr id="This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only control penalty function and constraints are provided. Leveraging the theory of reproducing kernel Hilbert spaces, we introduce novel kernel mean embeddings (KMEs) to identify the Markov transition operators associated with controlled diffusion processes. The KME learning approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions. Thus, unlike traditional dynamic programming methods, our approach exploits the ``kernel trick'' to break the curse of dimensionality. We demonstrate the effectiveness of our method through numerical examples, highlighting its ability to solve a large class of nonlinear optimal control problems.">
+        <tr id="Solving partial differential equations (PDEs) is a fundamental problem in engineering and science. While neural PDE solvers can be more efficient than established numerical solvers, they often require large amounts of training data that is costly to obtain. Active Learning (AL) could help surrogate models reach the same accuracy with smaller training sets by querying classical solvers with more informative initial conditions and PDE parameters. While AL is more common in other domains, it has yet to be studied extensively for neural PDE solvers. To bridge this gap, we introduce AL4PDE, a modular and extensible active learning benchmark. It provides multiple parametric PDEs and state-of-the-art surrogate models for the solver-in-the-loop setting, enabling the evaluation of existing and the development of new AL methods for PDE solving. We use the benchmark to evaluate batch active learning algorithms such as uncertainty- and feature-based methods. We show that AL reduces the average error by up to 71% compared to random sampling and significantly reduces worst-case errors. Moreover, AL generates similar datasets across repeated runs, with consistent distributions over the PDE parameters and initial conditions. The acquired datasets are reusable, providing benefits for surrogate models not involved in the data generation.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/69ffcc674bf67738c50bad11d4a1a6996a25767b" target='_blank'>
-              Data-Driven Optimal Feedback Laws via Kernel Mean Embeddings
+          <td><a href="https://www.semanticscholar.org/paper/1dd92c53455982680c81f73c1708da2a22eaa764" target='_blank'>
+              Active Learning for Neural PDE Solvers
               </a>
             </td>
           <td>
-            Petar Bevanda, Nicolas Hoischen, Stefan Sosnowski, Sandra Hirche, Boris Houska
+            Daniel Musekamp, Marimuthu Kalimuthu, David Holzmüller, Makoto Takamoto, Mathias Niepert
           </td>
-          <td>2024-07-23</td>
+          <td>2024-08-02</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>15</td>
+          <td>8</td>
         </tr>
 
-        <tr id="We study the model reduction by moment matching problem for linear systems in a data-driven framework. We show that reduced-order models can be directly computed from data without knowledge of the structure of the signal generator or of its internal state. The reduced-order models thus obtained match the moments of the unknown underlying system asymptotically. Our construction provides a simple way to enforce additional constraints in the reduced-order model. We demonstrate the applicability of the results using data from a high-dimensional model of a building.">
+        <tr id="We study nonequilibrium quantum dynamics of spin chains by employing principal component analysis (PCA) on data sets of wave function snapshots and examine how information propagates within these data sets. The quantities we employ are derived from the spectrum of the sample second moment matrix, built directly from data sets. Our investigations on several interacting spin chains featuring distinct spin or energy transport reveal that the growth of data information spreading follows the same dynamical exponents as that of the underlying quantum transport of spin or energy. Specifically, our approach enables an easy, data-driven, and importantly interpretable diagnostic to track energy transport with a limited number of samples, which is usually challenging without any assumption on the Hamiltonian form. These observations are obtained at a modest finite size and evolution time, which aligns with experimental and numerical constraints. Our framework directly applies to experimental quantum simulator data sets of dynamics in higher-dimensional systems, where classical simulation methods usually face significant limitations and apply equally to both near- and far-from-equilibrium quenches.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/83399652779edc533b785a20de6431d8d0060e66" target='_blank'>
-              Data-Driven Model Reduction by Moment Matching for Linear Systems Driven by an Unknown Implicit Signal Generator
+          <td><a href="https://www.semanticscholar.org/paper/94b4a5b7b344b91f9543dbd6c577fd548f273348" target='_blank'>
+              Diagnosing quantum transport from wave function snapshots
               </a>
             </td>
           <td>
-            Debraj Bhattacharjee, Alessandro Astolfi
+            D. S. Bhakuni, Roberto Verdel, Cristiano Muzzi, Riccardo Andreoni, Monika Aidelsburger, Marcello Dalmonte
           </td>
-          <td>2024-06-25</td>
-          <td>2024 European Control Conference (ECC)</td>
+          <td>2024-07-12</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>10</td>
         </tr>
 
-        <tr id="Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable -- additional dynamical information is needed. The theory of linear response around nonequilibrium steady states relies on path ensemble averaging, which makes this theory inapplicable to perturbations that affect the diffusion constant or temperature in a stochastic system. Here, we show that a separate, ``effective'' physical process can be used to describe the perturbed dynamics and that this dynamics in turn allows us to accurately calculate the response to a change in the diffusion. Interestingly, the effective dynamics contains an additional drift that is proportional to the ``score'' of the instantaneous probability density of the system -- this object has also been studied extensively in recent years in the context of denoising diffusion models in the machine learning literature. Exploiting recently developed algorithms for learning the score, we show that we can carry out nonequilibrium response calculations on systems for which the exact score cannot be obtained.">
+        <tr id="To understand and control the dynamics of coupled oscillators, it is important to reveal the structure of the interaction network from observed data. While various techniques have been developed for inferring the network of asynchronous systems, it remains challenging to infer the network of synchronized oscillators without external stimulations. In this study, we develop a method for non-invasively inferring the network of synchronized and/or de-synchronized oscillators. An approach to network inference would be to fit the data to a set of differential equations describing the dynamics of phase oscillators. However, we show that this method fails to infer the true network due to the problems that arise when we use short-time phase differences. Therefore, we propose a method based on the circle map, which describes the phase change in one oscillatory cycle. We demonstrate the efficacy of the proposed method through the successful inference of the network structure from simulated data of limit cycle oscillator models. Our method provides a unified and concise framework for network estimation for a wide class of oscillator systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f45af9914ab526c24b8c0bd202775dddc280a5c4" target='_blank'>
-              Computing Nonequilibrium Responses with Score-shifted Stochastic Differential Equations
+          <td><a href="https://www.semanticscholar.org/paper/a85617c5e51b81ee7f45457c35d92af54f040aed" target='_blank'>
+              Network inference from oscillatory signals based on circle map
               </a>
             </td>
           <td>
-            J'er'emie Klinger, Grant M. Rotskoff
+            Akari Matsuki, Hiroshi Kori, Ryota Kobayashi
           </td>
-          <td>2024-06-20</td>
+          <td>2024-07-10</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>24</td>
+          <td>1</td>
+          <td>2</td>
         </tr>
 
-        <tr id="We apply two data assimilation (DA) methods, a smoother and a filter, and a model-free machine learning (ML) shallow network to forecast two weakly turbulent systems. We analyse the effect of the spatial sparsity of observations on accuracy of the predictions obtained from these data-driven methods. Based on the results, we divide the spatial sparsity levels in three zones. First is the good-predictions zone in which both DA and ML methods work. We find that in the good-predictions zone the observations remain dense enough to accurately capture the fractal manifold of the system's dynamics, which is measured using the correlation dimension. The accuracy of the DA methods in this zone remains almost as good as for full-resolution observations. Second is the reasonable-predictions zone in which the DA methods still work but at reduced prediction accuracy. Third is the bad-predictions zone in which even the DA methods fail. We find that the sparsity level up to which the DA methods work is almost the same up to which chaos synchronisation of these systems can be achieved. The main implications of these results are that they (i) firmly establish the spatial resolution up to which the data-driven methods can be utilised, (ii) provide measures to determine if adding more sensors will improve the predictions, and (iii) quantify the advantage (in terms of the required measurement resolution) of using the governing equations within data-driven methods. We also discuss the applicability of these results to fully developed turbulence.">
+        <tr id="Physics-Informed Neural Networks (PINNs) have emerged as a robust framework for solving Partial Differential Equations (PDEs) by approximating their solutions via neural networks and imposing physics-based constraints on the loss function. Traditionally, Multilayer Perceptrons (MLPs) are the neural network of choice, and significant progress has been made in optimizing their training. Recently, Kolmogorov-Arnold Networks (KANs) were introduced as a viable alternative, with the potential of offering better interpretability and efficiency while requiring fewer parameters. In this paper, we present a fast JAX-based implementation of grid-dependent Physics-Informed Kolmogorov-Arnold Networks (PIKANs) for solving PDEs. We propose an adaptive training scheme for PIKANs, incorporating known MLP-based PINN techniques, introducing an adaptive state transition scheme to avoid loss function peaks between grid updates, and proposing a methodology for designing PIKANs with alternative basis functions. Through comparative experiments we demonstrate that these adaptive features significantly enhance training efficiency and solution accuracy. Our results illustrate the effectiveness of PIKANs in improving performance for PDE solutions, highlighting their potential as a superior alternative in scientific and engineering applications.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f37955fcf738b892c9cedb2952e279d466fad9b8" target='_blank'>
-              Predictability of weakly turbulent systems from spatially sparse observations using data assimilation and machine learning
+          <td><a href="https://www.semanticscholar.org/paper/c1aaa25c69658448f0abd4e2430cf6925f39fdd5" target='_blank'>
+              Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks
               </a>
             </td>
           <td>
-            Vikrant Gupta, Yuanqing Chen, Minping Wan
+            Spyros Rigas, M. Papachristou, Theofilos Papadopoulos, Fotios Anagnostopoulos, Georgios Alexandridis
           </td>
-          <td>2024-07-14</td>
+          <td>2024-07-24</td>
           <td>ArXiv</td>
-          <td>0</td>
+          <td>1</td>
           <td>1</td>
         </tr>
 
-        <tr id="We investigate learning the eigenfunctions of evolution operators for time-reversal invariant stochastic processes, a prime example being the Langevin equation used in molecular dynamics. Many physical or chemical processes described by this equation involve transitions between metastable states separated by high potential barriers that can hardly be crossed during a simulation. To overcome this bottleneck, data are collected via biased simulations that explore the state space more rapidly. We propose a framework for learning from biased simulations rooted in the infinitesimal generator of the process and the associated resolvent operator. We contrast our approach to more common ones based on the transfer operator, showing that it can provably learn the spectral properties of the unbiased system from biased data. In experiments, we highlight the advantages of our method over transfer operator approaches and recent developments based on generator learning, demonstrating its effectiveness in estimating eigenfunctions and eigenvalues. Importantly, we show that even with datasets containing only a few relevant transitions due to sub-optimal biasing, our approach recovers relevant information about the transition mechanism.">
+        <tr id="The research topic is: data-driven Bayesian state estimation with compressed measurement (BSCM) of model-free process, say for a (causal) tracking application. The dimension of the temporal measurement vector is lower than the dimension of the temporal state vector to be estimated. Hence the state estimation problem is an underdetermined inverse problem. The state-space-model (SSM) of the underlying dynamical process is assumed to be unknown and hence, we use the terminology 'model-free process'. In absence of the SSM, we can not employ traditional model-driven methods like Kalman Filter (KF) and Particle Filter (PF) and instead require data-driven methods. We first experimentally show that two existing unsupervised learning-based data-driven methods fail to address the BSCM problem for model-free process; they are data-driven nonlinear state estimation (DANSE) method and deep Markov model (DMM) method. The unsupervised learning uses unlabelled data comprised of only noisy measurements. While DANSE provides a good predictive performance to model the temporal measurement data as time-series, its unsupervised learning lacks a regularization for state estimation. We then investigate use of a semi-supervised learning approach, and develop a semi-supervised learning-based DANSE method, referred to as SemiDANSE. In the semi-supervised learning, we use a limited amount of labelled data along-with a large amount of unlabelled data, and that helps to bring the desired regularization for BSCM problem in the absence of SSM. The labelled data means pairwise measurement-and-state data. Using three chaotic dynamical systems (or processes) with nonlinear SSMs as benchmark, we show that the data-driven SemiDANSE provides competitive performance for BSCM against three SSM-informed methods - a hybrid method called KalmanNet, and two traditional model-driven methods called extended KF and unscented KF.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/33ff38eef166593508576694dab15cbdbd79cb82" target='_blank'>
-              From Biased to Unbiased Dynamics: An Infinitesimal Generator Approach
+          <td><a href="https://www.semanticscholar.org/paper/f2671168e70fb8ea79bbef366bd1d59fc9ae9415" target='_blank'>
+              Data-driven Bayesian State Estimation with Compressed Measurement of Model-free Process using Semi-supervised Learning
               </a>
             </td>
           <td>
-            Timothée Devergne, Vladimir Kostic, Michele Parrinello, Massimiliano Pontil
+            Anubhab Ghosh, Y. Eldar, Saikat Chatterjee
           </td>
-          <td>2024-06-13</td>
+          <td>2024-07-10</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>27</td>
         </tr>
 
-        <tr id="High-precision control for nonlinear systems is impeded by the low-fidelity dynamical model and external disturbance. Especially, the intricate coupling between internal uncertainty and external disturbance is usually difficult to be modeled explicitly. Here we show an effective and convergent algorithm enabling accurate estimation of the coupled disturbance via combining control and learning philosophies. Specifically, by resorting to Chebyshev series expansion, the coupled disturbance is firstly decomposed into an unknown parameter matrix and two known structures depending on system state and external disturbance respectively. A Regularized Least Squares (RLS) algorithm is subsequently formalized to learn the parameter matrix by using historical time-series data. Finally, a higher-order disturbance observer (HODO) is developed to achieve a high-precision estimation of the coupled disturbance by utilizing the learned portion. The efficiency of the proposed algorithm is evaluated through extensive simulations. We believe this work can offer a new option to merge learning schemes into the control framework for addressing existing intractable control problems.">
+        <tr id="Modern datasets in neuroscience enable unprecedented inquiries into the relationship between complex behaviors and the activity of many simultaneously recorded neurons. While latent variable models can successfully extract low-dimensional embeddings from such recordings, using them to generate realistic spiking data, especially in a behavior-dependent manner, still poses a challenge. Here, we present Latent Diffusion for Neural Spiking data (LDNS), a diffusion-based generative model with a low-dimensional latent space: LDNS employs an autoencoder with structured state-space (S4) layers to project discrete high-dimensional spiking data into continuous time-aligned latents. On these inferred latents, we train expressive (conditional) diffusion models, enabling us to sample neural activity with realistic single-neuron and population spiking statistics. We validate LDNS on synthetic data, accurately recovering latent structure, firing rates, and spiking statistics. Next, we demonstrate its flexibility by generating variable-length data that mimics human cortical activity during attempted speech. We show how to equip LDNS with an expressive observation model that accounts for single-neuron dynamics not mediated by the latent state, further increasing the realism of generated samples. Finally, conditional LDNS trained on motor cortical activity during diverse reaching behaviors can generate realistic spiking data given reach direction or unseen reach trajectories. In summary, LDNS simultaneously enables inference of low-dimensional latents and realistic conditional generation of neural spiking datasets, opening up further possibilities for simulating experimentally testable hypotheses.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2c2b582f6ad335402a40cb9dffeaea1baf4781dd" target='_blank'>
-              Disturbance Observer for Estimating Coupled Disturbances
+          <td><a href="https://www.semanticscholar.org/paper/4063dac20e1d0f5e11b6e07992c712df9558080d" target='_blank'>
+              Latent Diffusion for Neural Spiking Data
               </a>
             </td>
           <td>
-            Jindou Jia, Yuhang Liu, Kexin Guo, Xiang Yu, Lihua Xie, Lei Guo
+            J. Kapoor, Auguste Schulz, Julius Vetter, Felix Pei, Richard Gao, J. H. Macke
           </td>
-          <td>2024-07-18</td>
+          <td>2024-06-27</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>16</td>
+          <td>3</td>
         </tr>
 
-        <tr id="We study the problem of estimating the states of a linear system based on measured data. We investigate the problem in both deterministic and stochastic settings. In the deterministic case, we develop data-driven conditions under which we can reconstruct state trajectories uniquely. Also, we discuss the case in which we have some missing data in the given input/output measurements. In the stochastic case, we develop a Kalman filter-like algorithm to recursively estimate both states and outputs. Finally, we consider a multi-input multi-output system to elucidate the developed results.">
+        <tr id="This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only control penalty function and constraints are provided. Leveraging the theory of reproducing kernel Hilbert spaces, we introduce novel kernel mean embeddings (KMEs) to identify the Markov transition operators associated with controlled diffusion processes. The KME learning approach seamlessly integrates with modern convex operator-theoretic Hamilton-Jacobi-Bellman recursions. Thus, unlike traditional dynamic programming methods, our approach exploits the ``kernel trick'' to break the curse of dimensionality. We demonstrate the effectiveness of our method through numerical examples, highlighting its ability to solve a large class of nonlinear optimal control problems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/344c27f38393d70906627a195cc65ea2636e5a14" target='_blank'>
-              Data-Driven State Estimation for Linear Systems
+          <td><a href="https://www.semanticscholar.org/paper/69ffcc674bf67738c50bad11d4a1a6996a25767b" target='_blank'>
+              Data-Driven Optimal Feedback Laws via Kernel Mean Embeddings
               </a>
             </td>
           <td>
-            Vikas Kumar Mishra, S. Hiremath, N. Bajçinca
+            Petar Bevanda, Nicolas Hoischen, Stefan Sosnowski, Sandra Hirche, Boris Houska
           </td>
-          <td>2024-06-25</td>
-          <td>2024 European Control Conference (ECC)</td>
+          <td>2024-07-23</td>
+          <td>ArXiv</td>
           <td>0</td>
           <td>15</td>
         </tr>
 
-        <tr id="Macroscopic features of dynamical systems such as almost-invariant sets and coherent sets provide crucial high-level information on how the dynamics organises phase space. We introduce a method to identify time-parameterised families of almost-invariant sets in time-dependent dynamical systems, as well as the families' emergence and disappearance. In contrast to coherent sets, which may freely move about in phase space over time, our technique focuses on families of metastable sets that are quasi-stationary in space. Our straightforward approach extends successful transfer operator methods for almost-invariant sets to time-dependent dynamics and utilises the Ulam scheme for the generator of the transfer operator on a time-expanded domain. The new methodology is illustrated with an idealised fluid flow and with atmospheric velocity data. We identify atmospheric blocking events in the 2003 European heatwave and compare our technique to existing geophysical methods of blocking diagnosis.">
+        <tr id="We introduce data to predictive control, D2PC, a framework to facilitate the design of robust and predictive controllers from data. The proposed framework is designed for discrete-time stochastic linear systems with output measurements and provides a principled design of a predictive controller based on data. The framework starts with a parameter identification method based on the Expectation-Maximization algorithm, which incorporates pre-defined structural constraints. Additionally, we provide an asymptotically correct method to quantify uncertainty in parameter estimates. Next, we develop a strategy to synthesize robust dynamic output-feedback controllers tailored to the derived uncertainty characterization. Finally, we introduce a predictive control scheme that guarantees recursive feasibility and satisfaction of chance constraints. This framework marks a significant advancement in integrating data into robust and predictive control schemes. We demonstrate the efficacy of D2PC through a numerical example involving a $10$-dimensional spring-mass-damper system.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/85cdef684e76e594fd24e0e2863fe622d0a8314d" target='_blank'>
-              Identifying the onset and decay of quasi-stationary families of almost-invariant sets with an application to atmospheric blocking events
+          <td><a href="https://www.semanticscholar.org/paper/2ea52a361e1eddc6fae9770357307a43f124b006" target='_blank'>
+              From Data to Predictive Control: A Framework for Stochastic Linear Systems with Output Measurements
               </a>
             </td>
           <td>
-            Aleksandar Badza, Gary Froyland School of Mathematics, Statistics Unsw Sydney Nsw Australia
+            Haldun Balim, Andrea Carron, M. Zeilinger, Johannes Kohler
           </td>
-          <td>2024-07-09</td>
+          <td>2024-07-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>36</td>
         </tr>
 
-        <tr id="One of the core concepts in science, and something that happens intuitively in every-day dynamic systems modeling, is the combination of models or methods. Especially in dynamical systems modeling, often two or more structures are combined to obtain a more powerful or efficient architecture regarding a specific application (area). Further, even physical simulations are combined with machine learning architectures, to increase prediction accuracy or optimize the computational performance. In this work, we shortly discuss, which types of models are usually combined and propose a model interface that is capable of expressing a width variety of mixed algebraic, discrete and differential equation based models. Further, we examine different established, as well as new ways of combining these models from a system theoretical point of view and highlight two challenges - algebraic loops and local event affect functions in discontinuous models - that require a special approach. Finally, we propose a new wildcard topology, that is capable of describing the generic connection between two combined models in an easy to interpret fashion that can be learned as part of a gradient based optimization procedure. The contributions of this paper are highlighted at a proof of concept: Different connection topologies between two models are learned, interpreted and compared applying the proposed methodology and software implementation.">
+        <tr id="We study the model reduction by moment matching problem for linear systems in a data-driven framework. We show that reduced-order models can be directly computed from data without knowledge of the structure of the signal generator or of its internal state. The reduced-order models thus obtained match the moments of the unknown underlying system asymptotically. Our construction provides a simple way to enforce additional constraints in the reduced-order model. We demonstrate the applicability of the results using data from a high-dimensional model of a building.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fe81ab9d1a688154b1e40c6ca68ccf95c122d0c7" target='_blank'>
-              Learnable & Interpretable Model Combination in Dynamic Systems Modeling
+          <td><a href="https://www.semanticscholar.org/paper/83399652779edc533b785a20de6431d8d0060e66" target='_blank'>
+              Data-Driven Model Reduction by Moment Matching for Linear Systems Driven by an Unknown Implicit Signal Generator
               </a>
             </td>
           <td>
-            Tobias Thummerer, Lars Mikelsons
+            Debraj Bhattacharjee, Alessandro Astolfi
           </td>
-          <td>2024-06-12</td>
-          <td>ArXiv</td>
+          <td>2024-06-25</td>
+          <td>2024 European Control Conference (ECC)</td>
           <td>0</td>
-          <td>11</td>
+          <td>2</td>
         </tr>
 
-        <tr id="A data-driven approach to calculating tight-binding models for discrete coupled-mode systems is presented. Specifically, spectral and topological data is used to build an appropriate discrete model that accurately replicates these properties. This work is motivated by topological insulator systems that are often described by tight-binding models. The problem is formulated as the minimization of an appropriate residual (objective) function. Given bulk spectral data and a topological index (e.g. winding number), an appropriate discrete model is obtained to arbitrary precision. A nonlinear least squares method is used to determine the coefficients. The effectiveness of the scheme is highlighted against a Schr\"odinger equation with a periodic potential that can be described by the Su-Schrieffer-Heeger model.">
+        <tr id="Computer simulations based on partial differential equations (PDEs) describing physical phenomena, are widely used for analyzing the performance of high voltage insulation. Such simulation models require access to physical model parameters, which are often hard to obtain. The purpose of the present paper is to explore how Physics-Informed Neural Network (PINN) tailored for specific PDEs, can be used to extract relevant physical parameters from synthetic data. Electric potential or charge distributions in 1-dimensional coaxial and Cartesian domains were used as training data for PINN models. The following physical parameters were successfully extracted: (i) space charge profiles, (ii) mobilities of ions, and (iii) the radius of the inner electrode in the coaxial geometry. The impact of noisy training data on the accuracy was also studied for the different cases. The main finding is that PINN models can successfully be used to extract model parameters for electrical charge transport problems using synthetic data as input. This approach has large potential to strengthen the research on charge dynamics in gas, liquid, and solid insulation as well as other topics related to high voltage insulation systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b260d38c46caaea8a67dc40a10c56986fd078985" target='_blank'>
-              Data-driven approximations of topological insulator systems
+          <td><a href="https://www.semanticscholar.org/paper/f9d44af663a8e4f7e16a2dffe2c289b99726e746" target='_blank'>
+              Usage of Physics-Informed Neural Network to Extract Physical Parameters From High Voltage Experiments
               </a>
             </td>
           <td>
-            Justin T. Cole, Michael J. Nameika
+            O. Hjortstam, C. Björnson, F. Ågren, T. Hammarström, Y. V. Serdyuk, C. Häger
           </td>
-          <td>2024-07-01</td>
-          <td>ArXiv</td>
+          <td>2024-06-30</td>
+          <td>2024 IEEE 5th International Conference on Dielectrics (ICD)</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Although neural operator networks theoretically approximate any operator mapping, the limited generalization capability prevents them from learning correct physical dynamics when potential data biases exist, particularly in the practical PDE solving scenario where the available data amount is restricted or the resolution is extremely low. To address this issue, we propose and formulate the Physical Trajectory Residual Learning (DeltaPhi), which learns to predict the physical residuals between the pending solved trajectory and a known similar auxiliary trajectory. First, we transform the direct operator mapping between input-output function fields in original training data to residual operator mapping between input function pairs and output function residuals. Next, we learn the surrogate model for the residual operator mapping based on existing neural operator networks. Additionally, we design helpful customized auxiliary inputs for efficient optimization. Through extensive experiments, we conclude that, compared to direct learning, physical residual learning is preferred for PDE solving.">
+        <tr id="We apply two data assimilation (DA) methods, a smoother and a filter, and a model-free machine learning (ML) shallow network to forecast two weakly turbulent systems. We analyse the effect of the spatial sparsity of observations on accuracy of the predictions obtained from these data-driven methods. Based on the results, we divide the spatial sparsity levels in three zones. First is the good-predictions zone in which both DA and ML methods work. We find that in the good-predictions zone the observations remain dense enough to accurately capture the fractal manifold of the system's dynamics, which is measured using the correlation dimension. The accuracy of the DA methods in this zone remains almost as good as for full-resolution observations. Second is the reasonable-predictions zone in which the DA methods still work but at reduced prediction accuracy. Third is the bad-predictions zone in which even the DA methods fail. We find that the sparsity level up to which the DA methods work is almost the same up to which chaos synchronisation of these systems can be achieved. The main implications of these results are that they (i) firmly establish the spatial resolution up to which the data-driven methods can be utilised, (ii) provide measures to determine if adding more sensors will improve the predictions, and (iii) quantify the advantage (in terms of the required measurement resolution) of using the governing equations within data-driven methods. We also discuss the applicability of these results to fully developed turbulence.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/75ea87f76067c9b62442cad18c16c45c61d35489" target='_blank'>
-              DeltaPhi: Learning Physical Trajectory Residual for PDE Solving
+          <td><a href="https://www.semanticscholar.org/paper/f37955fcf738b892c9cedb2952e279d466fad9b8" target='_blank'>
+              Predictability of weakly turbulent systems from spatially sparse observations using data assimilation and machine learning
               </a>
             </td>
           <td>
-            Xihang Yue, Linchao Zhu, Yi Yang
+            Vikrant Gupta, Yuanqing Chen, Minping Wan
           </td>
-          <td>2024-06-14</td>
+          <td>2024-07-14</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>41</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus struggling with the curse of dimensionality (CoD). Physics-informed neural networks (PINNs) offer a promising solution due to their universal approximation, generalization ability, and mesh-free training. In principle, Monte Carlo fractional PINN (MC-fPINN) estimates fractional derivatives using Monte Carlo methods and thus could lift CoD. However, this may cause significant variance and errors, hence affecting convergence; in addition, MC-fPINN is sensitive to hyperparameters. In general, numerical methods and specifically PINNs for tempered fractional PDEs are under-developed. Herein, we extend MC-fPINN to tempered fractional PDEs to address these issues, resulting in the Monte Carlo tempered fractional PINN (MC-tfPINN). To reduce possible high variance and errors from Monte Carlo sampling, we replace the one-dimensional (1D) Monte Carlo with 1D Gaussian quadrature, applicable to both MC-fPINN and MC-tfPINN. We validate our methods on various forward and inverse problems of fractional and tempered fractional PDEs, scaling up to 100,000 dimensions. Our improved MC-fPINN/MC-tfPINN using quadrature consistently outperforms the original versions in accuracy and convergence speed in very high dimensions.">
+        <tr id="Macroscopic features of dynamical systems such as almost-invariant sets and coherent sets provide crucial high-level information on how the dynamics organises phase space. We introduce a method to identify time-parameterised families of almost-invariant sets in time-dependent dynamical systems, as well as the families' emergence and disappearance. In contrast to coherent sets, which may freely move about in phase space over time, our technique focuses on families of metastable sets that are quasi-stationary in space. Our straightforward approach extends successful transfer operator methods for almost-invariant sets to time-dependent dynamics and utilises the Ulam scheme for the generator of the transfer operator on a time-expanded domain. The new methodology is illustrated with an idealised fluid flow and with atmospheric velocity data. We identify atmospheric blocking events in the 2003 European heatwave and compare our technique to existing geophysical methods of blocking diagnosis.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6f554b1c8b8360b3842290f4ce5cc7ca4106693d" target='_blank'>
-              Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/85cdef684e76e594fd24e0e2863fe622d0a8314d" target='_blank'>
+              Identifying the onset and decay of quasi-stationary families of almost-invariant sets with an application to atmospheric blocking events
               </a>
             </td>
           <td>
-            Zheyuan Hu, Kenji Kawaguchi, Zhongqiang Zhang, G. Karniadakis
+            Aleksandar Badza, Gary Froyland School of Mathematics, Statistics Unsw Sydney Nsw Australia
           </td>
-          <td>2024-06-17</td>
+          <td>2024-07-09</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>127</td>
+          <td>0</td>
         </tr>
 
-        <tr id="This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of symbolic and numeric information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed subsequently to generate mesh-free predicted solutions. We generated a dataset with up to three million samples involving diverse one-dimensional PDEs to pretrain our model. Compared with baseline models trained specifically on benchmark datasets, our pretrained model achieves comparable accuracy via zero-shot inference, and the advantage expands after finetuning. For PDEs new or unseen in the pretraining stage, our model can adapt quickly by finetuning on a relatively small set of examples from the target equation. Additionally, PDEformer-1 demonstrates promising results in the inverse problem of PDE scalar coefficient recovery and coefficient field recovery.">
+        <tr id="High-precision control for nonlinear systems is impeded by the low-fidelity dynamical model and external disturbance. Especially, the intricate coupling between internal uncertainty and external disturbance is usually difficult to be modeled explicitly. Here we show an effective and convergent algorithm enabling accurate estimation of the coupled disturbance via combining control and learning philosophies. Specifically, by resorting to Chebyshev series expansion, the coupled disturbance is firstly decomposed into an unknown parameter matrix and two known structures depending on system state and external disturbance respectively. A Regularized Least Squares (RLS) algorithm is subsequently formalized to learn the parameter matrix by using historical time-series data. Finally, a higher-order disturbance observer (HODO) is developed to achieve a high-precision estimation of the coupled disturbance by utilizing the learned portion. The efficiency of the proposed algorithm is evaluated through extensive simulations. We believe this work can offer a new option to merge learning schemes into the control framework for addressing existing intractable control problems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/40c21c8b077c4c5aea793ff9f0cb0cf1332acd86" target='_blank'>
-              PDEformer-1: A Foundation Model for One-Dimensional Partial Differential Equations
+          <td><a href="https://www.semanticscholar.org/paper/2c2b582f6ad335402a40cb9dffeaea1baf4781dd" target='_blank'>
+              Disturbance Observer for Estimating Coupled Disturbances
               </a>
             </td>
           <td>
-            Zhanhong Ye, Xiang Huang, Leheng Chen, Zining Liu, Bingyang Wu, Hongsheng Liu, Zidong Wang, Bin Dong
+            Jindou Jia, Yuhang Liu, Kexin Guo, Xiang Yu, Lihua Xie, Lei Guo
           </td>
-          <td>2024-07-09</td>
+          <td>2024-07-18</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>5</td>
+          <td>17</td>
         </tr>
 
-        <tr id="The study of structures involving vortices in one component and bright solitary waves in another has a time-honored history in two-component atomic Bose-Einstein condensates. In the present work, we revisit this topic extending considerations well-past the near-integrable regime of nearly equal scattering lengths. Instead, we focus on stationary states and spectral stability of such structures for large values of the inter-component interaction coefficient. We find that the state can manifest dynamical instabilities for suitable parameter values. We also explore a phenomenological, yet quantitatively accurate upon suitable tuning, particle model which, in line also with earlier works, offers the potential of accurately following the associated stability and dynamical features. Finally, we probe the dynamics of the unstable vortex-bright structure, observing an unprecedented, to our knowledge, instability scenario in which the oscillatory instability leads to a patch of vorticity that harbors and eventually ejects multiple vortex-bright structures.">
+        <tr id="Filtering - the task of estimating the conditional distribution of states of a dynamical system given partial, noisy, observations - is important in many areas of science and engineering, including weather and climate prediction. However, the filtering distribution is generally intractable to obtain for high-dimensional, nonlinear systems. Filters used in practice, such as the ensemble Kalman filter (EnKF), are biased for nonlinear systems and have numerous tuning parameters. Here, we present a framework for learning a parameterized analysis map - the map that takes a forecast distribution and observations to the filtering distribution - using variational inference. We show that this methodology can be used to learn gain matrices for filtering linear and nonlinear dynamical systems, as well as inflation and localization parameters for an EnKF. Future work will apply this framework to learn new filtering algorithms.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6484c395c329306744208c49808d9af38aca3bbf" target='_blank'>
-              Stability and dynamics of massive vortices in two-component Bose-Einstein condensates
+          <td><a href="https://www.semanticscholar.org/paper/0caedb45ee3429ec36e56edd056c7ae412f7b6b8" target='_blank'>
+              Learning Optimal Filters Using Variational Inference
               </a>
             </td>
           <td>
-            J. D’Ambroise, Wenlong Wang, Christopher Ticknor, R. Carretero-Gonz´alez, P. Kevrekidis
+            Enoch Luk, Eviatar Bach, Ricardo Baptista, Andrew Stuart
           </td>
-          <td>2024-07-14</td>
+          <td>2024-06-26</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>53</td>
+          <td>1</td>
+          <td>10</td>
         </tr>
 
-        <tr id="We perform a comparative analysis of quintessence and $k$-essence scalar field models in the data analysis perspective. We study the quintessence field with an exponential potential and the $k$-essence field with an inverse square potential in the present work. Before delving into data analysis, we provide a brief perspective on dynamical evolution on both of the models and obtain the stability constraints on the model parameters. We adopt Bayesian inference procedure to estimate the model parameters that best-fit the data. A comprehensive analysis utilizing Observational Hubble data (OHD) and Pantheon+ compilation of Type Ia supernovae (SNIa) shows that $k$-essence model fits the data slightly better than the quintessence model while the evidence of these models in comparison with the $\Lambda$CDM model is weak. The value of the Hubble constant predicted by both the models is in close agreement with the value obtained by the Planck2018 collaboration assuming the $\Lambda$CDM model.">
+        <tr id="A data-driven approach to calculating tight-binding models for discrete coupled-mode systems is presented. Specifically, spectral and topological data is used to build an appropriate discrete model that accurately replicates these properties. This work is motivated by topological insulator systems that are often described by tight-binding models. The problem is formulated as the minimization of an appropriate residual (objective) function. Given bulk spectral data and a topological index (e.g. winding number), an appropriate discrete model is obtained to arbitrary precision. A nonlinear least squares method is used to determine the coefficients. The effectiveness of the scheme is highlighted against a Schr\"odinger equation with a periodic potential that can be described by the Su-Schrieffer-Heeger model.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/42380f8c1154a7b525a2b52752ab4cbca4ead1d4" target='_blank'>
-              Comparative Analysis of $k$-essence and Quintessence Scalar Field Models: A Data Analysis Approach
+          <td><a href="https://www.semanticscholar.org/paper/b260d38c46caaea8a67dc40a10c56986fd078985" target='_blank'>
+              Data-driven approximations of topological insulator systems
               </a>
             </td>
           <td>
-            Saddam Hussain, Sarath Nelleri, Kaushik Bhattacharya
+            Justin T. Cole, Michael J. Nameika
           </td>
-          <td>2024-06-11</td>
+          <td>2024-07-01</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>0</td>
         </tr>
 
         <tr id="
@@ -2869,317 +2988,318 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>29</td>
         </tr>
 
-        <tr id="The paper presents a framework for online learning of the Koopman operator using streaming data. Many complex systems for which data-driven modeling and control are sought provide streaming sensor data, the abundance of which can present computational challenges but cannot be ignored. Streaming data can intermittently sample dynamically different regimes or rare events which could be critical to model and control. Using ideas from subspace identification, we present a method where the Grassmannian distance between the subspace of an extended observability matrix and the streaming segment of data is used to assess the `novelty' of the data. If this distance is above a threshold, it is added to an archive and the Koopman operator is updated if not it is discarded. Therefore, our method identifies data from segments of trajectories of a dynamical system that are from different dynamical regimes, prioritizes minimizing the amount of data needed in updating the Koopman model and furthermore reduces the number of basis functions by learning them adaptively. Therefore, by dynamically adjusting the amount of data used and learning basis functions, our method optimizes the model's accuracy and the system order.">
+        <tr id="Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either"from scratch"to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, and highlight their advantages and shortcomings.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a7ee04d648defa5ecd02e1e1b2368c710c5df6c2" target='_blank'>
-              Online learning of Koopman operator using streaming data from different dynamical regimes
+          <td><a href="https://www.semanticscholar.org/paper/6515ce69075cc8fe93c06073e12dcf389d87c37b" target='_blank'>
+              Neural Network Representations of Multiphase Equations of State
               </a>
             </td>
           <td>
-            Kartik Loya, Phanindra Tallapragada
+            George A. Kevrekidis, Daniel A. Serino, Alexander Kaltenborn, J. Gammel, J. Burby, Marc L. Klasky
           </td>
-          <td>2024-07-18</td>
+          <td>2024-06-28</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>16</td>
         </tr>
 
-        <tr id="Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general Equation of State model are adherence to the Laws of Thermodynamics, incorporation of phase transitions, and multiscale accuracy. Analytic models that adhere to all three are hard to develop and cumbersome to work with, often resulting in sacrificing one of these elements for the sake of efficiency. In this work, two deep-learning methods are proposed that provably satisfy the first and second conditions on a large-enough region of thermodynamic variable space. The first is based on learning the generating function (thermodynamic potential) while the second is based on structure-preserving, symplectic neural networks, respectively allowing modifications near or on phase transition regions. They can be used either"from scratch"to learn a full Equation of State, or in conjunction with a pre-existing consistent model, functioning as a modification that better adheres to experimental data. We formulate the theory and provide several computational examples to justify both approaches, and highlight their advantages and shortcomings.">
+        <tr id="The paper presents a framework for online learning of the Koopman operator using streaming data. Many complex systems for which data-driven modeling and control are sought provide streaming sensor data, the abundance of which can present computational challenges but cannot be ignored. Streaming data can intermittently sample dynamically different regimes or rare events which could be critical to model and control. Using ideas from subspace identification, we present a method where the Grassmannian distance between the subspace of an extended observability matrix and the streaming segment of data is used to assess the `novelty' of the data. If this distance is above a threshold, it is added to an archive and the Koopman operator is updated if not it is discarded. Therefore, our method identifies data from segments of trajectories of a dynamical system that are from different dynamical regimes, prioritizes minimizing the amount of data needed in updating the Koopman model and furthermore reduces the number of basis functions by learning them adaptively. Therefore, by dynamically adjusting the amount of data used and learning basis functions, our method optimizes the model's accuracy and the system order.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6515ce69075cc8fe93c06073e12dcf389d87c37b" target='_blank'>
-              Neural Network Representations of Multiphase Equations of State
+          <td><a href="https://www.semanticscholar.org/paper/a7ee04d648defa5ecd02e1e1b2368c710c5df6c2" target='_blank'>
+              Online learning of Koopman operator using streaming data from different dynamical regimes
               </a>
             </td>
           <td>
-            George A. Kevrekidis, Daniel A. Serino, Alexander Kaltenborn, J. Gammel, J. Burby, Marc L. Klasky
+            Kartik Loya, Phanindra Tallapragada
           </td>
-          <td>2024-06-28</td>
+          <td>2024-07-18</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>16</td>
         </tr>
 
-        <tr id="Sampling-based kinodynamic motion planners (SKMPs) are powerful in finding collision-free trajectories for high-dimensional systems under differential constraints. Time-informed set (TIS) can provide the heuristic search domain to accelerate their convergence to the time-optimal solution. However, existing TIS approximation methods suffer from the curse of dimensionality, computational burden, and limited system applicable scope, e.g., linear and polynomial nonlinear systems. To overcome these problems, we propose a method by leveraging deep learning technology, Koopman operator theory, and random set theory. Specifically, we propose a Deep Invertible Koopman operator with control U model named DIKU to predict states forward and backward over a long horizon by modifying the auxiliary network with an invertible neural network. A sampling-based approach, ASKU, performing reachability analysis for the DIKU is developed to approximate the TIS of nonlinear control systems online. Furthermore, we design an online time-informed SKMP using a direct sampling technique to draw uniform random samples in the TIS. Simulation experiment results demonstrate that our method outperforms other existing works, approximating TIS in near real-time and achieving superior planning performance in several time-optimal kinodynamic motion planning problems.">
+        <tr id="Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This paper considers the problem of inferring unknown system parameters, including the time delays, from noisy and sparse experimental data observed from the system. We propose an extension of manifold-constrained Gaussian processes to conduct parameter inference for DDEs, whereas the time delay parameters have posed a challenge for existing methods that bypass numerical solvers. Our method uses a Bayesian framework to impose a Gaussian process model over the system trajectory, conditioned on the manifold constraint that satisfies the DDEs. For efficient computation, a linear interpolation scheme is developed to approximate the values of the time-delayed system outputs, along with corresponding theoretical error bounds on the approximated derivatives. Two simulation examples, based on Hutchinson's equation and the lac operon system, together with a real-world application using Ontario COVID-19 data, are used to illustrate the efficacy of our method.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/47eec5e6ac343847f3ccf8a58bf04f8fa124b137" target='_blank'>
-              Online Time-Informed Kinodynamic Motion Planning of Nonlinear Systems
+          <td><a href="https://www.semanticscholar.org/paper/59505531dc6e56a864c5a883b0860d09309620d3" target='_blank'>
+              Inference for Delay Differential Equations Using Manifold-Constrained Gaussian Processes
               </a>
             </td>
           <td>
-            Fei Meng, Jianbang Liu, Hao-bin Shi, Han Ma, Hongliang Ren, Max Q.-H. Meng
+            Yuxuan Zhao, Samuel W. K. Wong
           </td>
-          <td>2024-07-03</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>13</td>
+          <td>1</td>
         </tr>
 
-        <tr id="We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single framework. We can parametrically solve partial differential equations in a data-free manner and provide accurate sensitivities, meaning the derivatives of the solution space with respect to the design space. These capabilities enable gradient-based optimization without the typical sensitivity analysis costs, unlike adjoint methods that scale directly with the number of response functions. Our Finite Operator Learning (FOL) approach uses an uncomplicated feed-forward neural network model to directly map the discrete design space (i.e. parametric input space) to the discrete solution space (i.e. finite number of sensor points in the arbitrary shape domain) ensuring compliance with physical laws by designing them into loss functions. The discretized governing equations, as well as the design and solution spaces, can be derived from any well-established numerical techniques. In this work, we employ the Finite Element Method (FEM) to approximate fields and their spatial derivatives. Subsequently, we conduct Sobolev training to minimize a multi-objective loss function, which includes the discretized weak form of the energy functional, boundary conditions violations, and the stationarity of the residuals with respect to the design variables. Our study focuses on the steady-state heat equation within heterogeneous materials that exhibits significant phase contrast and possibly temperature-dependent conductivity. The network's tangent matrix is directly used for gradient-based optimization to improve the microstructure's heat transfer characteristics. ...">
+        <tr id="In this paper, we develop the Asymptotic-Preserving Neural Networks (APNNs) approach to study the forward and inverse problem for the semiconductor Boltzmann equation. The goal of the neural network is to resolve the computational challenges of conventional numerical methods and multiple scales of the model. To guarantee the network can operate uniformly in different regimes, it is desirable to carry the Asymptotic-Preservation (AP) property in the learning process. In a micro-macro decomposition framework, we design such an AP formulation of loss function. The convergence analysis of both the loss function and its neural network is shown, based on the Universal Approximation Theorem and hypocoercivity theory of the model equation. We show a series of numerical tests for forward and inverse problems of both the semiconductor Boltzmann and the Boltzmann-Poisson system to validate the effectiveness of our proposed method, which addresses the significance of the AP property when dealing with inverse problems of multiscale Boltzmann equations especially when only sparse or partially observed data are available.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6248ca7a394e7da69cd6d0cb638b974e5ed8f57e" target='_blank'>
-              Finite Operator Learning: Bridging Neural Operators and Numerical Methods for Efficient Parametric Solution and Optimization of PDEs
+          <td><a href="https://www.semanticscholar.org/paper/bb3329e7d90a830059df34e4bc6454db16ae0c60" target='_blank'>
+              Asymptotic-preserving neural networks for the semiconductor Boltzmann equation and its application on inverse problems
               </a>
             </td>
           <td>
-            Shahed Rezaei, Reza Najian Asl, Kianoosh Taghikhani, Ahmad Moeineddin, Michael Kaliske, Markus Apel
+            Liu Liu, Yating Wang, Xueyu Zhu, Zhenyi Zhu
           </td>
-          <td>2024-07-04</td>
+          <td>2024-07-23</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>18</td>
+          <td>1</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Stochastic dynamics on sparse graphs and disordered systems often lead to complex behaviors characterized by heterogeneity in time and spatial scales, slow relaxation, localization, and aging phenomena. The mathematical tools and approximation techniques required to analyze these complex systems are still under development, posing significant technical challenges and resulting in a reliance on numerical simulations. We introduce a novel computational framework for investigating the dynamics of sparse disordered systems with continuous degrees of freedom. Starting with a graphical model representation of the dynamic partition function for a system of linearly-coupled stochastic differential equations, we use dynamic cavity equations on locally tree-like factor graphs to approximate the stochastic measure. Here, cavity marginals are identified with local functionals of single-site trajectories. Our primary approximation involves a second-order truncation of a small-coupling expansion, leading to a Gaussian form for the cavity marginals. For linear dynamics with additive noise, this method yields a closed set of causal integro-differential equations for cavity versions of one-time and two-time averages. These equations provide an exact dynamical description within the local tree-like approximation, retrieving classical results for the spectral density of sparse random matrices. Global constraints, non-linear forces, and state-dependent noise terms can be addressed using a self-consistent perturbative closure technique. The resulting equations resemble those of dynamical mean-field theory in the mode-coupling approximation used for fully-connected models. However, due to their cavity formulation, the present method can also be applied to ensembles of sparse random graphs and employed as a message-passing algorithm on specific graph instances.">
+        <tr id="We introduce mochi_class, an extension of the Einstein-Boltzmann solver hi_class, designed to unlock the full phenomenological potential of Horndeski gravity. This extension allows for general input functions of time without the need for hard-coded parametrisations or covariant Lagrangians. By replacing the traditional $\alpha$-parametrisation with a set of stable basis functions, mochi_class ensures that the resulting effective theories are inherently free from gradient and ghost instabilities. Additionally, mochi_class features a quasi-static approximation implemented at the level of modified metric potentials, enhancing prediction accuracy, especially for models transitioning between a super- and sub-Compton regime. mochi_class can robustly handle a wide range of models without fine-tuning, and introduces a new approximation scheme that activates modifications to the standard cosmology deep in the matter-dominated era. Furthermore, it incorporates viability conditions on the equation of motion for the scalar field fluctuations, aiding in the identification of numerical instabilities. Through comprehensive validation against other Einstein-Boltzmann solvers, mochi_class demonstrates excellent performance and accuracy, broadening the scope of hi_class by facilitating the study of specific modified gravity models and enabling exploration of previously inaccessible regions of the Horndeski landscape. The code is publicly available at https://github.com/mcataneo/mochi_class_public">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1409599021b5a3a43a70ea04c2d775f534dd885c" target='_blank'>
-              Gaussian approximation of dynamic cavity equations for linearly-coupled stochastic dynamics
+          <td><a href="https://www.semanticscholar.org/paper/45c44ba92da169b2eb987805f3b6ad66528aeee4" target='_blank'>
+              mochi_class: Modelling Optimisation to Compute Horndeski In class
               </a>
             </td>
           <td>
-            Mattia Tarabolo, Luca Dall'Asta
+            Matteo Cataneo, Emilio Bellini
           </td>
-          <td>2024-06-20</td>
+          <td>2024-07-16</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This paper considers the problem of inferring unknown system parameters, including the time delays, from noisy and sparse experimental data observed from the system. We propose an extension of manifold-constrained Gaussian processes to conduct parameter inference for DDEs, whereas the time delay parameters have posed a challenge for existing methods that bypass numerical solvers. Our method uses a Bayesian framework to impose a Gaussian process model over the system trajectory, conditioned on the manifold constraint that satisfies the DDEs. For efficient computation, a linear interpolation scheme is developed to approximate the values of the time-delayed system outputs, along with corresponding theoretical error bounds on the approximated derivatives. Two simulation examples, based on Hutchinson's equation and the lac operon system, together with a real-world application using Ontario COVID-19 data, are used to illustrate the efficacy of our method.">
+        <tr id="In recent years, surrogate models based on deep neural networks have been widely used to solve partial differential equations for fluid flow physics. This kind of model focuses on global interpolation of the training data and thus requires a large network structure. The process is both time consuming and computationally costly. In the present study, we develop a neural network with local converging input (NNLCI) for high-fidelity prediction using unstructured data. The framework uses the local domain of dependence with converging coarse solutions as input, thereby greatly reducing computational resource and training time. As a validation case, the NNLCI method is applied to study two-dimensional inviscid supersonic flows in channels with bumps. Different bump geometries and locations are examined to benchmark the effectiveness and versatility of this new approach. The NNLCI method can accurately and efficiently capture the structure and dynamics of the entire flowfield, including regions with shock discontinuities. For a new bump configuration, the method can perform prediction with only one neural network, eliminating the need for repeated training of multiple networks for different geometries. A saving of computing wall time is achieved by several orders of magnitude against the high-fidelity simulation with the same level of accuracy. The demand on training data is modest, and the training data can be allocated sparsely. These features are especially advantageous compared with conventional global-to-global deep learning methods and physics-informed methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/59505531dc6e56a864c5a883b0860d09309620d3" target='_blank'>
-              Inference for Delay Differential Equations Using Manifold-Constrained Gaussian Processes
+          <td><a href="https://www.semanticscholar.org/paper/88415c3817a7058d9678f49a393b306a231a9953" target='_blank'>
+              Neural Network with Local Converging Input for Unstructured-Grid Computational Fluid Dynamics
               </a>
             </td>
           <td>
-            Yuxuan Zhao, Samuel W. K. Wong
+            Weiming Ding, Haoxiang Huang, T. Lee, Yingjie Liu, Vigor Yang
           </td>
-          <td>2024-06-21</td>
-          <td>ArXiv</td>
+          <td>2024-07-01</td>
+          <td>AIAA Journal</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="Diffusion regulates a phenomenal number of natural processes and the dynamics of many successful generative models. Existing models to learn the diffusion terms from observational data rely on complex bilevel optimization problems and properly model only the drift of the system. We propose a new simple model, JKOnet*, which bypasses altogether the complexity of existing architectures while presenting significantly enhanced representational capacity: JKOnet* recovers the potential, interaction, and internal energy components of the underlying diffusion process. JKOnet* minimizes a simple quadratic loss, runs at lightspeed, and drastically outperforms other baselines in practice. Additionally, JKOnet* provides a closed-form optimal solution for linearly parametrized functionals. Our methodology is based on the interpretation of diffusion processes as energy-minimizing trajectories in the probability space via the so-called JKO scheme, which we study via its first-order optimality conditions, in light of few-weeks-old advancements in optimization in the probability space.">
+        <tr id="Accurate quantum dynamics simulations of nonadiabatic processes are important for studies of electron transfer, energy transfer, and photochemical reactions in complex systems. In this comparative study, we benchmark various approximate nonadiabatic dynamics methods with mapping variables against numerically exact calculations based on the tensor-train (TT) representation of high-dimensional arrays, including TT-KSL for zero-temperature dynamics and TT-thermofield dynamics for finite-temperature dynamics. The approximate nonadiabatic dynamics methods investigated include mixed quantum-classical Ehrenfest mean-field and fewest-switches surface hopping, linearized semiclassical mapping dynamics, symmetrized quasiclassical dynamics, the spin-mapping method, and extended classical mapping models. Different model systems were evaluated, including the spin-boson model for nonadiabatic dynamics in the condensed phase, the linear vibronic coupling model for electronic transition through conical intersections, the photoisomerization model of retinal, and Tully's one-dimensional scattering models. Our calculations show that the optimal choice of approximate dynamical method is system-specific, and the accuracy is sensitively dependent on the zero-point-energy parameter and the initial sampling strategy for the mapping variables.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e136b8e7261e1835acc89bf0402e956bd4ee5225" target='_blank'>
-              Learning Diffusion at Lightspeed
+          <td><a href="https://www.semanticscholar.org/paper/328d4dede1c70e1ea2e979a03782edbe7fbd9ab1" target='_blank'>
+              Benchmarking various nonadiabatic semiclassical mapping dynamics methods with tensor-train thermo-field dynamics.
               </a>
             </td>
           <td>
-            Antonio Terpin, Nicolas Lanzetti, Florian Dörfler
+            Zengkui Liu, Ningyi Lyu, Zhubin Hu, Hao Zeng, Victor S. Batista, Xiang Sun
           </td>
-          <td>2024-06-18</td>
-          <td>ArXiv</td>
+          <td>2024-07-09</td>
+          <td>The Journal of chemical physics</td>
           <td>0</td>
-          <td>10</td>
+          <td>18</td>
         </tr>
 
-        <tr id="We introduce an innovative approach for solving high-dimensional Fokker-Planck-L\'evy (FPL) equations in modeling non-Brownian processes across disciplines such as physics, finance, and ecology. We utilize a fractional score function and Physical-informed neural networks (PINN) to lift the curse of dimensionality (CoD) and alleviate numerical overflow from exponentially decaying solutions with dimensions. The introduction of a fractional score function allows us to transform the FPL equation into a second-order partial differential equation without fractional Laplacian and thus can be readily solved with standard physics-informed neural networks (PINNs). We propose two methods to obtain a fractional score function: fractional score matching (FSM) and score-fPINN for fitting the fractional score function. While FSM is more cost-effective, it relies on known conditional distributions. On the other hand, score-fPINN is independent of specific stochastic differential equations (SDEs) but requires evaluating the PINN model's derivatives, which may be more costly. We conduct our experiments on various SDEs and demonstrate numerical stability and effectiveness of our method in dealing with high-dimensional problems, marking a significant advancement in addressing the CoD in FPL equations.">
+        <tr id="Reservoir computing has been shown to be a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. Its utility is significant because in real-world scenarios, the exact model equations are unknown. This Letter shows how the theory of dynamical system provides the underlying mechanism behind the prediction. Using numerical methods, by considering dynamical systems which show Hopf bifurcation, we demonstrate that the map produced by the reservoir after a successful training undergoes a Neimark-Sacker bifurcation such that the critical point of the map is in immediate proximity to that of the original dynamical system. In addition, we have compared and analyzed different structures in the phase space. Our findings provide insight into the functioning of machine learning algorithms for predicting critical transitions.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8627a1dd31e82891b19eb525d8d99ebc327fe094" target='_blank'>
-              Score-fPINN: Fractional Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker-Planck-Levy Equations
+          <td><a href="https://www.semanticscholar.org/paper/3e38c7638dd9a0b907d25cf396095bd4a2d25e12" target='_blank'>
+              Dynamical analysis of a parameter-aware reservoir computer
               </a>
             </td>
           <td>
-            Zheyuan Hu, Zhongqiang Zhang, G. Karniadakis, Kenji Kawaguchi
+            Dishant Sisodia, S. Jalan
           </td>
-          <td>2024-06-17</td>
+          <td>2024-07-20</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>127</td>
+          <td>26</td>
         </tr>
 
-        <tr id="Real-world problems, particularly in the sciences and engineering, are often analyzed using differential equations to understand physical phenomena. Many situations involve rates of change of independent variables, represented by derivatives, which lead to differential equations. Solving higher-order ordinary differential equations typically involves reducing them to systems of first-order equations, but this approach has challenges. To overcome these and enhance numerical methods, a novel one-step block method with eight partitions was developed for the direct solution of higher-order initial value problems. This method will target issues in physics, biology, chemistry and economics. The new method was formulated using the linear block approach and numerical analysis was ensure essential and sufficient conditions. The new method addresses second-order problems like simple harmonic motion, third-order issues such as oscillatory differential equations, and fourth-order problems like thin film dynamics. The new method demonstrates faster convergence and improved accuracy compared to existing solutions for second, third, and fourth-order oscillatory differential equations.">
+        <tr id="In this work, we present a novel methodology for performing the supervised classification of time-ordered noisy data; we call this methodology Entropic Sparse Probabilistic Approximation with Markov regularization (eSPA-Markov). It is an extension of entropic learning methodologies, allowing the simultaneous learning of segmentation patterns, entropy-optimal feature space discretizations, and Bayesian classification rules. We prove the conditions for the existence and uniqueness of the learning problem solution and propose a one-shot numerical learning algorithm that—in the leading order—scales linearly in dimension. We show how this technique can be used for the computationally scalable identification of persistent (metastable) regime affiliations and regime switches from high-dimensional non-stationary and noisy time series, i.e., when the size of the data statistics is small compared to their dimensionality and when the noise variance is larger than the variance in the signal. We demonstrate its performance on a set of toy learning problems, comparing eSPA-Markov to state-of-the-art techniques, including deep learning and random forests. We show how this technique can be used for the analysis of noisy time series from DNA and RNA Nanopore sequencing.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/104875937aeb83cd6f3ad125733de7fa030115ca" target='_blank'>
-              The Numerical Application of Dynamic Problems Involving Mass in Motion Governed by Higher Order Oscillatory Differential Equations
+          <td><a href="https://www.semanticscholar.org/paper/eadfee466307a1a3b8e63299cb3e600477c1f902" target='_blank'>
+              On Entropic Learning from Noisy Time Series in the Small Data Regime
               </a>
             </td>
           <td>
-            Yusuf Skwame, D. J. Zirra, Sabo John
+            Davide Bassetti, Lukáš Pospíšil, I. Horenko
           </td>
-          <td>2024-08-01</td>
-          <td>Physical Science International Journal</td>
+          <td>2024-06-28</td>
+          <td>Entropy</td>
           <td>0</td>
-          <td>1</td>
+          <td>26</td>
         </tr>
 
-        <tr id="We consider a class of infinite-dimensional dynamical systems driven by non-linear parabolic partial differential equations with initial condition $\theta$ modelled by a Gaussian process `prior' probability measure. Given discrete samples of the state of the system evolving in space-time, one obtains updated `posterior' measures on a function space containing all possible trajectories. We give a general set of conditions under which these non-Gaussian posterior distributions are approximated, in Wasserstein distance for the supremum-norm metric, by the law of a Gaussian random function. We demonstrate the applicability of our results to periodic non-linear reaction diffusion equations \begin{align*} \frac{\partial}{\partial t} u - \Delta u&= f(u) \\ u(0)&= \theta \end{align*} where $f$ is any smooth and compactly supported reaction function. In this case the limiting Gaussian measure can be characterised as the solution of a time-dependent Schr\"odinger equation with `rough' Gaussian initial conditions whose covariance operator we describe.">
+        <tr id="
+ Turbulence closure modeling using machine learning is at an early crossroads. The extraordinary success of machine learning (ML) in a variety of challenging fields had given rise to an expectation of similar transformative advances in the area of turbulence closure modeling. However, by most accounts, the current rate of progress toward accurate and predictive ML-RANS (Reynolds Averaged Navier-Stokes) closure models has been very slow. Upon retrospection, the absence of rapid transformative progress can be attributed to two factors: the underestimation of the intricacies of turbulence modeling and the overestimation of ML’s ability to capture all features without employing targeted strategies. To pave the way for more meaningful ML closures tailored to address the nuances of turbulence, this article seeks to review the foundational flow physics to assess the challenges in the context of data-driven approaches. Revisiting analogies with statistical mechanics and stochastic systems, the key physical complexities and mathematical limitations are explicated. It is noted that the current ML approaches do not systematically address the inherent limitations of a statistical approach or the inadequacies of the mathematical forms of closure expressions. The study underscores the drawbacks of supervised learning-based closures and stresses the importance of a more discerning ML modeling framework. As ML methods evolve (which is happening at a rapid pace) and our understanding of the turbulence phenomenon improves, the inferences expressed here should be suitably modified.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/db83d3bfd7b84fe9f13762bbba8065506f1c2480" target='_blank'>
-              Bernstein-von Mises theorems for time evolution equations
+          <td><a href="https://www.semanticscholar.org/paper/d5cf3709be3b3ab9de17733558b062f9c6b30ac8" target='_blank'>
+              Turbulence Closure Modeling with Machine Learning: A Foundational Physics Perspective
               </a>
             </td>
           <td>
-            Richard Nickl
+            S. Girimaji
           </td>
-          <td>2024-07-20</td>
-          <td>ArXiv</td>
+          <td>2024-07-23</td>
+          <td>New Journal of Physics</td>
           <td>0</td>
-          <td>30</td>
+          <td>42</td>
         </tr>
 
-        <tr id="We introduce mochi_class, an extension of the Einstein-Boltzmann solver hi_class, designed to unlock the full phenomenological potential of Horndeski gravity. This extension allows for general input functions of time without the need for hard-coded parametrisations or covariant Lagrangians. By replacing the traditional $\alpha$-parametrisation with a set of stable basis functions, mochi_class ensures that the resulting effective theories are inherently free from gradient and ghost instabilities. Additionally, mochi_class features a quasi-static approximation implemented at the level of modified metric potentials, enhancing prediction accuracy, especially for models transitioning between a super- and sub-Compton regime. mochi_class can robustly handle a wide range of models without fine-tuning, and introduces a new approximation scheme that activates modifications to the standard cosmology deep in the matter-dominated era. Furthermore, it incorporates viability conditions on the equation of motion for the scalar field fluctuations, aiding in the identification of numerical instabilities. Through comprehensive validation against other Einstein-Boltzmann solvers, mochi_class demonstrates excellent performance and accuracy, broadening the scope of hi_class by facilitating the study of specific modified gravity models and enabling exploration of previously inaccessible regions of the Horndeski landscape. The code is publicly available at https://github.com/mcataneo/mochi_class_public">
+        <tr id="Gaussian Processes (GPs) and Linear Dynamical Systems (LDSs) are essential time series and dynamic system modeling tools. GPs can handle complex, nonlinear dynamics but are computationally demanding, while LDSs offer efficient computation but lack the expressive power of GPs. To combine their benefits, we introduce a universal method that allows an LDS to mirror stationary temporal GPs. This state-space representation, known as the Markovian Gaussian Process (Markovian GP), leverages the flexibility of kernel functions while maintaining efficient linear computation. Unlike existing GP-LDS conversion methods, which require separability for most multi-output kernels, our approach works universally for single- and multi-output stationary temporal kernels. We evaluate our method by computing covariance, performing regression tasks, and applying it to a neuroscience application, demonstrating that our method provides an accurate state-space representation for stationary temporal GPs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/45c44ba92da169b2eb987805f3b6ad66528aeee4" target='_blank'>
-              mochi_class: Modelling Optimisation to Compute Horndeski In class
+          <td><a href="https://www.semanticscholar.org/paper/f45b6ab8336d143d48c626e23d36a99a22707758" target='_blank'>
+              Markovian Gaussian Process: A Universal State-Space Representation for Stationary Temporal Gaussian Process
               </a>
             </td>
           <td>
-            Matteo Cataneo, Emilio Bellini
+            Weihan Li, Yule Wang, Chengrui Li, Anqi Wu
           </td>
-          <td>2024-07-16</td>
+          <td>2024-06-29</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Modeling dynamical systems, e.g. in climate and engineering sciences, often necessitates solving partial differential equations. Neural operators are deep neural networks designed to learn nontrivial solution operators of such differential equations from data. As for all statistical models, the predictions of these models are imperfect and exhibit errors. Such errors are particularly difficult to spot in the complex nonlinear behaviour of dynamical systems. We introduce a new framework for approximate Bayesian uncertainty quantification in neural operators using function-valued Gaussian processes. Our approach can be interpreted as a probabilistic analogue of the concept of currying from functional programming and provides a practical yet theoretically sound way to apply the linearized Laplace approximation to neural operators. In a case study on Fourier neural operators, we show that, even for a discretized input, our method yields a Gaussian closure--a structured Gaussian process posterior capturing the uncertainty in the output function of the neural operator, which can be evaluated at an arbitrary set of points. The method adds minimal prediction overhead, can be applied post-hoc without retraining the neural operator, and scales to large models and datasets. We showcase the efficacy of our approach through applications to different types of partial differential equations.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2fb48eb416a7b362eb444cb5d9c111a6939db5fe" target='_blank'>
-              Linearization Turns Neural Operators into Function-Valued Gaussian Processes
+          <td><a href="https://www.semanticscholar.org/paper/1e47886cf1fed1baf5e2839789863c0355296cdc" target='_blank'>
+              The Distance Between: An Algorithmic Approach to Comparing Stochastic Models to Time-Series Data
               </a>
             </td>
           <td>
-            Emilia Magnani, Marvin Pförtner, Tobias Weber, Philipp Hennig
+            Brock D. Sherlock, Marko A. A. Boon, Maria Vlasiou, A. Coster
           </td>
-          <td>2024-06-07</td>
-          <td>ArXiv</td>
+          <td>2024-07-26</td>
+          <td>Bulletin of Mathematical Biology</td>
           <td>0</td>
-          <td>3</td>
+          <td>25</td>
         </tr>
 
-        <tr id="In recent years, surrogate models based on deep neural networks have been widely used to solve partial differential equations for fluid flow physics. This kind of model focuses on global interpolation of the training data and thus requires a large network structure. The process is both time consuming and computationally costly. In the present study, we develop a neural network with local converging input (NNLCI) for high-fidelity prediction using unstructured data. The framework uses the local domain of dependence with converging coarse solutions as input, thereby greatly reducing computational resource and training time. As a validation case, the NNLCI method is applied to study two-dimensional inviscid supersonic flows in channels with bumps. Different bump geometries and locations are examined to benchmark the effectiveness and versatility of this new approach. The NNLCI method can accurately and efficiently capture the structure and dynamics of the entire flowfield, including regions with shock discontinuities. For a new bump configuration, the method can perform prediction with only one neural network, eliminating the need for repeated training of multiple networks for different geometries. A saving of computing wall time is achieved by several orders of magnitude against the high-fidelity simulation with the same level of accuracy. The demand on training data is modest, and the training data can be allocated sparsely. These features are especially advantageous compared with conventional global-to-global deep learning methods and physics-informed methods.">
+        <tr id="For many industrial processes, a digital twin is available, which is essentially a highly complex model whose parameters may not be properly tuned for the specific process. By relying on the availability of such a digital twin, this paper introduces a novel approach to data-driven control, where the digital twin is used to generate samples and suitable controllers for various perturbed versions of its parameters. A supervised learning algorithm is then employed to estimate a direct mapping from the data to the best controller to use. This map consists of a model reduction step, followed by a neural network architecture whose output provides the parameters of the controller. The data-to-controller map is pre-computed based on artificially generated data, but its execution once deployed is computationally very efficient, thus providing a simple and inexpensive way to tune and re-calibrate controllers directly from data. The benefits of this novel approach are illustrated via numerical simulations.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/88415c3817a7058d9678f49a393b306a231a9953" target='_blank'>
-              Neural Network with Local Converging Input for Unstructured-Grid Computational Fluid Dynamics
+          <td><a href="https://www.semanticscholar.org/paper/6916b9be2764f075e341e143b9e58edc122152ad" target='_blank'>
+              From Data to Control: A Two-Stage Simulation-Based Approach
               </a>
             </td>
           <td>
-            Weiming Ding, Haoxiang Huang, T. Lee, Yingjie Liu, Vigor Yang
+            Federico Dettù, Braghadeesh Lakshminarayanan, Simone Formentin, Cristian R. Rojas
           </td>
-          <td>2024-07-01</td>
-          <td>AIAA Journal</td>
+          <td>2024-06-25</td>
+          <td>2024 European Control Conference (ECC)</td>
           <td>0</td>
-          <td>1</td>
+          <td>3</td>
         </tr>
 
-        <tr id="This two-part tutorial dives into the field of data-driven power flow linearization (DPFL), a domain gaining increased attention. DPFL stands out for its higher approximation accuracy, wide adaptability, and better ability to implicitly incorporate the latest system attributes. This renders DPFL a potentially superior option for managing the significant fluctuations from renewable energy sources, a step towards realizing a more sustainable energy future, by translating the higher model accuracy into increased economic efficiency and less energy losses. To conduct a deep and rigorous reexamination, this tutorial first classifies existing DPFL methods into DPFL training algorithms and supportive techniques. Their mathematical models, analytical solutions, capabilities, limitations, and generalizability are systematically examined, discussed, and summarized. In addition, this tutorial reviews existing DPFL experiments, examining the settings of test systems, the fidelity of datasets, and the comparison made among a limited number of DPFL methods. Further, this tutorial implements extensive numerical comparisons of all existing DPFL methods (40 methods in total) and four classic physics-driven approaches, focusing on their generalizability, applicability, accuracy, and computational efficiency. Through these simulationmethodss, this tutorial aims to reveal the actual performance of all the methods (including the performances exposed to data noise or outliers), guiding the selection of appropriate linearization methods. Furthermore, this tutorial discusses future directions based on the theoretical and numerical insights gained. As the first part, this paper reexamines DPFL theories, covering all the training algorithms and supportive techniques. Capabilities, limitations, and aspects of generalizability, which were previously unmentioned in the literature, have been identified.">
+        <tr id="Model predictive control (MPC) is a powerful control method for handling complex nonlinear systems that are subject to constraints. However, the real-time application of this approach can be severely limited by the need to solve constrained nonlinear optimization problems at each sampling time. To this end, this work introduces a novel learning-based iterative solver that provides highly accurate predictions, optimality certification, and fast evaluation of the MPC solution at each sampling time. To learn this iterative solver, we propose an unsupervised training algorithm that builds on the Karush-Kuhn-Tucker optimality conditions, modified by a Fischer-Burmeister formulation, and eliminates the need for prior sampling of exact optimizer solutions. By exploiting efficient vector-Jacobian and Jacobian-vector products via automatic differentiation, the proposed training algorithm can be efficiently executed. We demonstrate the potential of the proposed learning-based iterative solver on the example of nonlinear model predictive control of a nonlinear double integrator. We show its advantages when compared to exact optimizer solutions and with an imitation learning-based approach that directly obtains a data-based approximation of the MPC control law.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1bdfa4f227320698ee10d100d4da18f732e22c80" target='_blank'>
-              Data-driven Power Flow Linearization: Theory
+          <td><a href="https://www.semanticscholar.org/paper/04655a12d07dee491135aaae2f055b737e275291" target='_blank'>
+              Learning Iterative Solvers for Accurate and Fast Nonlinear Model Predictive Control via Unsupervised Training
               </a>
             </td>
           <td>
-            Mengshuo Jia, Gabriela Hug, Ning Zhang, Zhaojian Wang, Yi Wang, Chongqing Kang
+            Lukas Lüken, Sergio Lucia
           </td>
-          <td>2024-06-10</td>
-          <td>ArXiv</td>
+          <td>2024-06-25</td>
+          <td>2024 European Control Conference (ECC)</td>
           <td>0</td>
-          <td>31</td>
+          <td>2</td>
         </tr>
 
-        <tr id="We propose kernel-based approaches for the construction of a single-step and multi-step predictor of the velocity form of nonlinear (NL) systems, which describes the time-difference dynamics of the corresponding NL system and admits a highly structured representation. The predictors in turn allow to formulate completely data-driven representations of the velocity form. The kernel-based formulation that we derive, inherently respects the structured quasi-linear and specific time-dependent relationship of the velocity form. This results in an efficient multi-step predictor for the velocity form and hence for nonlinear systems. Moreover, by using the velocity form, our methods open the door for data-driven behavioral analysis and control of nonlinear systems with global stability and performance guarantees.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6b4583a2f8fb5852420ac4a8c1d46a5e7cd4adf9" target='_blank'>
-              Kernel-based multi-step predictors for data-driven analysis and control of nonlinear systems through the velocity form
+          <td><a href="https://www.semanticscholar.org/paper/a94495dae3c918bd50c5f83ca6c9f29d9b4dba12" target='_blank'>
+              Active learning for adaptive surrogate model improvement in high-dimensional problems
               </a>
             </td>
           <td>
-            C. Verhoek, Roland T'oth
+            Yulin Guo, Paromita Nath, Sankaran Mahadevan, Paul Witherell
           </td>
-          <td>2024-08-01</td>
-          <td>ArXiv</td>
+          <td>2024-07-01</td>
+          <td>Structural and Multidisciplinary Optimization</td>
           <td>0</td>
-          <td>6</td>
+          <td>7</td>
         </tr>
 
-        <tr id="In a sequence of papers, the author examined several statistical affinity measures for selecting the coarse degrees of freedom (CDOFs) or coarse nodes (Cnodes) in algebraic multigrid (AMG) for systems of elliptic partial differential equations (PDEs). These measures were applied to a set of relaxed vectors that exposes the problematic error components. Once the CDOFs are determined using any one of these measures, the interpolation operator is constructed in a bootstrap AMG (BAMG) procedure. However, in a recent paper of Kahl and Rottmann, the statistical least angle regression (LARS) method was utilized in the coarsening procedure and shown to be promising in the CDOF selection. This method is generally used in the statistics community to select the most relevant variables in constructing a parsimonious model for a very complicated and high‐dimensional model or data set (i.e., variable selection for a “reduced” model). As pointed out by Kahl and Rottmann, the LARS procedure has the ability to detect group relations between variables, which can be more useful than binary relations that are derived from strength‐of‐connection, or affinity measures, between pairs of variables. Moreover, by using an updated Cholesky factorization approach in the regression computation, the LARS procedure can be performed efficiently even when the original set of variables is large; and due to the LARS formulation itself (i.e., its ‐norm constraint), sparse interpolation operators can be generated. In this article, we extend the LARS coarsening approach to systems of PDEs. Furthermore, we incorporate some modifications to the LARS approach based on the so‐called elastic net and relaxed lasso methods, which are well known and thoroughly analyzed in the statistics community for ameliorating several major issues with LARS as a variable selection procedure. We note that the original LARS coarsening approach may have addressed some of these issues in similar or other ways but due to the limited details provided there, it is difficult to determine the extent of their similarities. Incorporating these modifications (or effecting them in similar ways) leads to improved robustness in the LARS coarsening procedure, and numerical experiments indicate that the changes lead to faster convergence in the multigrid method. Moreover, the relaxed lasso modification permits an indirect BAMG (iBAMG) extension to the interpolation operator. This iBAMG extension applied in an intra‐ or inter‐variable interpolation setting (i.e., nodal‐based coarsening), as well as in variable‐based coarsening, which will not preserve the nodal structure of a finest‐level discretization on the lower levels of the multilevel hierarchy, will be examined. For the variable‐based coarsening, because of the parsimonious feature of LARS, the performance is reasonably good when applied to systems of PDEs albeit at a substantial additional cost over a nodal‐based procedure.">
+        <tr id="Inferring parameters of models of biochemical kinetics from single-cell data remains challenging because of the uncertainty arising from the intractability of the likelihood function of stochastic reaction networks. Such uncertainty falls beyond current error quantification measures, which focus on the effects of finite sample size and identifiability but lack theoretical guarantees when likelihood approximations are needed. Here, we propose an inference method for stochastic reaction networks with nonlinear and rational propensities at steady state that provides bounds on the parameters via convex optimisation over sets constrained by moment equations and moment matrices. Our approach takes observations from the stochastic reaction network and forms moment intervals, which are then used to constrain parameters through convex sets. The bounds on the parameters contain the true parameters under the condition that the moment intervals contain the true stationary moments, thus providing uncertainty quantification and error guarantees. Our approach does not need to predict moments and distributions for given parameters (i.e., it avoids solving or simulating the forward problem), and hence circumvents intractable likelihood computations or computationally expensive simulations. We demonstrate its use for uncertainty quantification, data integration and prediction of latent species statistics through synthetic data from common nonlinear biochemical models including the Schl\"ogl model, the toggle switch and post-transcriptional regulation.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9cd541114204fbe8a6e43f7aea58c521464d1e1f" target='_blank'>
-              Least angle regression, relaxed lasso, and elastic net for algebraic multigrid of systems of elliptic partial differential equations
+          <td><a href="https://www.semanticscholar.org/paper/de4b88b799eae872be620beb74ef0b6049b65d90" target='_blank'>
+              Moment-based parameter inference with error guarantees for stochastic reaction networks
               </a>
             </td>
           <td>
-            Barry Lee
+            Zekai Li, Mauricio Barahona, Philipp Thomas
           </td>
-          <td>2024-06-18</td>
-          <td>Numerical Linear Algebra with Applications</td>
-          <td>1</td>
-          <td>1</td>
+          <td>2024-06-25</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Reservoir computing has been shown to be a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. Its utility is significant because in real-world scenarios, the exact model equations are unknown. This Letter shows how the theory of dynamical system provides the underlying mechanism behind the prediction. Using numerical methods, by considering dynamical systems which show Hopf bifurcation, we demonstrate that the map produced by the reservoir after a successful training undergoes a Neimark-Sacker bifurcation such that the critical point of the map is in immediate proximity to that of the original dynamical system. In addition, we have compared and analyzed different structures in the phase space. Our findings provide insight into the functioning of machine learning algorithms for predicting critical transitions.">
+        <tr id="In this study, we delve into the Structured State Space Model (S4), Change Point Detection methodologies, and the Switching Non-linear Dynamics System (SNLDS). Our central proposition is an enhanced inference technique and long-range dependency method for SNLDS. The cornerstone of our approach is the fusion of S4 and SNLDS, leveraging the strengths of both models to effectively address the intricacies of long-range dependencies in switching time series. Through rigorous testing, we demonstrate that our proposed methodology adeptly segments and reproduces long-range dependencies in both the 1-D Lorenz dataset and the 2-D bouncing ball dataset. Notably, our integrated approach outperforms the standalone SNLDS in these tasks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3e38c7638dd9a0b907d25cf396095bd4a2d25e12" target='_blank'>
-              Dynamical analysis of a parameter-aware reservoir computer
+          <td><a href="https://www.semanticscholar.org/paper/737fccae30a52b719925aa3bdefbccf7758f66f5" target='_blank'>
+              Long Range Switching Time Series Prediction via State Space Model
               </a>
             </td>
           <td>
-            Dishant Sisodia, S. Jalan
+            Jiaming Zhang, Yang Ding, Yunfeng Gao
           </td>
-          <td>2024-07-20</td>
+          <td>2024-07-27</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>26</td>
+          <td>0</td>
         </tr>
 
-        <tr id="The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations, where differentiable programming plays a crucial role in calculating model sensitivities, inverting model parameters, and training hybrid models that combine differential equations with data-driven approaches. Furthermore, recognizing the strong synergies between inverse methods and machine learning offers the opportunity to establish a coherent framework applicable to both fields. Differentiating functions based on the numerical solution of differential equations is non-trivial. Numerous methods based on a wide variety of paradigms have been proposed in the literature, each with pros and cons specific to the type of problem investigated. Here, we provide a comprehensive review of existing techniques to compute derivatives of numerical solutions of differential equations. We first discuss the importance of gradients of solutions of differential equations in a variety of scientific domains. Second, we lay out the mathematical foundations of the various approaches and compare them with each other. Third, we cover the computational considerations and explore the solutions available in modern scientific software. Last but not least, we provide best-practices and recommendations for practitioners. We hope that this work accelerates the fusion of scientific models and data, and fosters a modern approach to scientific modelling.">
+        <tr id="This study presents a novel approach that leverages Neural Ordinary Differential Equations (Neural ODEs) to unravel the intricate relationships between inputs and outputs in Large Language Models (LLMs), and employs robust control to fine-tune outputs to meet predefined standards. Central to our methodology is the transformation of LLM inputs and outputs into a lower-dimensional latent space, facilitating a detailed examination of the information processing pathways within LLMs. Neural ODEs play a pivotal role in this investigation by providing a dynamic model that captures the continuous evolution of data within the LLMs. Additionally, robust control mechanisms are applied to strategically adjust the model's outputs, ensuring they not only maintain high quality and reliability but also adhere to specific performance criteria. This fusion of Neural ODEs and robust control represents a significant advancement in LLM interpretability, offering a comprehensive framework that elucidates the previously opaque mechanisms of these complex models. Our empirical results validate the effectiveness of this integrated approach, making a substantial contribution to the field of explainable AI by merging advanced machine learning techniques with the critical need for transparency and control in AI outputs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e3ef6261d72acb3b8f584e24594af1af686836c8" target='_blank'>
-              Differentiable Programming for Differential Equations: A Review
+          <td><a href="https://www.semanticscholar.org/paper/e11388eb181a61495a9fb75dd0509dda44b5e3b3" target='_blank'>
+              Unveiling LLM Mechanisms Through Neural ODEs and Control Theory
               </a>
             </td>
           <td>
-            Facundo Sapienza, Jordi Bolibar, Frank Schäfer, Brian Groenke, Avik Pal, Victor Boussange, Patrick Heimbach, Giles Hooker, Fernando P'erez, Per-Olof Persson, Christopher Rackauckas
+            Yukun Zhang
           </td>
-          <td>2024-06-14</td>
+          <td>2024-06-23</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>0</td>
         </tr>
 
-        <tr id="We introduce and analyze generalised polynomial chaos (gPC), considering both intrusive and non-intrusive approaches, as an uncertainty quantification method in studies of probabilistic robustness. The considered gPC methods are complementary to Monte Carlo (MC) methods and are shown to be fast and scalable, allowing for comprehensive and efficient exploration of parameter spaces. These properties enable robustness analysis of a wider set of models, compared to computationally expensive MC methods, while retaining desired levels of accuracy. We discuss the application of gPC methods to systems in biology and neuroscience, notably subject to multiple parametric uncertainties, and we examine a well-known model of neural dynamics as a case study.">
+        <tr id="Natural and technological networks exhibit dynamics that can lead to complex cooperative behaviors, such as synchronization in coupled oscillators and rhythmic activity in neuronal networks. Understanding these collective dynamics is crucial for deciphering a range of phenomena from brain activity to power grid stability. Recent interest in co-evolutionary networks has highlighted the intricate interplay between dynamics on and of the network with mixed time scales. Here, we explore the collective behavior of excitable oscillators in a simple networks of two Theta neurons with adaptive coupling without self-interaction. Through a combination of bifurcation analysis and numerical simulations, we seek to understand how the level of adaptivity in the coupling strength, $a$, influences the dynamics. We first investigate the dynamics possible in the non-adaptive limit; our bifurcation analysis reveals stability regions of quiescence and spiking behaviors, where the spiking frequencies mode-lock in a variety of configurations. Second, as we increase the adaptivity $a$, we observe a widening of the associated Arnol'd tongues, which may overlap and give room for multi-stable configurations. For larger adaptivity, the mode-locked regions may further undergo a period-doubling cascade into chaos. Our findings contribute to the mathematical theory of adaptive networks and offer insights into the potential mechanisms underlying neuronal communication and synchronization.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/abb89db7124ec1925a107b3eb959ec0287242359" target='_blank'>
-              Efficient gPC-based quantification of probabilistic robustness for systems in neuroscience
+          <td><a href="https://www.semanticscholar.org/paper/7ddfebfd3c68f11d067d5fd26480c3939e159e0a" target='_blank'>
+              Co-evolutionary dynamics for two adaptively coupled Theta neurons
               </a>
             </td>
           <td>
-            Uros Sutulovic, Daniele Proverbio, Rami Katz, Giulia Giordano
+            Felix Augustsson, E. A. Martens
           </td>
-          <td>2024-06-19</td>
+          <td>2024-07-01</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>21</td>
         </tr>
 
-        <tr id="Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and self-assembled structures encoded in minima of an energy landscape. Here, we extend this paradigm to dynamic functionalities, such as motion and shape change, that are instead encoded in limit cycles or pathways of a dynamical system. We identify the two ingredients needed to learn time-dependent behaviors irrespective of experimental platforms: (i) learning rules with time delays and (ii) exposure to examples that break time-reversal symmetry during training. After providing a hands-on demonstration of these requirements using programmable LEGO toys, we turn to realistic particle-based simulations where the training rules are not programmed on a computer. Instead, we elucidate how they emerge from physico-chemical processes involving the causal propagation of fields, like in recent experiments on moving oil droplets with chemotactic signalling. Our trainable particles can self-assemble into structures that move or change shape on demand, either by retrieving the dynamic behavior previously seen during training, or by learning on the fly. This rich phenomenology is captured by a modified Hopfield spin model amenable to analytical treatment. The principles illustrated here provide a step towards von Neumann's dream of engineering synthetic living systems that adapt to the environment.">
+        <tr id="Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of the numerical solution without increasing the overall mesh degree of freedom count. Conventional sophisticated mesh movement methods are extremely expensive and struggle to handle scenarios with complex boundary geometries. However, existing learning-based methods require re-training from scratch given a different PDE type or boundary geometry, which limits their applicability, and also often suffer from robustness issues in the form of inverted elements. In this paper, we introduce the Universal Mesh Movement Network (UM2N), which -- once trained -- can be applied in a non-intrusive, zero-shot manner to move meshes with different size distributions and structures, for solvers applicable to different PDE types and boundary geometries. UM2N consists of a Graph Transformer (GT) encoder for extracting features and a Graph Attention Network (GAT) based decoder for moving the mesh. We evaluate our method on advection and Navier-Stokes based examples, as well as a real-world tsunami simulation case. Our method outperforms existing learning-based mesh movement methods in terms of the benchmarks described above. In comparison to the conventional sophisticated Monge-Amp\`ere PDE-solver based method, our approach not only significantly accelerates mesh movement, but also proves effective in scenarios where the conventional method fails. Our project page is at https://erizmr.github.io/UM2N/.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/65200d8b0fc58bbbf5835e07be38dc47b087a743" target='_blank'>
-              Learning dynamical behaviors in physical systems
+          <td><a href="https://www.semanticscholar.org/paper/569f07b5381b1df88a804a15614ac2ddef7715f2" target='_blank'>
+              Towards Universal Mesh Movement Networks
               </a>
             </td>
           <td>
-            R. Mandal, Rosalind Huang, Michel Fruchart, P. Moerman, Suriyanarayanan Vaikuntanathan, Arvind Murugan, Vincenzo Vitelli
+            Mingrui Zhang, Chunyang Wang, Stephan Kramer, Joseph G. Wallwork, Siyi Li, Jiancheng Liu, Xiang Chen, M. Piggott
           </td>
-          <td>2024-06-12</td>
+          <td>2024-06-29</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>25</td>
+          <td>38</td>
         </tr>
 
-        <tr id="Model predictive control (MPC) is a powerful control method for handling complex nonlinear systems that are subject to constraints. However, the real-time application of this approach can be severely limited by the need to solve constrained nonlinear optimization problems at each sampling time. To this end, this work introduces a novel learning-based iterative solver that provides highly accurate predictions, optimality certification, and fast evaluation of the MPC solution at each sampling time. To learn this iterative solver, we propose an unsupervised training algorithm that builds on the Karush-Kuhn-Tucker optimality conditions, modified by a Fischer-Burmeister formulation, and eliminates the need for prior sampling of exact optimizer solutions. By exploiting efficient vector-Jacobian and Jacobian-vector products via automatic differentiation, the proposed training algorithm can be efficiently executed. We demonstrate the potential of the proposed learning-based iterative solver on the example of nonlinear model predictive control of a nonlinear double integrator. We show its advantages when compared to exact optimizer solutions and with an imitation learning-based approach that directly obtains a data-based approximation of the MPC control law.">
+        <tr id="In this article, a distributed neural network modeling framework including a novel neural hybrid system model is proposed for enhancing the scalability of neural network models in modeling dynamical systems. First, high-dimensional training data samples will be mapped to a low-dimensional feature space through the principal component analysis (PCA) featuring process. Following that, the feature space is bisected into multiple partitions based on the variation of the Shannon entropy under the maximum entropy (ME) bisecting process. The behavior of subsystems in the prespecified state space partitions will then be approximated using a group of shallow neural networks (SNNs) known as extreme learning machines (ELMs), and then it can further simplify the model by merging the redundant lattices based on their training error performance. The proposed modeling framework can handle high-dimensional dynamical system modeling problems with the advantages of reducing model complexity and improving model performance in training and verification. To demonstrate the effectiveness of the proposed modeling framework, examples of modeling the LASA dataset and an industrial robot are presented.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/04655a12d07dee491135aaae2f055b737e275291" target='_blank'>
-              Learning Iterative Solvers for Accurate and Fast Nonlinear Model Predictive Control via Unsupervised Training
+          <td><a href="https://www.semanticscholar.org/paper/7a2a2b97f2bbf0735400cc24119a8d6645252543" target='_blank'>
+              A Distributed Neural Hybrid System Learning Framework in Modeling Complex Dynamical Systems.
               </a>
             </td>
           <td>
-            Lukas Lüken, Sergio Lucia
+            Yejiang Yang, Tao Wang, Weiming Xiang
           </td>
-          <td>2024-06-25</td>
-          <td>2024 European Control Conference (ECC)</td>
+          <td>2024-06-28</td>
+          <td>IEEE transactions on neural networks and learning systems</td>
           <td>0</td>
           <td>2</td>
         </tr>
@@ -3199,34 +3319,34 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>26</td>
         </tr>
 
-        <tr id="To advance our understanding of the magnetohydrodynamic (MHD) processes in liquid metals, in this paper we propose an approach combining the classical methods in the dynamo theory based on numerical simulations of the partial differential equations governing the evolution of the magnetic field with the statistical methods. In this study, we intend to answer the following ``optimization'' question: Can we find a statistical explanation what makes a flow to favour magnetic field generation in the linear regime (i.e. the kinematic dynamo is considered), where the Lorenz force is neglected? The flow is assumed to be steady and incompressible, and the magnetic field generation is governed by the magnetic induction equation. The behaviour of its solution is determined by the dominant (i.e. with the largest real part) eigenvalue of the magnetic induction operator. Considering an ensemble of 2193 randomly generated flows, we solved the kinematic dynamo problem and performed an attempt to find a correlation between the dominant eigenvalue and the standard quantities used in hydrodynamics -- vorticity and kinetic helicity. We have found that there is no visible relation between the property of the flow to be a kinematic dynamo and these quantities. This enables us to conclude that the problem requires a more elaborated approach to ``recognize'' if the flow is a dynamo or not; we plan to solve it using contemporary data-driven approach based on deep neural networks.">
+        <tr id="A surrogate model approximates the outputs of a solver of Partial Differential Equations (PDEs) with a low computational cost. In this article, we propose a method to build learning-based surrogates in the context of parameterized PDEs, which are PDEs that depend on a set of parameters but are also temporal and spatial processes. Our contribution is a method hybridizing the Proper Orthogonal Decomposition and several Support Vector Regression machines. This method is conceived to work in real-time, thus aimed for being used in the context of digital twins, where a user can perform an interactive analysis of results based on the proposed surrogate. We present promising results on two use cases concerning electrical machines. These use cases are not toy examples but are produced an industrial computational code, they use meshes representing non-trivial geometries and contain non-linearities.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9cb7930ec7e8ea8ad0c81e79c9fa58cacaf4204f" target='_blank'>
-              What makes a steady flow to favour kinematic magnetic field generation: A statistical analysis
+          <td><a href="https://www.semanticscholar.org/paper/e63bc34c8490fd304b6cbb27c3dc5e2405d617e2" target='_blank'>
+              A Fast Learning-Based Surrogate of Electrical Machines using a Reduced Basis
               </a>
             </td>
           <td>
-            Francisco Stefano de Almeida, R. Chertovskih, Sílvio M. A. Gama, Rui Gonccalves
+            Alejandro Rib'es, Nawfal Benchekroun, Théo Delagnes
           </td>
-          <td>2024-07-24</td>
+          <td>2024-06-27</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>11</td>
+          <td>0</td>
         </tr>
 
-        <tr id="The purpose of this paper is to propose a novel perspective, based on Willems'"behavior theory", on the design of an unknown-input observer for a given linear time-invariant discrete-time state-space model, with unknown disturbances affecting both the state and the output equations. The problem is first addressed assuming that the original system model is known, and later assuming that the model is unknown but historical data satisfying a certain assumption are available. In both cases, fundamental concepts in behavior theory, as the projection of a behavior, the inclusion of a behavior in another one, and the use of kernel and image representations, provide quite powerful tools to determine necessary and sufficient conditions for the existence of an unknown-input observer (UIO), as well as algorithms to design one of them, if it exists.">
+        <tr id="The intersection of artificial intelligence (AI) and partial differential equations (PDEs), emphasizing how AI techniques can revolutionize the analysis and solution of PDEs in various scientific and engineering applications. Traditional methods for solving PDEs often face challenges related to computational complexity, high-dimensionality, and nonlinearity. By leveraging advanced AI algorithms, particularly deep learning and neural networks, we propose novel approaches to approximate solutions, reduce computational costs, and handle complex boundary conditions more effectively. The study highlights the advantages of AI-driven methods in terms of accuracy, efficiency, and scalability, presenting case studies from fluid dynamics, quantum mechanics, and financial mathematics. Our findings suggest that AI has the potential to significantly enhance the analytical capabilities and practical applications of PDEs, paving the way for new advancements in both theoretical research and real-world problem solving">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9d5ab8824253eedddbefb06d51b96d8e58632d5f" target='_blank'>
-              Behaviors, trajectories and data: A novel perspective on the design of unknown-input observers
+          <td><a href="https://www.semanticscholar.org/paper/c86e95ee6e33bf3061f0363c446c469fe71a1b5c" target='_blank'>
+              AI Based Analysis and Partial Differential Equations
               </a>
             </td>
           <td>
-            G. Disarò, M. E. Valcher
+            M. Krishna Reddy, N. Vijayabhaskar Reddy
           </td>
-          <td>2024-07-26</td>
-          <td>ArXiv</td>
+          <td>2024-07-21</td>
+          <td>International Journal of Advanced Research in Science, Communication and Technology</td>
+          <td>0</td>
           <td>0</td>
-          <td>33</td>
         </tr>
 
         <tr id="None">
@@ -3241,241 +3361,226 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2024-07-01</td>
           <td>Scientific Reports</td>
           <td>0</td>
-          <td>29</td>
+          <td>30</td>
         </tr>
 
-        <tr id="Stars orbiting a supermassive black hole in the center of galaxies undergo very efficient diffusion in their orbital orientations. This is"Vector Resonant Relaxation", a diffusion process formally occurring on the unit sphere. Such a dynamics is intrinsically non-linear, stochastic, and correlated, hence bearing deep similarities with turbulence in fluid mechanics or plasma physics. In that context, we show how generic methods stemming from statistical closure theory, namely the celebrated"Martin-Siggia-Rose formalism", can be used to characterize the correlations describing the redistribution of orbital orientations. In particular, limiting ourselves to the leading order truncation in this closure scheme, the so-called"Direct Interaction Approximation", and placing ourselves in the limit of an isotropic distribution of orientations, we explicitly compare the associated prediction for the two-point correlation function with measures from numerical simulations. We discuss the successes and limitations of this approach and present possible future venues.">
+        <tr id="The purpose of this paper is to propose a novel perspective, based on Willems'"behavior theory", on the design of an unknown-input observer for a given linear time-invariant discrete-time state-space model, with unknown disturbances affecting both the state and the output equations. The problem is first addressed assuming that the original system model is known, and later assuming that the model is unknown but historical data satisfying a certain assumption are available. In both cases, fundamental concepts in behavior theory, as the projection of a behavior, the inclusion of a behavior in another one, and the use of kernel and image representations, provide quite powerful tools to determine necessary and sufficient conditions for the existence of an unknown-input observer (UIO), as well as algorithms to design one of them, if it exists.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3e181cfb0c7c1e8ba73a1eb46297222d975f2e04" target='_blank'>
-              Vector Resonant Relaxation and Statistical Closure Theory. I. Direct Interaction Approximation
+          <td><a href="https://www.semanticscholar.org/paper/9d5ab8824253eedddbefb06d51b96d8e58632d5f" target='_blank'>
+              Behaviors, trajectories and data: A novel perspective on the design of unknown-input observers
               </a>
             </td>
           <td>
-            Sofia Flores, Jean-Baptiste Fouvry
+            G. Disarò, M. E. Valcher
           </td>
-          <td>2024-06-27</td>
+          <td>2024-07-26</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>13</td>
+          <td>33</td>
         </tr>
 
-        <tr id="Data driven system identification is the technique for learning models from input/output data. To increase the robustness of the model estimation, prior knowledge can be incorporated, the so-called gray-box identification. In finite impulse response (FIR) models, prior knowledge of the process under investigation can be introduced by regularization. In the regularization term basic impulse response characteristics such as smoothness and exponentially decaying behavior can be incorporated. For estimation of time-delay systems, the novel impulse response and time-delay preserving (IRDP) regularization matrix is proposed. In this contribution this method is extended to the estimation of multiple input single output (MISO) processes and is compared to other state-of-the-art approaches. A linear process with four inputs and different input dynamics and time-delays is investigated. The focus of the evaluation is placed on model quality, time-delay estimation, and computation time. The simulation results point out the superiority of the novel regularization approach in comparison to state-of-the-art methods.">
+        <tr id="Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-invested problem, especially when input-output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a8735d69bbb91950534f1fe2742f48352fd17202" target='_blank'>
-              Handling of Time Delays in MISO Processes with Regularized Finite Impulse Response Models
+          <td><a href="https://www.semanticscholar.org/paper/c5ebe3e35ead48c1cec6afd16f55a4873eabdbd1" target='_blank'>
+              Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids
               </a>
             </td>
           <td>
-            Christopher Illg, Tarek Kösters, Oliver Nelles
+            Saurabh Deshpande, Hussein Rappel, Mark Hobbs, Stéphane P. A. Bordas, Jakub Lengiewicz
           </td>
-          <td>2024-06-25</td>
-          <td>2024 European Control Conference (ECC)</td>
+          <td>2024-07-15</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Networks in machine learning offer examples of complex high-dimensional dynamical systems inspired by and reminiscent of biological systems. Here, we study the learning dynamics of generalized Hopfield networks, which permit visualization of internal memories. These networks have been shown to proceed through a “feature-to-prototype” transition, as the strength of network nonlinearity is increased, wherein the learned, or terminal, states of internal memories transition from mixed to pure states. Focusing on the prototype learning dynamics of the internal memories, we observe stereotypical dynamics of memories wherein similar subgroups of memories sequentially split at well-defined saddles. The splitting order is interpretable and reproducible from one simulation to the other. The dynamics prior to splits are robust to variations in many features of the system. To develop a more rigorous understanding of these global dynamics, we study smaller subsystems that exhibit similar properties to the full system. Within these smaller systems, we combine analytical calculations with numerical simulations to study the dynamics of the feature-to-prototype transition, and the emergence of saddle points in the learning landscape. We exhibit regimes where saddles appear and disappear through saddle-node bifurcations, qualitatively changing the distribution of learned memories as the strength of the nonlinearity is varied—allowing us to systematically investigate the mechanisms that underlie the emergence of the learning dynamics. Several features of the learning dynamics are reminiscent of the Waddington's caricature of cellular differentiation, and we attempt to make this analogy more precise. Memories can thus differentiate in a predictive and controlled way, revealing bridges between experimental biology, dynamical systems theory, and machine learning.
-
-
-
-
- Published by the American Physical Society
- 2024
-
-
-">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/acfb0996b8a2dd52af629b0fc803ccf66a9f85a9" target='_blank'>
-              Waddington landscape for prototype learning in generalized Hopfield networks
+          <td><a href="https://www.semanticscholar.org/paper/4eb1f5b104b75cee5eba224ac4724ead85e4c238" target='_blank'>
+              Physics-informed neural network simulation of thermal cavity flow
               </a>
             </td>
           <td>
-            Nacer Eddine Boukacem, Allen Leary, Robin Thériault, Felix Gottlieb, Madhav Mani, Paul François
+            Eric Fowler, Christopher J McDevitt, Subrata Roy
           </td>
-          <td>2024-07-23</td>
-          <td>Physical Review Research</td>
+          <td>2024-07-02</td>
+          <td>Scientific Reports</td>
           <td>0</td>
-          <td>1</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Many real-world applications demand accurate and fast predictions, as well as reliable uncertainty estimates. However, quantifying uncertainty on high-dimensional predictions is still a severely under-invested problem, especially when input-output relationships are non-linear. To handle this problem, the present work introduces an innovative approach that combines autoencoder deep neural networks with the probabilistic regression capabilities of Gaussian processes. The autoencoder provides a low-dimensional representation of the solution space, while the Gaussian process is a Bayesian method that provides a probabilistic mapping between the low-dimensional inputs and outputs. We validate the proposed framework for its application to surrogate modeling of non-linear finite element simulations. Our findings highlight that the proposed framework is computationally efficient as well as accurate in predicting non-linear deformations of solid bodies subjected to external forces, all the while providing insightful uncertainty assessments.">
+        <tr id="Partial differential equations (PDEs) are extensively utilized for modeling various physical phenomena. These equations often depend on certain parameters, necessitating either the identification of optimal parameters or solving the equation across multiple parameters to understand how a structure might react under different conditions. Performing an exhaustive search over the parameter space requires solving the PDE multiple times, which is generally impractical. To address this challenge, Reduced Order Models (ROMs) are constructed from a snapshot dataset comprising parameter-solution pairs. ROMs facilitate the rapid solving of PDEs for new parameters. Recently, Deep Learning ROMs (DL-ROMs) have been introduced as a new method to obtain ROM. Additionally, the PDE of interest may depend on the domain, which can be characterized by parameters or measurements and may evolve with the system, requiring parametrization for ROM construction. In this paper, we develop a Deep-ROM capable of extracting and efficiently utilizing domain parametrization. Unlike traditional domain parametrization methods, our approach does not require user-defined control points and can effectively handle domains with varying numbers of components. Moreover, our model can derive meaningful parametrization even when a domain mesh is unavailable, a common scenario in biomedical applications. Our work leverages Deep Neural Networks to effectively reduce the dimensionality of the PDE and the domain characteristic function.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c5ebe3e35ead48c1cec6afd16f55a4873eabdbd1" target='_blank'>
-              Gaussian process regression + deep neural network autoencoder for probabilistic surrogate modeling in nonlinear mechanics of solids
+          <td><a href="https://www.semanticscholar.org/paper/90e23c188396aefabed7701142b8c0a910c3d228" target='_blank'>
+              Deep Learning Reduced Order Modelling on Parametric and Data driven domains
               </a>
             </td>
           <td>
-            Saurabh Deshpande, Hussein Rappel, Mark Hobbs, Stéphane P. A. Bordas, Jakub Lengiewicz
+            Martina Bukavc, Iva Manojlovi'c, B. Muha, Domagoj Vlah University of Notre Dame, Notre Dame, In, University of Utah Department of Biomedical Engineering, Computing, Departmento Mathematics, Faculty of Computer Science, U. Zagreb
           </td>
-          <td>2024-07-15</td>
+          <td>2024-07-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>24</td>
         </tr>
 
-        <tr id="The Fisher Information Matrix (FIM) provides a way for quantifying the information content of an observable random variable concerning unknown parameters within a model that characterizes the variable. When parameters in a model are directly linked to individual features, the diagonal elements of the FIM can signify the relative importance of each feature. However, in scenarios where feature interactions may exist, a comprehensive exploration of the full FIM is necessary rather than focusing solely on its diagonal elements. This paper presents an end-to-end black box system identification approach that integrates the FIM into the training process to gain insights into dynamic importance and overall model structure. A decision module is added to the first layer of the network to determine the relevance scores using the entire FIM as input. The forward propagation is then performed on element-wise multiplication of inputs and relevance scores. Simulation results demonstrate that the proposed methodology effectively captures various types of interactions between dynamics, outperforming existing methods limited to polynomial interactions. Moreover, the effectiveness of this novel approach is confirmed through its application in identifying a real-world industrial system, specifically the PH neutralization process.">
+        <tr id="We consider a typical learning problem of point estimations for modeling of nonlinear functions or dynamical systems in which generalization, i.e., verifying a given learned model, can be embedded as an integral part of the learning process or dynamics. In particular, we consider an empirical risk minimization based learning problem that exploits gradient methods from continuous-time perspective with small random perturbations, which is guided by the training dataset loss. Here, we provide an asymptotic probability estimate in the small noise limit based-on the Freidlin-Wentzell theory of large deviations, when the sample path of the random process corresponding to the randomly perturbed gradient dynamical system hits a certain target set, i.e., a rare event, when the latter is specified by the testing dataset loss landscape. Interestingly, the proposed framework can be viewed as one way of improving generalization and robustness in learning problems that provides new insights leading to optimal point estimates which is guided by training data loss, while, at the same time, the learning dynamics has an access to the testing dataset loss landscape in some form of future achievable or anticipated target goal. Moreover, as a by-product, we establish a connection with optimal control problem, where the target set, i.e., the rare event, is considered as the desired outcome or achievable target goal for a certain optimal control problem, for which we also provide a verification result reinforcing the rationale behind the proposed framework. Finally, we present a computational algorithm that solves the corresponding variational problem leading to an optimal point estimates and, as part of this work, we also present some numerical results for a typical case of nonlinear regression problem.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/223d9021fa6b1a08ec49a719354add6931b3f923" target='_blank'>
-              Dynamic importance learning using fisher information gain for nonlinear system identification
+          <td><a href="https://www.semanticscholar.org/paper/3eb8a6a20e76ca76075c140c11561ca482a74778" target='_blank'>
+              Embedding generalization within the learning dynamics: An approach based-on sample path large deviation theory
               </a>
             </td>
           <td>
-            V. M. Eivaghi, M. A. Shoorehdeli
+            G. Befekadu
           </td>
-          <td>2024-06-08</td>
+          <td>2024-08-04</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>24</td>
+          <td>10</td>
         </tr>
 
-        <tr id="Probabilistic state estimation is essential for robots navigating uncertain environments. Accurately and efficiently managing uncertainty in estimated states is key to robust robotic operation. However, nonlinearities in robotic platforms pose significant challenges that require advanced estimation techniques. Gaussian variational inference (GVI) offers an optimization perspective on the estimation problem, providing analytically tractable solutions and efficiencies derived from the geometry of Gaussian space. We propose a Sequential Gaussian Variational Inference (S-GVI) method to address nonlinearity and provide efficient sequential inference processes. Our approach integrates sequential Bayesian principles into the GVI framework, which are addressed using statistical approximations and gradient updates on the information geometry. Validations through simulations and real-world experiments demonstrate significant improvements in state estimation over the Maximum A Posteriori (MAP) estimation method.">
+        <tr id="Networks in machine learning offer examples of complex high-dimensional dynamical systems inspired by and reminiscent of biological systems. Here, we study the learning dynamics of generalized Hopfield networks, which permit visualization of internal memories. These networks have been shown to proceed through a “feature-to-prototype” transition, as the strength of network nonlinearity is increased, wherein the learned, or terminal, states of internal memories transition from mixed to pure states. Focusing on the prototype learning dynamics of the internal memories, we observe stereotypical dynamics of memories wherein similar subgroups of memories sequentially split at well-defined saddles. The splitting order is interpretable and reproducible from one simulation to the other. The dynamics prior to splits are robust to variations in many features of the system. To develop a more rigorous understanding of these global dynamics, we study smaller subsystems that exhibit similar properties to the full system. Within these smaller systems, we combine analytical calculations with numerical simulations to study the dynamics of the feature-to-prototype transition, and the emergence of saddle points in the learning landscape. We exhibit regimes where saddles appear and disappear through saddle-node bifurcations, qualitatively changing the distribution of learned memories as the strength of the nonlinearity is varied—allowing us to systematically investigate the mechanisms that underlie the emergence of the learning dynamics. Several features of the learning dynamics are reminiscent of the Waddington's caricature of cellular differentiation, and we attempt to make this analogy more precise. Memories can thus differentiate in a predictive and controlled way, revealing bridges between experimental biology, dynamical systems theory, and machine learning.
+
+
+
+
+ Published by the American Physical Society
+ 2024
+
+
+">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/811d7774eca3cb0fd2b941a37229cdba2c834554" target='_blank'>
-              Sequential Gaussian Variational Inference for Nonlinear State Estimation applied to Robotic Applications
+          <td><a href="https://www.semanticscholar.org/paper/acfb0996b8a2dd52af629b0fc803ccf66a9f85a9" target='_blank'>
+              Waddington landscape for prototype learning in generalized Hopfield networks
               </a>
             </td>
           <td>
-            Min-Won Seo, Solmaz S. Kia
+            Nacer Eddine Boukacem, Allen Leary, Robin Thériault, Felix Gottlieb, Madhav Mani, Paul François
           </td>
-          <td>2024-07-07</td>
-          <td>ArXiv</td>
+          <td>2024-07-23</td>
+          <td>Physical Review Research</td>
           <td>0</td>
-          <td>17</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it remains unclear in many aspects how to effectively train PINNs if the solutions of PDEs exhibit stiff behaviors or high frequencies. In this paper, we propose a new method for training PINNs using variable-scaling techniques. This method is simple and it can be applied to a wide range of problems including PDEs with rapidly-varying solutions. Throughout various numerical experiments, we will demonstrate the effectiveness of the proposed method for these problems and confirm that it can significantly improve the training efficiency and performance of PINNs. Furthermore, based on the analysis of the neural tangent kernel (NTK), we will provide theoretical evidence for this phenomenon and show that our methods can indeed improve the performance of PINNs.">
+        <tr id="The formation of dynamical patterns is one of the most striking features of non-equilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as non-reciprocal interactions. These non-equilibrium phenomena are challenging for modern theories. Here, we introduce a model mixture of active (self-propelled) and passive (diffusive) particles with non-reciprocal effective interactions, which is amenable to exact mathematical analysis. We exploit state-of-the-art methods to derive exact hydrodynamic equations for the particle densities. We study the resulting collective behavior, including the linear stability of homogeneous states and phase coexistence in large systems. This reveals a novel phase diagram with the spinodal associated with active phase separation protruding through the associated binodal, heralding the emergence of dynamical steady states. We analyze these states in the thermodynamic limit of large system size, showing, for example, that sharp interfaces may travel at finite velocities, but traveling phase-separated states are forbidden. The model's mathematical tractability enables precise new conclusions beyond those available by numerical simulation of particle models or field theories.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9124ec1fca5f99e93eb695497f13fd9c818c0fa1" target='_blank'>
-              VS-PINN: A Fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior
+          <td><a href="https://www.semanticscholar.org/paper/2db205ad1b1ae5cb38f6a1257d35fe0eec005cfc" target='_blank'>
+              Dynamical patterns in active-passive particle mixtures with non-reciprocal interactions: Exact hydrodynamic analysis
               </a>
             </td>
           <td>
-            Seungchan Ko, Sang Hyeon Park
+            James Mason, Robert L. Jack, Maria Bruna
           </td>
-          <td>2024-06-10</td>
+          <td>2024-08-07</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>2</td>
         </tr>
 
-        <tr id="We present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://dx.doi.org/10.2139/ssrn.4766623), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy.">
+        <tr id="Data driven system identification is the technique for learning models from input/output data. To increase the robustness of the model estimation, prior knowledge can be incorporated, the so-called gray-box identification. In finite impulse response (FIR) models, prior knowledge of the process under investigation can be introduced by regularization. In the regularization term basic impulse response characteristics such as smoothness and exponentially decaying behavior can be incorporated. For estimation of time-delay systems, the novel impulse response and time-delay preserving (IRDP) regularization matrix is proposed. In this contribution this method is extended to the estimation of multiple input single output (MISO) processes and is compared to other state-of-the-art approaches. A linear process with four inputs and different input dynamics and time-delays is investigated. The focus of the evaluation is placed on model quality, time-delay estimation, and computation time. The simulation results point out the superiority of the novel regularization approach in comparison to state-of-the-art methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a80ea310f8f136bc43ebd91e533eefb2294c2ee9" target='_blank'>
-              Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-informed Neural Networks Framework for Interface Problems
+          <td><a href="https://www.semanticscholar.org/paper/a8735d69bbb91950534f1fe2742f48352fd17202" target='_blank'>
+              Handling of Time Delays in MISO Processes with Regularized Finite Impulse Response Models
               </a>
             </td>
           <td>
-            Sumanta Roy, C. Annavarapu, P. Roy, A. K. Sarma
+            Christopher Illg, T. Kösters, Oliver Nelles
           </td>
-          <td>2024-06-07</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>1</td>
+          <td>2024-06-25</td>
+          <td>2024 European Control Conference (ECC)</td>
+          <td>0</td>
+          <td>2</td>
         </tr>
 
-        <tr id="This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for controlling such systems, focusing on the measure-valued process of the system's state and the control actions that depend on noisy and incomplete data. Our approach uses a stochastic optimal control framework with a probability measure-valued state, which accommodates noisy measurements and integrates them into control decisions through a Bayesian update mechanism. We characterize the control optimality in terms of a sequence of interlaced Hamilton Jacobi Bellman (HJB) equations coupled with controlled impulse steps at the measurement times. For the case of Gaussian-controlled processes, we derive an equivalent HJB equation whose state variable is finite-dimensional, namely the state's mean and covariance. We demonstrate the effectiveness of our methods through numerical examples. These include control under perfect observations, control under no observations, and control under noisy observations. Our numerical results highlight significant differences in the control strategies and their performance, emphasizing the challenges and computational demands of dealing with uncertainty in state observation.">
+        <tr id="Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a partial differential equation (PDE) at a future time-step using a neural operator. Despite the popularity of neural operators, their use to predict solution functions over a domain given only data over the boundary (such as a spatially varying Dirichlet boundary condition) remains unexplored. In this paper, we refer to such problems as boundary-to-domain problems; they have a wide range of applications in areas such as fluid mechanics, solid mechanics, heat transfer etc. We present a novel FNO-based architecture, named Lifting Product FNO (or LP-FNO) which can map arbitrary boundary functions defined on the lower-dimensional boundary to a solution in the entire domain. Specifically, two FNOs defined on the lower-dimensional boundary are lifted into the higher dimensional domain using our proposed lifting product layer. We demonstrate the efficacy and resolution independence of the proposed LP-FNO for the 2D Poisson equation.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e6ba24031ebf3376cb6db64dd547b84c989cf92e" target='_blank'>
-              Continuous time Stochastic optimal control under discrete time partial observations
+          <td><a href="https://www.semanticscholar.org/paper/f352a2d81715807d302b4b1be51ece5c849052d2" target='_blank'>
+              Learning the boundary-to-domain mapping using Lifting Product Fourier Neural Operators for partial differential equations
               </a>
             </td>
           <td>
-            Christian Bayer, Boualem Djehiche, Eliza Rezvanova, Raúl Tempone
+            Aditya Kashi, Arka Daw, Muralikrishnan Gopalakrishnan Meena, Hao Lu
           </td>
-          <td>2024-07-25</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>24</td>
+          <td>4</td>
         </tr>
 
-        <tr id="We present the hidden-layer concatenated physics informed neural network (HLConcPINN) method, which combines hidden-layer concatenated feed-forward neural networks, a modified block time marching strategy, and a physics informed approach for approximating partial differential equations (PDEs). We analyze the convergence properties and establish the error bounds of this method for two types of PDEs: parabolic (exemplified by the heat and Burgers' equations) and hyperbolic (exemplified by the wave and nonlinear Klein-Gordon equations). We show that its approximation error of the solution can be effectively controlled by the training loss for dynamic simulations with long time horizons. The HLConcPINN method in principle allows an arbitrary number of hidden layers not smaller than two and any of the commonly-used smooth activation functions for the hidden layers beyond the first two, with theoretical guarantees. This generalizes several recent neural-network techniques, which have theoretical guarantees but are confined to two hidden layers in the network architecture and the $\tanh$ activation function. Our theoretical analyses subsequently inform the formulation of appropriate training loss functions for these PDEs, leading to physics informed neural network (PINN) type computational algorithms that differ from the standard PINN formulation. Ample numerical experiments are presented based on the proposed algorithm to validate the effectiveness of this method and confirm aspects of the theoretical analyses.">
+        <tr id="PurposeSimulation-based digital twins represent an effort to provide high-accuracy real-time insights into operational physical processes. However, the computation time of many multi-physical simulation models is far from real-time. It might even exceed sensible time frames to produce sufficient data for training data-driven reduced-order models. This study presents TwinLab, a framework for data-efficient, yet accurate training of neural-ODE type reduced-order models with only two data sets.Design/methodology/approachCorrelations between test errors of reduced-order models and distinct features of corresponding training data are investigated. Having found the single best data sets for training, a second data set is sought with the help of similarity and error measures to enrich the training process effectively.FindingsAdding a suitable second training data set in the training process reduces the test error by up to 49% compared to the best base reduced-order model trained only with one data set. Such a second training data set should at least yield a good reduced-order model on its own and exhibit higher levels of dissimilarity to the base training data set regarding the respective excitation signal. Moreover, the base reduced-order model should have elevated test errors on the second data set. The relative error of the time series ranges from 0.18% to 0.49%. Prediction speed-ups of up to a factor of 36,000 are observed.Originality/valueThe proposed computational framework facilitates the automated, data-efficient extraction of non-intrusive reduced-order models for digital twins from existing simulation models, independent of the simulation software.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/756e42c72cc211bde08b9880438d676e69260474" target='_blank'>
-              Error Analysis and Numerical Algorithm for PDE Approximation with Hidden-Layer Concatenated Physics Informed Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/4aeb7a00d93947f8e222188bb9f980ac834448d1" target='_blank'>
+              TwinLab: a framework for data-efficient training of non-intrusive reduced-order models for digital twins
               </a>
             </td>
           <td>
-            Yianxia Qian, Yongchao Zhang, Suchuan Dong
+            Maximilian Kannapinn, M. Schäfer, Oliver Weeger
           </td>
-          <td>2024-06-10</td>
+          <td>2024-07-04</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>2</td>
         </tr>
 
-        <tr id="Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0b774b7e6f09a7e0224e2806d7eeec8722233491" target='_blank'>
-              Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems.
-              </a>
-            </td>
-          <td>
-            Klaus Lehnertz
-          </td>
-          <td>2024-06-07</td>
-          <td>Chaos</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-
-        <tr id="Ever since the concepts of dynamic programming were introduced, one of the most difficult challenges has been to adequately address high-dimensional control problems. With growing dimensionality, the utilisation of Deep Neural Networks promises to circumvent the issue of an otherwise exponentially increasing complexity. The paper specifically investigates the sampling issues the Deep Galerkin Method is subjected to. It proposes a drift relaxation-based sampling approach to alleviate the symptoms of high-variance policy approximations. This is validated on mean-field control problems; namely, the variations of the opinion dynamics presented by the Sznajd and the Hegselmann-Krause model. The resulting policies induce a significant cost reduction over manually optimised control functions and show improvements on the Linear-Quadratic Regulator problem over the Deep FBSDE approach.">
+        <tr id="This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for controlling such systems, focusing on the measure-valued process of the system's state and the control actions that depend on noisy and incomplete data. Our approach uses a stochastic optimal control framework with a probability measure-valued state, which accommodates noisy measurements and integrates them into control decisions through a Bayesian update mechanism. We characterize the control optimality in terms of a sequence of interlaced Hamilton Jacobi Bellman (HJB) equations coupled with controlled impulse steps at the measurement times. For the case of Gaussian-controlled processes, we derive an equivalent HJB equation whose state variable is finite-dimensional, namely the state's mean and covariance. We demonstrate the effectiveness of our methods through numerical examples. These include control under perfect observations, control under no observations, and control under noisy observations. Our numerical results highlight significant differences in the control strategies and their performance, emphasizing the challenges and computational demands of dealing with uncertainty in state observation.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/436f33e4de177b45b5684897ce37764ab9e4d1a5" target='_blank'>
-              Optimal Control of Agent-Based Dynamics under Deep Galerkin Feedback Laws
+          <td><a href="https://www.semanticscholar.org/paper/e6ba24031ebf3376cb6db64dd547b84c989cf92e" target='_blank'>
+              Continuous time Stochastic optimal control under discrete time partial observations
               </a>
             </td>
           <td>
-            Frederik Kelbel
+            Christian Bayer, Boualem Djehiche, Eliza Rezvanova, Raúl Tempone
           </td>
-          <td>2024-06-13</td>
+          <td>2024-07-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>24</td>
         </tr>
 
-        <tr id="Diffusion models excel at creating visually-convincing images, but they often struggle to meet subtle constraints inherent in the training data. Such constraints could be physics-based (e.g., satisfying a PDE), geometric (e.g., respecting symmetry), or semantic (e.g., including a particular number of objects). When the training data all satisfy a certain constraint, enforcing this constraint on a diffusion model not only improves its distribution-matching accuracy but also makes it more reliable for generating valid synthetic data and solving constrained inverse problems. However, existing methods for constrained diffusion models are inflexible with different types of constraints. Recent work proposed to learn mirror diffusion models (MDMs) in an unconstrained space defined by a mirror map and to impose the constraint with an inverse mirror map, but analytical mirror maps are challenging to derive for complex constraints. We propose neural approximate mirror maps (NAMMs) for general constraints. Our approach only requires a differentiable distance function from the constraint set. We learn an approximate mirror map that pushes data into an unconstrained space and a corresponding approximate inverse that maps data back to the constraint set. A generative model, such as an MDM, can then be trained in the learned mirror space and its samples restored to the constraint set by the inverse map. We validate our approach on a variety of constraints, showing that compared to an unconstrained diffusion model, a NAMM-based MDM substantially improves constraint satisfaction. We also demonstrate how existing diffusion-based inverse-problem solvers can be easily applied in the learned mirror space to solve constrained inverse problems.">
+        <tr id="Biological neural networks can perform complex computations to predict their environment, far above the limited predictive capabilities of individual neurons. While conventional approaches to understanding these computations often focus on isolating the contributions of single neurons, here we argue that a deeper understanding requires considering emergent dynamics - dynamics that make the whole system"more than the sum of its parts". Specifically, we examine the relationship between prediction performance and emergence by leveraging recent quantitative metrics of emergence, derived from Partial Information Decomposition, and by modelling the prediction of environmental dynamics in a bio-inspired computational framework known as reservoir computing. Notably, we reveal a bidirectional coupling between prediction performance and emergence, which generalises across task environments and reservoir network topologies, and is recapitulated by three key results: 1) Optimising hyperparameters for performance enhances emergent dynamics, and vice versa; 2) Emergent dynamics represent a near sufficient criterion for prediction success in all task environments, and an almost necessary criterion in most environments; 3) Training reservoir computers on larger datasets results in stronger emergent dynamics, which contain task-relevant information crucial for performance. Overall, our study points to a pivotal role of emergence in facilitating environmental predictions in a bio-inspired computational architecture.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/41e376b129ad93d8ea21f2780e8a91014ca3759f" target='_blank'>
-              Neural Approximate Mirror Maps for Constrained Diffusion Models
+          <td><a href="https://www.semanticscholar.org/paper/2572feb06e7ea060ecb305043a5d4b589af5886d" target='_blank'>
+              Evolving reservoir computers reveals bidirectional coupling between predictive power and emergent dynamics
               </a>
             </td>
           <td>
-            Berthy T. Feng, Ricardo Baptista, Katherine L. Bouman
+            Hanna M. Tolle, A. Luppi, Anil K. Seth, P. Mediano
           </td>
-          <td>2024-06-18</td>
+          <td>2024-06-27</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>5</td>
+          <td>26</td>
         </tr>
 
-        <tr id="In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to learn low-dimensional representations of nonlinear time series without supervision and can have provable recovery guarantees. The learned representation can be used for downstream machine-learning tasks such as clustering and classification. The method is based on the assumption that the observed sequences arise from a common domain, but each sequence obeys its own autoregressive models that are related to each other through low-rank regularization. We cast the problem as a computationally efficient convex matrix parameter recovery problem using monotone Variational Inequality and encode the common domain assumption via low-rank constraint across the learned representations, which can learn the geometry for the entire domain as well as faithful representations for the dynamics of each individual sequence using the domain information in totality. We show the competitive performance of our method on real-world time-series data with the baselines and demonstrate its effectiveness for symbolic text modeling and RNA sequence clustering.">
+        <tr id="This paper introduces a novel nonlinear stochastic model predictive control path integral (MPPI) method, which considers chance constraints on system states. The proposed belief-space stochastic MPPI (BSS-MPPI) applies Monte-Carlo sampling to evaluate state distributions resulting from underlying systematic disturbances, and utilizes a Control Barrier Function (CBF) inspired heuristic in belief space to fulfill the specified chance constraints. Compared to several previous stochastic predictive control methods, our approach applies to general nonlinear dynamics without requiring the computationally expensive system linearization step. Moreover, the BSS-MPPI controller can solve optimization problems without limiting the form of the objective function and chance constraints. By multi-threading the sampling process using a GPU, we can achieve fast real-time planning for time- and safety-critical tasks such as autonomous racing. Our results on a realistic race-car simulation study show significant reductions in constraint violation compared to some of the prior MPPI approaches, while being comparable in computation times.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/374d6dcbbd6b7bc58c4e0fdbbfe9c1648975a899" target='_blank'>
-              Nonlinear time-series embedding by monotone variational inequality
+          <td><a href="https://www.semanticscholar.org/paper/ec0a95b01ae133b323176ef995b8490fff8991be" target='_blank'>
+              Chance-Constrained Information-Theoretic Stochastic Model Predictive Control with Safety Shielding
               </a>
             </td>
           <td>
-            Jonathan Y. Zhou, Yao Xie
+            Ji Yin, P. Tsiotras, K. Berntorp
           </td>
-          <td>2024-06-11</td>
+          <td>2024-08-01</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>49</td>
         </tr>
 
-        <tr id="Flow estimation problems are ubiquitous in scientific imaging. Often, the underlying flows are subject to physical constraints that can be exploited in the flow estimation; for example, incompressible (divergence-free) flows are expected for many fluid experiments, while irrotational (curl-free) flows arise in the analysis of optical distortions and wavefront sensing. In this work, we propose a Physics- Inspired Neural Network (PINN) named HDNet, which performs a Helmholtz decomposition of an arbitrary flow field, i.e., it decomposes the input flow into a divergence-only and a curl-only component. HDNet can be trained exclusively on synthetic data generated by reverse Helmholtz decomposition, which we call Helmholtz synthesis. As a PINN, HDNet is fully differentiable and can easily be integrated into arbitrary flow estimation problems.">
+        <tr id="The development of novel materials in recent years has been accelerated greatly by the use of computational modelling techniques aimed at elucidating the complex physics controlling microstructure formation in materials, the properties of which control material function. One such technique is the phase field method, a field theoretic approach that couples various thermophysical fields to microscopic order parameter fields that track the phases of microstructure. Phase field models are framed as multiple, non-linear, partial differential equations, which are extremely challenging to compute efficiently. Recent years have seen an explosion of computational algorithms aimed at enhancing the efficiency of phase field simulations. One such technique, adaptive mesh refinement (AMR), dynamically adapts numerical meshes to be highly refined around steep spatial gradients of the PDE fields and coarser where the fields are smooth. This reduces the number of computations per time step significantly, thus reducing the total time of computation. What AMR doesn't do is allow for adaptive time stepping. This work combines AMR with a neural network algorithm that uses a U-Net with a Convolutional Long-Short Term Memory (CLSTM) base to accelerate phase field simulations. Our neural network algorithm is described in detail and tested in on simulations of directional solidification of a dilute binary alloy, a paradigm that is highly practical for its relevance to the solidification of alloys.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3cf74daf478f8997bca401680db82727a5ce0ee6" target='_blank'>
-              HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition
+          <td><a href="https://www.semanticscholar.org/paper/f7c3b439cab9bc1574b9ee846128f87f45347f16" target='_blank'>
+              LeapFrog: Getting the Jump on Multi-Scale Materials Simulations Using Machine Learning
               </a>
             </td>
           <td>
-            Miao Qi, R. Idoughi, Wolfgang Heidrich
+            Damien Pinto, M. Greenwood, N. Provatas
           </td>
-          <td>2024-06-12</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>12</td>
+          <td>36</td>
         </tr>
 
         <tr id="Temporal data modelling techniques with neural networks are useful in many domain applications, including time-series forecasting and control engineering. This paper aims at developing a recurrent version of stochastic configuration networks (RSCNs) for problem solving, where we have no underlying assumption on the dynamic orders of the input variables. Given a collection of historical data, we first build an initial RSCN model in the light of a supervisory mechanism, followed by an online update of the output weights by using a projection algorithm. Some theoretical results are established, including the echo state property, the universal approximation property of RSCNs for both the offline and online learnings, and the convergence of the output weights. The proposed RSCN model is remarkably distinguished from the well-known echo state networks (ESNs) in terms of the way of assigning the input random weight matrix and a special structure of the random feedback matrix. A comprehensive comparison study among the long short-term memory (LSTM) network, the original ESN, and several state-of-the-art ESN methods such as the simple cycle reservoir (SCR), the polynomial ESN (PESN), the leaky-integrator ESN (LIESN) and RSCN is carried out. Numerical results clearly indicate that the proposed RSCN performs favourably over all of the datasets.">
@@ -3493,64 +3598,95 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>1</td>
         </tr>
 
-        <tr id="This letter presents a high-dimensional analysis of the training dynamics for a single-layer nonlinear contrastive learning model. The empirical distribution of the model weights converges to a deterministic measure governed by a McKean-Vlasov nonlinear partial differential equation (PDE). Under L2 regularization, this PDE reduces to a closed set of low-dimensional ordinary differential equations (ODEs), reflecting the evolution of the model performance during the training process. We analyze the fixed point locations and their stability of the ODEs unveiling several interesting findings. First, only the hidden variable's second moment affects feature learnability at the state with uninformative initialization. Second, higher moments influence the probability of feature selection by controlling the attraction region, rather than affecting local stability. Finally, independent noises added in the data argumentation degrade performance but negatively correlated noise can reduces the variance of gradient estimation yielding better performance. Despite of the simplicity of the analyzed model, it exhibits a rich phenomena of training dynamics, paving a way to understand more complex mechanism behind practical large models.">
+        <tr id="Reliable uncertainty measures are required when using data based machine learning interatomic potentials (MLIPs) for atomistic simulations. In this work, we propose for sparse Gaussian Process Regression type MLIP a stochastic uncertainty measure akin to the query-by-committee approach often used in conjunction with neural network based MLIPs. The uncertainty measure is coined \textit{"label noise"} ensemble uncertainty as it emerges from adding noise to the energy labels in the training data. We find that this method of calculating an ensemble uncertainty is as well calibrated as the one obtained from the closed-form expression for the posterior variance when the sparse GPR is treated as a projected process. Comparing the two methods, our proposed ensemble uncertainty is, however, faster to evaluate than the closed-form expression. Finally, we demonstrate that the proposed uncertainty measure acts better to support a Bayesian search for optimal structure of Au$_{20}$ clusters.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6a791eb3679c0d2b194a35ba38ca2fe814772263" target='_blank'>
-              Training Dynamics of Nonlinear Contrastive Learning Model in the High Dimensional Limit
+          <td><a href="https://www.semanticscholar.org/paper/cbe74de7bdeef59e212d49ccb746e4deaac70d5f" target='_blank'>
+              Efficient ensemble uncertainty estimation in Gaussian Processes Regression
               </a>
             </td>
           <td>
-            Lineghuan Meng, Chuang Wang
+            Mads-Peter V. Christiansen, Nikolaj Rønne, Bjork Hammer
           </td>
-          <td>2024-06-11</td>
+          <td>2024-07-17</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Modeling thermal states for complex space missions, such as the surface exploration of airless bodies, requires high computation, whether used in ground-based analysis for spacecraft design or during onboard reasoning for autonomous operations. For example, a finite-element thermal model with hundreds of elements can take significant time to simulate, which makes it unsuitable for onboard reasoning during time-sensitive scenarios such as descent and landing, proximity operations, or in-space assembly. Further, the lack of fast and accurate thermal modeling drives thermal designs to be more conservative and leads to spacecraft with larger mass and higher power budgets. The emerging paradigm of physics-informed machine learning (PIML) presents a class of hybrid modeling architectures that address this challenge by combining simplified physics models with machine learning (ML) models resulting in models which maintain both interpretability and robustness. Such techniques enable designs with reduced mass and power through onboard thermal-state estimation and control and may lead to improved onboard handling of off-nominal states, including unplanned down-time. The PIML model or hybrid model presented here consists of a neural network which predicts reduced nodalizations (distribution and size of coarse mesh) given on-orbit thermal load conditions, and subsequently a (relatively coarse) finite-difference model operates on this mesh to predict thermal states. We compare the computational performance and accuracy of the hybrid model to a data-driven neural net model, and a high-fidelity finite-difference model of a prototype Earth-orbiting small spacecraft. The PIML based active nodalization approach provides significantly better generalization than the neural net model and coarse mesh model, while reducing computing cost by up to 1.7x compared to the high-fidelity model.">
+        <tr id="Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require thousands to millions of realisations of the forward model, leading to high computational costs. Surrogate models are often used to approximate these simulations. However, many surrogate models suffer from the fundamental limitation of being unable to estimate plausible high-dimensional outputs, inevitably compromising their use in the UQ framework. To address this challenge, this study introduces an efficient surrogate modelling workflow tailored for high-dimensional outputs. Specifically, a two-step approach is developed: (1) a dimensionality reduction technique is used for extracting data features and mapping the original output space into a reduced space; and (2) a multivariate surrogate model is constructed directly on the reduced space. The combined approach is shown to improve the accuracy of the surrogate model while retaining the computational efficiency required for UQ inversion. The proposed surrogate method, combined with Bayesian inference, is evaluated for a civil engineering application by performing inverse analyses on a laterally loaded pile problem. The results demonstrate the superiority of the proposed framework over traditional surrogate methods in dealing with high-dimensional outputs for sequential inversion analysis.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/04894c31eb0dcaa0ede3881b219f3bfbb359c4b6" target='_blank'>
-              Physics-Informed Machine Learning Towards A Real-Time Spacecraft Thermal Simulator
+          <td><a href="https://www.semanticscholar.org/paper/dace1d7c26c300e5c21c5561b92782d077d84947" target='_blank'>
+              A two-step surrogate method for sequential uncertainty quantification in high-dimensional inverse problems
               </a>
             </td>
           <td>
-            Manaswin Oddiraju, Zaki Hasnain, Saptarshi Bandyopadhyay, Eric Sunada, Souma Chowdhury
+            Ningxin Yang, Truong Le, Lidija Zdravkovi'c, David M. Potts
           </td>
-          <td>2024-07-08</td>
+          <td>2024-07-16</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>9</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Solving partial differential equations (PDEs) and their inverse problems using Physics-informed neural networks (PINNs) is a rapidly growing approach in the physics and machine learning community. Although several architectures exist for PINNs that work remarkably in practice, our theoretical understanding of their performances is somewhat limited. In this work, we study the behavior of a Bayesian PINN estimator of the solution of a PDE from $n$ independent noisy measurement of the solution. We focus on a class of equations that are linear in their parameters (with unknown coefficients $\theta_\star$). We show that when the partial differential equation admits a classical solution (say $u_\star$), differentiable to order $\beta$, the mean square error of the Bayesian posterior mean is at least of order $n^{-2\beta/(2\beta + d)}$. Furthermore, we establish a convergence rate of the linear coefficients of $\theta_\star$ depending on the order of the underlying differential operator. Last but not least, our theoretical results are validated through extensive simulations.">
+        <tr id="The probability that a configuration of a physical system reacts, or transitions from one metastable state to another, is quantified by the committor function. This function contains richly detailed mechanistic information about transition pathways, but a full parameterization of the committor requires building representing a high-dimensional function, a generically challenging task. Recent efforts to leverage neural networks as a means to solve high-dimensional partial differential equations, often called"physics-informed"machine learning, have brought the committor into computational reach. Here, we build on the semigroup approach to learning the committor and assess its utility for predicting dynamical quantities such as transition rates. We show that a careful reframing of the objective function and improved adaptive sampling strategies provide highly accurate representations of the committor. Furthermore, by directly applying the Hill relation, we show that these committors provide accurate transition rates for molecular system.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d332b278e945ecc01ec826948d1f3554cba5312b" target='_blank'>
-              On the estimation rate of Bayesian PINN for inverse problems
+          <td><a href="https://www.semanticscholar.org/paper/61781a644a9abeb378998d8505d6add714bb238b" target='_blank'>
+              Committor guided estimates of molecular transition rates
               </a>
             </td>
           <td>
-            Yi Sun, Debarghya Mukherjee, Yves Atchadé
+            Andrew R. Mitchell, Grant M. Rotskoff
           </td>
-          <td>2024-06-21</td>
+          <td>2024-08-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>24</td>
         </tr>
 
-        <tr id="Advances in experimental techniques allow the collection of high-space-and-time resolution data that track individual motile entities over time. This poses the question of how to use these data to efficiently and effectively calibrate motion models. However, typical mathematical models often overlook the inherent aspects of data collection, such as the discreteness and the experimental noise of the measured locations. In this paper, we focus on velocity-jump models suitable to describe single-agent motion in one spatial dimension, characterised by successive Markovian transitions between a finite network of $n$ states, each with a specified velocity and a fixed rate of switching to every other state. Since the problem of finding the exact distributions of discrete-time noisy data is generally intractable, we derive a series of approximations for the data distributions and compare them to in-silico data generated by the models using four example network structures. These comparisons suggest that the approximations are accurate given sufficiently infrequent state switching, or equivalently, a sufficiently high data collection frequency. Moreover, for infrequent switching, the PDFs comparisons highlight the importance of accounting for the correlation between subsequent measured locations, due to the likely permanence in the state visited in the previous measurement. The approximate distributions computed can be used for fast parameter inference and model selection between a range of velocity-jump models using single-agent tracking data.">
+        <tr id="In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to estimate a linear ordinary differential equation from functional data in a technique called Principal Differential Analysis, by formulating a functional regression in which the highest-order derivative of a function is modelled as a time-varying linear combination of its lower-order derivatives. Principal Differential Analysis was introduced as a technique for data reduction and representation, using solutions of the estimated differential equation as a basis to represent the functional data. In this work, we re-formulate PDA as a generative statistical model in which functional observations arise as solutions of a deterministic ODE that is forced by a smooth random error process. This viewpoint defines a flexible class of functional models based on differential equations and leads to an improved understanding and characterisation of the sources of variability in Principal Differential Analysis. It does, however, result in parameter estimates that can be heavily biased under the standard estimation approach of PDA. Therefore, we introduce an iterative bias-reduction algorithm that can be applied to improve parameter estimates. We also examine the utility of our approach when the form of the deterministic part of the differential equation is unknown and possibly non-linear, where Principal Differential Analysis is treated as an approximate model based on time-varying linearisation. We demonstrate our approach on simulated data from linear and non-linear differential equations and on real data from human movement biomechanics. Supplementary R code for this manuscript is available at \url{https://github.com/edwardgunning/UnderstandingOfPDAManuscript}.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8f4862ab7ce4151b9c0569c8c9b73d89ab08ca0e" target='_blank'>
-              Approximate solutions of a general stochastic velocity-jump process subject to discrete-time noisy observations
+          <td><a href="https://www.semanticscholar.org/paper/8d0be3d0b8344a99cb8ce9f30ed01a1653af4baa" target='_blank'>
+              An Understanding of Principal Differential Analysis
               </a>
             </td>
           <td>
-            Arianna Ceccarelli, Alexander P. Browning, Ruth E. Baker
+            Edward Gunning, Giles Hooker
           </td>
-          <td>2024-06-28</td>
+          <td>2024-06-26</td>
           <td>ArXiv</td>
           <td>0</td>
+          <td>3</td>
+        </tr>
+
+        <tr id="
+Of great relevance to climate engineering is the systematic relationship between the radiative forcing to the climate system and the response of the system, a relationship often represented by the linear response function (LRF) of the system. However, estimating the LRF often becomes an ill-posed inverse problem due to high-dimensionality and non-unique relationships between the forcing and response. Recent advances in machine learning make it possible to address the ill-posed inverse problem through regularization and sparse system fitting. Here we develop a convolutional neural network (CNN) for regularized inversion. The CNN is trained using the surface temperature responses from a set of Green’s function perturbation experiments as imagery input data together with data sample densification. The resulting CNN model can infer the forcing pattern responsible for the temperature response from out-of-sample forcing scenarios. This promising proof-of-concept suggests a possible strategy for estimating the optimal forcing to negate certain undesirable effects of climate change. The limited success of this effort underscores the challenges of solving an inverse problem for a climate system with inherent nonlinearity.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/f4dd739f36233f85b623bc7abb71b0aaaed422e9" target='_blank'>
+              Neural networks to find the optimal forcing for offsetting the anthropogenic climate change effects
+              </a>
+            </td>
+          <td>
+            Huiying Ren, Jian Lu, Z. J. Hou, Tse-Chun Chen, L. R. Leung, Fukai Liu
+          </td>
+          <td>2024-07-03</td>
+          <td>Artificial Intelligence for the Earth Systems</td>
+          <td>0</td>
+          <td>11</td>
+        </tr>
+
+        <tr id="Modeling thermal states for complex space missions, such as the surface exploration of airless bodies, requires high computation, whether used in ground-based analysis for spacecraft design or during onboard reasoning for autonomous operations. For example, a finite-element thermal model with hundreds of elements can take significant time to simulate, which makes it unsuitable for onboard reasoning during time-sensitive scenarios such as descent and landing, proximity operations, or in-space assembly. Further, the lack of fast and accurate thermal modeling drives thermal designs to be more conservative and leads to spacecraft with larger mass and higher power budgets. The emerging paradigm of physics-informed machine learning (PIML) presents a class of hybrid modeling architectures that address this challenge by combining simplified physics models with machine learning (ML) models resulting in models which maintain both interpretability and robustness. Such techniques enable designs with reduced mass and power through onboard thermal-state estimation and control and may lead to improved onboard handling of off-nominal states, including unplanned down-time. The PIML model or hybrid model presented here consists of a neural network which predicts reduced nodalizations (distribution and size of coarse mesh) given on-orbit thermal load conditions, and subsequently a (relatively coarse) finite-difference model operates on this mesh to predict thermal states. We compare the computational performance and accuracy of the hybrid model to a data-driven neural net model, and a high-fidelity finite-difference model of a prototype Earth-orbiting small spacecraft. The PIML based active nodalization approach provides significantly better generalization than the neural net model and coarse mesh model, while reducing computing cost by up to 1.7x compared to the high-fidelity model.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/04894c31eb0dcaa0ede3881b219f3bfbb359c4b6" target='_blank'>
+              Physics-Informed Machine Learning Towards A Real-Time Spacecraft Thermal Simulator
+              </a>
+            </td>
+          <td>
+            Manaswin Oddiraju, Zaki Hasnain, Saptarshi Bandyopadhyay, Eric Sunada, Souma Chowdhury
+          </td>
+          <td>2024-07-08</td>
+          <td>ArXiv</td>
           <td>0</td>
+          <td>9</td>
         </tr>
 
         <tr id="In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear interaction functions and time-fractional orders. In these coupled systems, we enforce non-negativity of the solutions, aligning with realistic scenarios in biology and ecology. There are several salient features of our inverse problem study: the drastic reduction in measurement/observation data due to averaging effects, the nonlinear coupling between multiple equations, and the nonlocality arising from fractional-type derivatives. These factors present significant challenges to our inverse problem, and such inverse problems have never been explored in previous literature. To address these challenges, we develop new and effective schemes. Our approach involves properly controlling the injection of different source terms to obtain multiple sets of mean flux data. This allows us to achieve unique identifiability results and accurately determine the unknown parameters. Finally, we establish a connection between our study and practical applications in biology, further highlighting the relevance of our work in real-world contexts.">
@@ -3583,34 +3719,34 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>15</td>
         </tr>
 
-        <tr id="In functional data analysis, replicate observations of a smooth functional process and its derivatives offer a unique opportunity to flexibly estimate continuous-time ordinary differential equation models. Ramsay (1996) first proposed to estimate a linear ordinary differential equation from functional data in a technique called Principal Differential Analysis, by formulating a functional regression in which the highest-order derivative of a function is modelled as a time-varying linear combination of its lower-order derivatives. Principal Differential Analysis was introduced as a technique for data reduction and representation, using solutions of the estimated differential equation as a basis to represent the functional data. In this work, we re-formulate PDA as a generative statistical model in which functional observations arise as solutions of a deterministic ODE that is forced by a smooth random error process. This viewpoint defines a flexible class of functional models based on differential equations and leads to an improved understanding and characterisation of the sources of variability in Principal Differential Analysis. It does, however, result in parameter estimates that can be heavily biased under the standard estimation approach of PDA. Therefore, we introduce an iterative bias-reduction algorithm that can be applied to improve parameter estimates. We also examine the utility of our approach when the form of the deterministic part of the differential equation is unknown and possibly non-linear, where Principal Differential Analysis is treated as an approximate model based on time-varying linearisation. We demonstrate our approach on simulated data from linear and non-linear differential equations and on real data from human movement biomechanics. Supplementary R code for this manuscript is available at \url{https://github.com/edwardgunning/UnderstandingOfPDAManuscript}.">
+        <tr id="Solving partial differential equations (PDEs) and their inverse problems using Physics-informed neural networks (PINNs) is a rapidly growing approach in the physics and machine learning community. Although several architectures exist for PINNs that work remarkably in practice, our theoretical understanding of their performances is somewhat limited. In this work, we study the behavior of a Bayesian PINN estimator of the solution of a PDE from $n$ independent noisy measurement of the solution. We focus on a class of equations that are linear in their parameters (with unknown coefficients $\theta_\star$). We show that when the partial differential equation admits a classical solution (say $u_\star$), differentiable to order $\beta$, the mean square error of the Bayesian posterior mean is at least of order $n^{-2\beta/(2\beta + d)}$. Furthermore, we establish a convergence rate of the linear coefficients of $\theta_\star$ depending on the order of the underlying differential operator. Last but not least, our theoretical results are validated through extensive simulations.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8d0be3d0b8344a99cb8ce9f30ed01a1653af4baa" target='_blank'>
-              An Understanding of Principal Differential Analysis
+          <td><a href="https://www.semanticscholar.org/paper/d332b278e945ecc01ec826948d1f3554cba5312b" target='_blank'>
+              On the estimation rate of Bayesian PINN for inverse problems
               </a>
             </td>
           <td>
-            Edward Gunning, Giles Hooker
+            Yi Sun, Debarghya Mukherjee, Yves Atchadé
           </td>
-          <td>2024-06-26</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
+          <td>7</td>
         </tr>
 
-        <tr id="In this paper, a novel data-driven approach for the development of soft sensors (SSs) for multi-step-ahead prediction of industrial process variables is proposed. This method is based on the recent developments in Koopman operator theory and dynamic mode decomposition (DMD). It is derived from Hankel DMD with control (HDMDc) to deal with highly nonlinear dynamics using augmented linear models, exploiting input and output regressors. The proposed multi-step-ahead HDMDc (MSA-HDMDc) is designed to perform multi-step prediction and capture complex dynamics with a linear approximation for a highly nonlinear system. This enables the construction of SSs capable of estimating the output of a process over a long period of time and/or using the developed SSs for model predictive control purposes. Hyperparameter tuning and model order reduction are specifically designed to perform multi-step-ahead predictions. Two real-world case studies consisting of a sulfur recovery unit and a debutanizer column, which are widely used as benchmarks in the SS field, are used to validate the proposed methodology. Data covering multiple system operating points are used for identification. The proposed MSA-HDMDc outperforms currently adopted methods in the SSs domain, such as autoregressive models with exogenous inputs and finite impulse response models, and proves to be robust to the variability of systems operating points.">
+        <tr id="Neural networks are popular data-driven modeling tools that come with high data collection costs. This paper proposes a residual-based multipeaks adaptive sampling (RMAS) algorithm, which can reduce the demand for a large number of samples in the identification of stochastic dynamical systems. Compared to classical residual-based sampling algorithms, the RMAS algorithm achieves higher system identification accuracy without relying on any hyperparameters. Subsequently, combining the RMAS algorithm and neural network, a few-shot identification (FSI) method for stochastic dynamical systems is proposed, which is applied to the identification of a vegetation biomass change model and the Rayleigh-Van der Pol impact vibration model. We show that the RMAS algorithm modifies residual-based sampling algorithms and, in particular, reduces the system identification error by 76% with the same sample sizes. Moreover, the surrogate model accurately predicts the first escape probability density function and the P bifurcation behavior in the systems, with the error of less than 1.59×10-2. Finally, the robustness of the FSI method is validated.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2e0e6ed6f54bb1c9a50518c9d0827eb6b3eeea90" target='_blank'>
-              Soft Sensors for Industrial Processes Using Multi-Step-Ahead Hankel Dynamic Mode Decomposition with Control
+          <td><a href="https://www.semanticscholar.org/paper/295396f31e547b6c81f17b2bb53b2116ac400a8e" target='_blank'>
+              A few-shot identification method for stochastic dynamical systems based on residual multipeaks adaptive sampling.
               </a>
             </td>
           <td>
-            Luca Patané, F. Sapuppo, M. Xibilia
+            Xiao-Kai An, Lin Du, Feng Jiang, Yu-jia Zhang, Zi-Chen Deng, Jürgen Kurths
           </td>
-          <td>2024-08-01</td>
-          <td>Electronics</td>
+          <td>2024-07-01</td>
+          <td>Chaos</td>
           <td>0</td>
-          <td>26</td>
+          <td>7</td>
         </tr>
 
         <tr id="The paper considers the observer synthesis for nonlinear, time-varying plants with uncertain parameters under multiharmonic disturbance. It is assumed that the relative degree of the plant is known, the regressor linearly depends on the state vector and may have a nonlinear relationship with the output signal. The proposed solution consists of three steps. Initially, an unknown input state observer is synthesized. This observer, however, necessitates the measurement of output derivatives equal to the plant's relative degree. To relax this limitation, an alternative representation of the observer is introduced. Further, based on this observer, the unknown parameters and disturbances are reconstructed using an autoregression model and the dynamic regressor extension and mixing (DREM) approach. This approach allows the estimates to be obtained in a finite time. Finally, based on these estimates, an observer has been constructed that does not require measurements of the output derivatives. The effectiveness and efficiency of this solution are demonstrated through a computer simulation.">
@@ -3628,79 +3764,79 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>6</td>
         </tr>
 
-        <tr id="When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series for these nonlinear functionals, by applying nonlinear response theory in a path integral formalism, where the emerging kernels are shown to be expressed in terms of connected equilibrium correlation functions. The first cumulant is the mean force, the second cumulant characterizes the non-equilibrium force fluctuations (noise), and higher order cumulants quantify non-Gaussian fluctuations. We discuss the interpretation of this formalism in relation to Langevin dynamics. We highlight two example scenarios of this formalism: i) For a particle driven with prescribed trajectory, the formalism yields the non-equilibrium statistics of the interaction force with the fluid. ii) For a particle confined in a moving trapping potential, the formalism yields the non-equilibrium statistics of the trapping force. In simulations of a model of nonlinearly interacting Brownian particles, we find that nonlinear phenomena, such as shear-thinning and oscillating noise covariance, appear in third or second order response, respectively.">
+        <tr id="Advances in experimental techniques allow the collection of high-space-and-time resolution data that track individual motile entities over time. This poses the question of how to use these data to efficiently and effectively calibrate motion models. However, typical mathematical models often overlook the inherent aspects of data collection, such as the discreteness and the experimental noise of the measured locations. In this paper, we focus on velocity-jump models suitable to describe single-agent motion in one spatial dimension, characterised by successive Markovian transitions between a finite network of $n$ states, each with a specified velocity and a fixed rate of switching to every other state. Since the problem of finding the exact distributions of discrete-time noisy data is generally intractable, we derive a series of approximations for the data distributions and compare them to in-silico data generated by the models using four example network structures. These comparisons suggest that the approximations are accurate given sufficiently infrequent state switching, or equivalently, a sufficiently high data collection frequency. Moreover, for infrequent switching, the PDFs comparisons highlight the importance of accounting for the correlation between subsequent measured locations, due to the likely permanence in the state visited in the previous measurement. The approximate distributions computed can be used for fast parameter inference and model selection between a range of velocity-jump models using single-agent tracking data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/452a0b698c99157a7fec6246f2787dc73de21682" target='_blank'>
-              Nonlinear Langevin functionals for a driven probe
+          <td><a href="https://www.semanticscholar.org/paper/8f4862ab7ce4151b9c0569c8c9b73d89ab08ca0e" target='_blank'>
+              Approximate solutions of a general stochastic velocity-jump process subject to discrete-time noisy observations
               </a>
             </td>
           <td>
-            Juliana Caspers, Matthias Kruger
+            Arianna Ceccarelli, Alexander P. Browning, Ruth E. Baker
           </td>
-          <td>2024-07-10</td>
+          <td>2024-06-28</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Inverse problems describe the process of estimating the causal factors from a set of measurements or data. Mapping of often incomplete or degraded data to parameters is ill-posed, thus data-driven iterative solutions are required, for example when reconstructing clean images from poor signals. Diffusion models have shown promise as potent generative tools for solving inverse problems due to their superior reconstruction quality and their compatibility with iterative solvers. However, most existing approaches are limited to linear inverse problems represented as Stochastic Differential Equations (SDEs). This simplification falls short of addressing the challenging nature of real-world problems, leading to amplified cumulative errors and biases. We provide an explanation for this gap through the lens of measure-preserving dynamics of Random Dynamical Systems (RDS) with which we analyse Temporal Distribution Discrepancy and thus introduce a theoretical framework based on RDS for SDE diffusion models. We uncover several strategies that inherently enhance the stability and generalizability of diffusion models for inverse problems and introduce a novel score-based diffusion framework, the \textbf{D}ynamics-aware S\textbf{D}E \textbf{D}iffusion \textbf{G}enerative \textbf{M}odel (D$^3$GM). The \textit{Measure-preserving property} can return the degraded measurement to the original state despite complex degradation with the RDS concept of \textit{stability}. Our extensive experimental results corroborate the effectiveness of D$^3$GM across multiple benchmarks including a prominent application for inverse problems, magnetic resonance imaging. Code and data will be publicly available.">
+        <tr id="The chaotic nature of fluid flow and the uncertainties in initial conditions limit predictability. Small errors that occur in the initial condition can grow exponentially until they saturate at $\mathcal{O}$(1). Ensemble forecasting averages multiple runs with slightly different initial conditions and other data to produce more accurate results and extend the predictability horizon. However, they can be computationally expensive. We develop a penalty-based ensemble method with a shared coefficient matrix to reduce required memory and computational cost and thereby allow larger ensemble sizes. Penalty methods relax the incompressibility condition to decouple the pressure and velocity, reducing memory requirements. This report gives stability proof and an error estimate of the penalty-based ensemble method, extends it to the Navier-Stokes equations with random variables using Monte Carlo sampling, and validates the method's accuracy and efficiency with three numerical experiments.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bf17cd0dcbb94d9ebc02ca488860c685bf255511" target='_blank'>
-              Stability and Generalizability in SDE Diffusion Models with Measure-Preserving Dynamics
+          <td><a href="https://www.semanticscholar.org/paper/52cdf874930613b2823b442be8bdfe4e5d17d2e9" target='_blank'>
+              Numerical Analysis of Penalty-based Ensemble Methods
               </a>
             </td>
           <td>
-            Weitong Zhang, Chengqi Zang, Liu Li, Sarah Cechnicka, Ouyang Cheng, Bernhard Kainz
+            Rui Fang
           </td>
-          <td>2024-06-19</td>
+          <td>2024-07-13</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
+          <td>2</td>
+          <td>2</td>
         </tr>
 
-        <tr id="We are interested in the computational study of shock hydrodynamics, i.e. problems involving compressible solids, liquids, and gases that undergo large deformation. These problems are dynamic and nonlinear and can exhibit complex instabilities. Due to advances in high performance computing it is possible to parameterize a hydrodynamic problem and perform a computational study yielding $\mathcal{O}\left({\rm TB}\right)$ of simulation state data. We present an interactive machine learning tool that can be used to compress, browse, and interpolate these large simulation datasets. This tool allows computational scientists and researchers to quickly visualize"what-if"situations, perform sensitivity analyses, and optimize complex hydrodynamic experiments.">
+        <tr id="Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the computation of which typically involves an intractable high-dimensional integral. Among available approximation methods, sampling-based approaches come with strong theoretical guarantees but scale poorly to large problems, while variational approaches scale well but offer few theoretical guarantees. In particular, variational methods are known to produce overconfident estimates of posterior uncertainty and are typically non-identifiable, with many latent variable configurations generating equivalent predictions. Here, we address these challenges by showing how diffusion-based models (DBMs), which have recently produced state-of-the-art performance in generative modeling tasks, can be repurposed for performing calibrated, identifiable Bayesian inference. By exploiting a previously established connection between the stochastic and probability flow ordinary differential equations (pfODEs) underlying DBMs, we derive a class of models, inflationary flows, that uniquely and deterministically map high-dimensional data to a lower-dimensional Gaussian distribution via ODE integration. This map is both invertible and neighborhood-preserving, with controllable numerical error, with the result that uncertainties in the data are correctly propagated to the latent space. We demonstrate how such maps can be learned via standard DBM training using a novel noise schedule and are effective at both preserving and reducing intrinsic data dimensionality. The result is a class of highly expressive generative models, uniquely defined on a low-dimensional latent space, that afford principled Bayesian inference.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7a3d102318eac008b4f999d4fed788b9945f727e" target='_blank'>
-              Machine Learning Visualization Tool for Exploring Parameterized Hydrodynamics
+          <td><a href="https://www.semanticscholar.org/paper/17907a21b0ea22f5a5548076e21700dea63c3931" target='_blank'>
+              Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Models
               </a>
             </td>
           <td>
-            C. Jekel, D. Sterbentz, T. M. Stitt, P. Mocz, R. Rieben, D. A. White, J. Belof
+            Daniela de Albuquerque, John Pearson
           </td>
-          <td>2024-06-20</td>
+          <td>2024-07-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>21</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Beyond estimating parameters of interest from data, one of the key goals of statistical inference is to properly quantify uncertainty in these estimates. In Bayesian inference, this uncertainty is provided by the posterior distribution, the computation of which typically involves an intractable high-dimensional integral. Among available approximation methods, sampling-based approaches come with strong theoretical guarantees but scale poorly to large problems, while variational approaches scale well but offer few theoretical guarantees. In particular, variational methods are known to produce overconfident estimates of posterior uncertainty and are typically non-identifiable, with many latent variable configurations generating equivalent predictions. Here, we address these challenges by showing how diffusion-based models (DBMs), which have recently produced state-of-the-art performance in generative modeling tasks, can be repurposed for performing calibrated, identifiable Bayesian inference. By exploiting a previously established connection between the stochastic and probability flow ordinary differential equations (pfODEs) underlying DBMs, we derive a class of models, inflationary flows, that uniquely and deterministically map high-dimensional data to a lower-dimensional Gaussian distribution via ODE integration. This map is both invertible and neighborhood-preserving, with controllable numerical error, with the result that uncertainties in the data are correctly propagated to the latent space. We demonstrate how such maps can be learned via standard DBM training using a novel noise schedule and are effective at both preserving and reducing intrinsic data dimensionality. The result is a class of highly expressive generative models, uniquely defined on a low-dimensional latent space, that afford principled Bayesian inference.">
+        <tr id="Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally approximate. Recent work on using neural network models to reconstruct the mapping from the data space to the parameters from a set of synthetic parameter-data pairs suffers from the curse of dimensionality, resulting in inaccurate estimation as the data size grows. We propose a dimension-reduced approach to likelihood-free estimation which combines the ideas of reconstruction map estimation with dimension-reduction approaches based on subject-specific knowledge. We examine the properties of reconstruction map estimation with and without dimension reduction and explore the trade-off between approximation error due to information loss from reducing the data dimension and approximation error. Numerical examples show that the proposed approach compares favorably with reconstruction map estimation, approximate Bayesian computation, and synthetic likelihood estimation.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/17907a21b0ea22f5a5548076e21700dea63c3931" target='_blank'>
-              Inflationary Flows: Calibrated Bayesian Inference with Diffusion-Based Models
+          <td><a href="https://www.semanticscholar.org/paper/e928447f6c322a7beac72466a09947bc31240ec4" target='_blank'>
+              Dimension-reduced Reconstruction Map Learning for Parameter Estimation in Likelihood-Free Inference Problems
               </a>
             </td>
           <td>
-            Daniela de Albuquerque, John Pearson
+            Rui Zhang, O. Chkrebtii, Dongbin Xiu
           </td>
-          <td>2024-07-11</td>
+          <td>2024-07-19</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>9</td>
         </tr>
 
-        <tr id="Scenario-based optimization and control has proven to be an efficient approach to account for system uncertainty. In particular, the performance of scenario-based model predictive control (MPC) schemes depends on the accuracy of uncertainty quantification. However, current learning- and scenario-based MPC (sMPC) approaches employ a single timeinvariant probabilistic model (learned offline), which may not accurately describe time-varying uncertainties. Instead, this paper presents a model-agnostic meta-learning (MAML) of Bayesian neural networks (BNN) for adaptive uncertainty quantification that would be subsequently used for adaptive-scenario-tree model predictive control design of nonlinear systems with unknown dynamics to enhance control performance. In particular, the proposed approach learns both a global BNN model and an updating law to refine the BNN model. At each time step, the updating law transforms the global BNN model into more precise local BNN models in real time. The adapted local model is then used to generate scenarios for sMPC design at each time step. A probabilistic safety certificate is incorporated in the scenario generation to ensure that the trajectories of the generated scenarios contain the real trajectory of the system and that all the scenarios adhere to the constraints with a high probability. Experiments using closed-loop simulations of a numerical example demonstrate that the proposed approach can improve the performance of scenario-based MPC compared to using only one BNN model learned offline for all time steps.">
+        <tr id="Several forms for constructing novel physics-informed neural-networks (PINN) for the solution of partial-differential-algebraic equations based on derivative operator splitting are proposed, using the nonlinear Kirchhoff rod as a prototype for demonstration. The open-source DeepXDE is likely the most well documented framework with many examples. Yet, we encountered some pathological problems and proposed novel methods to resolve them. Among these novel methods are the PDE forms, which evolve from the lower-level form with fewer unknown dependent variables to higher-level form with more dependent variables, in addition to those from lower-level forms. Traditionally, the highest-level form, the balance-of-momenta form, is the starting point for (hand) deriving the lowest-level form through a tedious (and error prone) process of successive substitutions. The next step in a finite element method is to discretize the lowest-level form upon forming a weak form and linearization with appropriate interpolation functions, followed by their implementation in a code and testing. The time-consuming tedium in all of these steps could be bypassed by applying the proposed novel PINN directly to the highest-level form. We developed a script based on JAX. While our JAX script did not show the pathological problems of DDE-T (DDE with TensorFlow backend), it is slower than DDE-T. That DDE-T itself being more efficient in higher-level form than in lower-level form makes working directly with higher-level form even more attractive in addition to the advantages mentioned further above. Since coming up with an appropriate learning-rate schedule for a good solution is more art than science, we systematically codified in detail our experience running optimization through a normalization/standardization of the network-training process so readers can reproduce our results.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/473eca6073be70a1728a3138bc7e859f877dc3e3" target='_blank'>
-              Adaptive Uncertainty Quantification for Scenario-based Control Using Meta-learning of Bayesian Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/ea66520b54fdb2078af780a8675f7d6bbe935817" target='_blank'>
+              Partial-differential-algebraic equations of nonlinear dynamics by Physics-Informed Neural-Network: (I) Operator splitting and framework assessment
               </a>
             </td>
           <td>
-            Yajie Bao, Javad Mohammadpour Velni
+            L. Vu-Quoc, A. Humer
           </td>
-          <td>2024-07-19</td>
+          <td>2024-07-13</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>13</td>
+          <td>32</td>
         </tr>
 
         <tr id="Machine Learning (ML) is extensively used for predicting transfer times for general purpose Wide Area Networks (WANs) or public Internet applications, but for Research and Education Networks (RENs) two major gaps exist in literature. First, RENs i.e. networks carrying large data flows have received limited attention by the networking community. RENs behave differently compared to the general purpose Internet applications and other network types. Hence, ML models from other network types cannot be used interchangeably for large data transfers. Second, the ML models are used as blackboxes to train on measured network values and then used to predict transfer times or other runtime network parameters. In this paper, we present a dynamical systems model of the large data transfers typical of RENs in the form of a system of Ordinary Differential Equations (ODEs) inspired by the Lotka-Volterra competition model. We present a transfer time prediction component called Dynamic Transfer Time Predictor (DTTP) which solves the ODEs and predicts the future transfer times. Second we formulate a loss function based on Lyapunov function called Lyapunov Drift Correction (LDC) that self-corrects the transfer time prediction errors dynamically.To design and develop our model, we studied real-world datasets consisting of over 100 million transfer records collected from platforms such as Open Science Grid (OSG), Large Hadron Collider Optical Private Network (LHCOPN), Worldwide LHC Grid (WLCG), as well as the RENs of Internet2 and ESNet. We integrate our model into well-known neural network models and regressors and present evaluation results.">
@@ -3718,19 +3854,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>38</td>
         </tr>
 
-        <tr id="Energy based models (EBMs) are appealing for their generality and simplicity in data likelihood modeling, but have conventionally been difficult to train due to the unstable and time-consuming implicit MCMC sampling during contrastive divergence training. In this paper, we present a novel energy-based generative framework, Variational Potential Flow (VAPO), that entirely dispenses with implicit MCMC sampling and does not rely on complementary latent models or cooperative training. The VAPO framework aims to learn a potential energy function whose gradient (flow) guides the prior samples, so that their density evolution closely follows an approximate data likelihood homotopy. An energy loss function is then formulated to minimize the Kullback-Leibler divergence between density evolution of the flow-driven prior and the data likelihood homotopy. Images can be generated after training the potential energy, by initializing the samples from Gaussian prior and solving the ODE governing the potential flow on a fixed time interval using generic ODE solvers. Experiment results show that the proposed VAPO framework is capable of generating realistic images on various image datasets. In particular, our proposed framework achieves competitive FID scores for unconditional image generation on the CIFAR-10 and CelebA datasets.">
+        <tr id="Scenario-based optimization and control has proven to be an efficient approach to account for system uncertainty. In particular, the performance of scenario-based model predictive control (MPC) schemes depends on the accuracy of uncertainty quantification. However, current learning- and scenario-based MPC (sMPC) approaches employ a single timeinvariant probabilistic model (learned offline), which may not accurately describe time-varying uncertainties. Instead, this paper presents a model-agnostic meta-learning (MAML) of Bayesian neural networks (BNN) for adaptive uncertainty quantification that would be subsequently used for adaptive-scenario-tree model predictive control design of nonlinear systems with unknown dynamics to enhance control performance. In particular, the proposed approach learns both a global BNN model and an updating law to refine the BNN model. At each time step, the updating law transforms the global BNN model into more precise local BNN models in real time. The adapted local model is then used to generate scenarios for sMPC design at each time step. A probabilistic safety certificate is incorporated in the scenario generation to ensure that the trajectories of the generated scenarios contain the real trajectory of the system and that all the scenarios adhere to the constraints with a high probability. Experiments using closed-loop simulations of a numerical example demonstrate that the proposed approach can improve the performance of scenario-based MPC compared to using only one BNN model learned offline for all time steps.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6bc60701775b0cc308c3beaf6e494e8920626217" target='_blank'>
-              Variational Potential Flow: A Novel Probabilistic Framework for Energy-Based Generative Modelling
+          <td><a href="https://www.semanticscholar.org/paper/473eca6073be70a1728a3138bc7e859f877dc3e3" target='_blank'>
+              Adaptive Uncertainty Quantification for Scenario-based Control Using Meta-learning of Bayesian Neural Networks
               </a>
             </td>
           <td>
-            J. Loo, Michelle Adeline, Arghya Pal, Vishnu Monn Baskaran, Chee-Ming Ting, Raphaël C.-W. Phan
+            Yajie Bao, Javad Mohammadpour Velni
           </td>
-          <td>2024-07-21</td>
+          <td>2024-07-19</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>10</td>
+          <td>13</td>
         </tr>
 
         <tr id="The efficient solution (fast and accurate) of parametric partial differential equations (pPDE) is of major interest in many domains of science and engineering, enabling evaluations of the quantities of interest, optimization, control, and uncertainty propagation—all them under stringent real-time constraints. Different methodologies have been proposed in the past within the model order reduction (MOR) community, based on the use of reduced bases (RB) or the separated representation at the heart of the so-called proper generalized decompositions (PGD). In PGD, an alternate-direction strategy is employed to circumvent the integration issues of operating in multi-dimensional domains. Recently, physics informed neural networks (PINNs), a particular collocation schema where the unknown field is approximated by a neural network (NN), have emerged in the domain of scientific machine learning. PNNs combine the versatility of NN-based approximation with the ease of collocating pPDE. The present paper proposes a combination of both procedures to find an efficient solution for pPDE, that can either be viewed as an efficient collocation procedure for PINN, or as a monolithic PGD that bypasses the use of the fixed-point alternated directions.">
@@ -3740,67 +3876,52 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
               </a>
             </td>
           <td>
-            C. Ghnatios, Francisco Chinesta
+            C. Ghnatios, F. Chinesta
           </td>
           <td>2024-07-29</td>
           <td>Mathematics</td>
           <td>0</td>
-          <td>13</td>
+          <td>14</td>
         </tr>
 
-        <tr id="Transformer-based models have demonstrated exceptional performance across diverse domains, becoming the state-of-the-art solution for addressing sequential machine learning problems. Even though we have a general understanding of the fundamental components in the transformer architecture, little is known about how they operate or what are their expected dynamics. Recently, there has been an increasing interest in exploring the relationship between attention mechanisms and Hopfield networks, promising to shed light on the statistical physics of transformer networks. However, to date, the dynamical regimes of transformer-like models have not been studied in depth. In this paper, we address this gap by using methods for the study of asymmetric Hopfield networks in nonequilibrium regimes --namely path integral methods over generating functionals, yielding dynamics governed by concurrent mean-field variables. Assuming 1-bit tokens and weights, we derive analytical approximations for the behavior of large self-attention neural networks coupled to a softmax output, which become exact in the large limit size. Our findings reveal nontrivial dynamical phenomena, including nonequilibrium phase transitions associated with chaotic bifurcations, even for very simple configurations with a few encoded features and a very short context window. Finally, we discuss the potential of our analytic approach to improve our understanding of the inner workings of transformer models, potentially reducing computational training costs and enhancing model interpretability.">
+        <tr id="The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach must consider not only the multivariate dependencies of the desired signal but also the multivariate dependencies of the interfering noise. In our previous research, we introduced a method using machine learning to extract the maximum portion of ``predictable information"from univariate signal. We extend this approach to multivariate signals, with the key idea being to properly incorporate the interdependencies of the noise back into the interdependent reconstruction of the signal. The method works successfully for various multivariate signals, including chaotic signals and highly oscillating sinusoidal signals which are corrupted by spatially correlated intensive noise. It consistently outperforms other existing multivariate denoising methods across a wide range of scenarios.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c2a1c230935b9a3eeb376741764f658296dcdd3b" target='_blank'>
-              Dynamical Mean-Field Theory of Self-Attention Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/53d763f53bd7322558de4eef640fa8ea0e0002cc" target='_blank'>
+              Unsupervised Reservoir Computing for Multivariate Denoising of Severely Contaminated Signals
               </a>
             </td>
           <td>
-            Ángel Poc-López, Miguel Aguilera
+            Jaesung Choi, Pilwon Kim
           </td>
-          <td>2024-06-11</td>
+          <td>2024-07-26</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="In the realm of experimental fluid mechanics, accurately reconstructing high-resolution flow fields is notably challenging due to often sparse and incomplete data across time and space domains. This is exacerbated by the limitations of current experimental tools and methods, which leave critical areas without measurable data. This research suggests a feasible solution to this problem by employing an inverse physics-informed neural network (PINN) to merge available sparse data with physical laws. The method's efficacy is demonstrated using flow around a cylinder as a case study, with three distinct training sets. One was the sparse velocity data from a domain, and the other two datasets were limited velocity data obtained from the domain boundaries and sensors around the cylinder wall. The coefficient of determination (R2) coefficient and mean squared error (RMSE) metrics, indicative of model performance, have been determined for the velocity components of all models. For the 28 sensors model, the R2 value stands at 0.996 with an associated RMSE of 0.0251 for the u component, while for the v component, the R2 value registers at 0.969, accompanied by an RMSE of 0.0169. The outcomes indicate that the method can successfully recreate the actual velocity field with considerable precision with more than 28 sensors around the cylinder, highlighting PINN's potential as an effective data assimilation technique for experimental fluid mechanics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/10c366d3620b0cb9b8ea13515c105a9559a32ae2" target='_blank'>
-              Flow field reconstruction from sparse sensor measurements with physics-informed neural networks
-              </a>
-            </td>
-          <td>
-            Mohammad Yasin Hosseini, Yousef Shiri
-          </td>
-          <td>2024-07-01</td>
-          <td>Physics of Fluids</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-
-        <tr id="Many industrial processes can be described by distributed parameter systems (DPSs) governed by partial differential equations (PDEs). In this research, a spatiotemporal network is proposed for DPS modeling without any process knowledge. Since traditional linear modeling methods may not work well for nonlinear DPSs, the proposed method considers the nonlinear space-time separation, which is transformed into a Lagrange dual optimization problem under the orthogonal constraint. The optimization problem can be solved by the proposed neural network with good structural interpretability. The spatial construction method is employed to derive the continuous spatial basis functions (SBFs) based on the discrete spatial features. The nonlinear temporal model is derived by the Gaussian process regression (GPR). Benefiting from spatial construction and GPR, the proposed method enables spatially continuous modeling and provides a reliable output range under the given confidence level. Experiments on a catalytic reaction process and a battery thermal process demonstrate the effectiveness and superiority of the proposed method.">
+        <tr id="This paper establishes a method for solving partial differential equations using a multi-step physics-informed deep operator neural network. The network is trained by embedding physics-informed constraints. Different from traditional neural networks for solving partial differential equations, the proposed method uses a deep neural operator network to indirectly construct the mapping relationship between the variable functions and solution functions. This approach makes full use of the hidden information between the variable functions and independent variables. The process whereby the model captures incredibly complex and highly nonlinear relationships is simplified, thereby making network learning easier and enhancing the extraction of information about the independent variables in partial differential systems. In terms of solving partial differential equations, we verify that the multi-step physics-informed deep operator neural network markedly improves the solution accuracy compared with a traditional physics-informed deep neural operator network, especially when the problem involves complex physical phenomena with large gradient changes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6bcfa839d7defe2cde7d0acf69e5a592bdf81de3" target='_blank'>
-              Spatiotemporal Transformation-Based Neural Network With Interpretable Structure for Modeling Distributed Parameter Systems.
+          <td><a href="https://www.semanticscholar.org/paper/ac5d801ec2ae339a109eb310769fe243cbff7025" target='_blank'>
+              Multi-Step Physics-Informed Deep Operator Neural Network for Directly Solving Partial Differential Equations
               </a>
             </td>
           <td>
-            Peng Wei, Han-Xiong Li
+            Jing Wang, Yubo Li, Anping Wu, Zheng Chen, Jun Huang, Qingfeng Wang, Feng Liu
           </td>
-          <td>2024-07-25</td>
-          <td>IEEE transactions on neural networks and learning systems</td>
+          <td>2024-06-25</td>
+          <td>Applied Sciences</td>
           <td>0</td>
-          <td>22</td>
+          <td>6</td>
         </tr>
 
-        <tr id="In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and engineering applications. The computational challenges we address with the proposed methodology are: (i) the need for repeated evaluations of expensive forward models; (ii) the potential existence of multiple modes; and (iii) the fact that gradient of, or adjoint solver for, the forward model might not be feasible. While existing Bayesian inference methods meet some of these challenges individually, we propose a framework that tackles all three systematically. Our approach builds upon the Fisher-Rao gradient flow in probability space, yielding a dynamical system for probability densities that converges towards the target distribution at a uniform exponential rate. This rapid convergence is advantageous for the computational burden outlined in (i). We apply Gaussian mixture approximations with operator splitting techniques to simulate the flow numerically; the resulting approximation can capture multiple modes thus addressing (ii). Furthermore, we employ the Kalman methodology to facilitate a derivative-free update of these Gaussian components and their respective weights, addressing the issue in (iii). The proposed methodology results in an efficient derivative-free sampler flexible enough to handle multi-modal distributions: Gaussian Mixture Kalman Inversion (GMKI). The effectiveness of GMKI is demonstrated both theoretically and numerically in several experiments with multimodal target distributions, including proof-of-concept and two-dimensional examples, as well as a large-scale application: recovering the Navier-Stokes initial condition from solution data at positive times.">
+        <tr id="Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models targeting the properties of matter at the atomic scale. Both established and state-of-the-art approaches, with almost no exceptions, are built to be exactly equivariant to translations, permutations, and rotations of the atoms. Incorporating symmetries -- rotations in particular -- constrains the model design space and implies more complicated architectures that are often also computationally demanding. There are indications that non-symmetric models can easily learn symmetries from data, and that doing so can even be beneficial for the accuracy of the model. We put a model that obeys rotational invariance only approximately to the test, in realistic scenarios involving simulations of gas-phase, liquid, and solid water. We focus specifically on physical observables that are likely to be affected -- directly or indirectly -- by symmetry breaking, finding negligible consequences when the model is used in an interpolative, bulk, regime. Even for extrapolative gas-phase predictions, the model remains very stable, even though symmetry artifacts are noticeable. We also discuss strategies that can be used to systematically reduce the magnitude of symmetry breaking when it occurs, and assess their impact on the convergence of observables.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0d77575c529cb455ba8ac5289fe0e14615a7c4f1" target='_blank'>
-              Efficient, Multimodal, and Derivative-Free Bayesian Inference With Fisher-Rao Gradient Flows
+          <td><a href="https://www.semanticscholar.org/paper/5dc964683c6ce6be616e96982ba7cf5172752d68" target='_blank'>
+              Probing the effects of broken symmetries in machine learning
               </a>
             </td>
           <td>
-            Yifan Chen, Daniel Zhengyu Huang, Jiaoyang Huang, Sebastian Reich, Andrew M. Stuart
+            Marcel F. Langer, S. Pozdnyakov, Michele Ceriotti
           </td>
           <td>2024-06-25</td>
           <td>ArXiv</td>
@@ -3808,139 +3929,109 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>9</td>
         </tr>
 
-        <tr id="We construct time-evolving gravitational potential models for a Milky Way-mass galaxy from the FIRE-2 suite of cosmological-baryonic simulations using basis function expansions. These models capture the angular variation with spherical harmonics for the halo and azimuthal harmonics for the disk, and the radial or meridional plane variation with splines. We fit low-order expansions (4 angular/harmonic terms) to the galaxy's potential for each snapshot, spaced roughly 25 Myr apart, over the last 4 Gyr of its evolution, then extract the forces at discrete times and interpolate them between adjacent snapshots for forward orbit integration. Our method reconstructs the forces felt by simulation particles with high fidelity, with 95% of both stars and dark matter, outside of self-gravitating subhalos, exhibiting errors $\leq4\%$ in both the disk and the halo. Imposing symmetry on the model systematically increases these errors, particularly for disk particles, which show greater sensitivity to imposed symmetries. The majority of orbits recovered using the models exhibit positional errors $\leq10\%$ for 2-3 orbital periods, with higher errors for orbits that spend more time near the galactic center. Approximate integrals of motion are retrieved with high accuracy even with a larger potential sampling interval of 200 Myr. After 4 Gyr of integration, 43% and 70% of orbits have total energy and angular momentum errors within 10%, respectively. Consequently, there is higher reliability in orbital shape parameters such as pericenters and apocenters, with errors $\sim10\%$ even after multiple orbital periods. These techniques have diverse applications, including studying satellite disruption in cosmological contexts.">
+        <tr id="Physics‐Informed Neural Networks (PINNs) have solved numerous mechanics problems by training to minimize the loss functions of governing partial differential equations (PDEs). Despite successful development of PINNs in various systems, computational efficiency and fidelity prediction have remained profound challenges. To fill such gaps, this study proposed a Physics‐Informed Neural Operator Solver (PINOS) to achieve accurate and fast simulations without any required data set. The training of PINOS adopts a weak form based on the principle of least work for static simulations and a storng form for dynamic systems in solid mechanics. Results from numerical examples indicated that PINOS is capable of approximating solutions notably faster than the benchmarks of PINNs in both static an dynamic systems. The comparisons also showed that PINOS reached a convergence speed of over 20 times faster than finite element software in two‐dimensional and three‐dimensional static problems. Furthermore, this study examined the zero‐shot super‐resolution capability by developing Super‐Resolution PINOS (SR‐PINOS) that was trained on a coarse mesh and validated on fine mesh. The numerical results demonstrate the great performance of the model to obtain accurate solutions with a speed up, suggesting effectiveness in increasing sampling points and scaling a simulation. This study also discusses the differentiation methods of PINOS and SR‐PINOS and suggests potential implementations related to forward applications for promising machine learning methods for structural designs and optimization.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/de24194c7be3b3d4cbdf06cc58d5aad48f9bf27a" target='_blank'>
-              Efficient and accurate force replay in cosmological-baryonic simulations
+          <td><a href="https://www.semanticscholar.org/paper/bebd3feaac10c5ad88eafaf917f41d32f2aa051e" target='_blank'>
+              Physics‐informed neural operator solver and super‐resolution for solid mechanics
               </a>
             </td>
           <td>
-            Arpit Arora, Robyn E. Sanderson, Christopher Regan, N. Garavito-Camargo, Emily Bregou, N. Panithanpaisal, Andrew Wetzel, E. Cunningham, S. Loebman, A. Dropulic, Nora Shipp
+            Chawit Kaewnuratchadasorn, Jiaji Wang, Chul‐Woo Kim
           </td>
-          <td>2024-07-17</td>
-          <td>ArXiv</td>
+          <td>2024-07-11</td>
+          <td>Computer-Aided Civil and Infrastructure Engineering</td>
           <td>0</td>
-          <td>22</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models targeting the properties of matter at the atomic scale. Both established and state-of-the-art approaches, with almost no exceptions, are built to be exactly equivariant to translations, permutations, and rotations of the atoms. Incorporating symmetries -- rotations in particular -- constrains the model design space and implies more complicated architectures that are often also computationally demanding. There are indications that non-symmetric models can easily learn symmetries from data, and that doing so can even be beneficial for the accuracy of the model. We put a model that obeys rotational invariance only approximately to the test, in realistic scenarios involving simulations of gas-phase, liquid, and solid water. We focus specifically on physical observables that are likely to be affected -- directly or indirectly -- by symmetry breaking, finding negligible consequences when the model is used in an interpolative, bulk, regime. Even for extrapolative gas-phase predictions, the model remains very stable, even though symmetry artifacts are noticeable. We also discuss strategies that can be used to systematically reduce the magnitude of symmetry breaking when it occurs, and assess their impact on the convergence of observables.">
+        <tr id="Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we improve the convergence of the loss during training in most practical scenarios. This work analyzes the computational cost of the resulting hybrid Least-Squares/Gradient-Descent optimizer and explains how to implement it efficiently. In particular, we show that a traditional implementation based on backward-mode automatic differentiation leads to a prohibitively expensive algorithm. To remedy this, we propose using either forward-mode automatic differentiation or an ultraweak-type scheme that avoids the differentiation of trial functions in the discrete weak formulation. The proposed alternatives are up to 100 times faster than the traditional one, recovering a computational cost-per-iteration similar to that of a conventional gradient-descent-based optimizer alone. To support our analysis, we derive computational estimates and conduct numerical experiments in one- and two-dimensional problems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5dc964683c6ce6be616e96982ba7cf5172752d68" target='_blank'>
-              Probing the effects of broken symmetries in machine learning
+          <td><a href="https://www.semanticscholar.org/paper/17eda77a3cdea99de9f795c5bb3e5312a9f5c667" target='_blank'>
+              Optimizing Variational Physics-Informed Neural Networks Using Least Squares
               </a>
             </td>
           <td>
-            Marcel F. Langer, S. Pozdnyakov, Michele Ceriotti
+            C. Uriarte, Manuela Bastidas, David Pardo, Jamie M. Taylor, Sergio Rojas
           </td>
-          <td>2024-06-25</td>
+          <td>2024-07-29</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>9</td>
+          <td>3</td>
         </tr>
 
-        <tr id="In this work, we propose a set of physics-informed geometric operators (GOs) to enrich the geometric data provided for training surrogate/discriminative models, dimension reduction, and generative models, typically employed for performance prediction, dimension reduction, and creating data-driven parameterisations, respectively. However, as both the input and output streams of these models consist of low-level shape representations, they often fail to capture shape characteristics essential for performance analyses. Therefore, the proposed GOs exploit the differential and integral properties of shapes--accessed through Fourier descriptors, curvature integrals, geometric moments, and their invariants--to infuse high-level intrinsic geometric information and physics into the feature vector used for training, even when employing simple model architectures or low-level parametric descriptions. We showed that for surrogate modelling, along with the inclusion of the notion of physics, GOs enact regularisation to reduce over-fitting and enhance generalisation to new, unseen designs. Furthermore, through extensive experimentation, we demonstrate that for dimension reduction and generative models, incorporating the proposed GOs enriches the training data with compact global and local geometric features. This significantly enhances the quality of the resulting latent space, thereby facilitating the generation of valid and diverse designs. Lastly, we also show that GOs can enable learning parametric sensitivities to a great extent. Consequently, these enhancements accelerate the convergence rate of shape optimisers towards optimal solutions.">
+        <tr id="Time-varying optimization problems are central to many engineering applications, where performance metrics and system constraints evolve dynamically with time. A number of algorithms have been proposed in recent years to solve such problems; a common feature of all these methods is that they implicitly require precise knowledge of the temporal variability of the solutions in order to exactly track the optimizers. In this paper, we seek to lift these stringent assumptions. Our main result is a fundamental characterization, showing that an algorithm can track an optimal trajectory if and only if it contains a model of the temporal variability of the problem. We refer to this concept to as the internal model principle of time-varying optimization. By recasting the optimization objective as a nonlinear regulation problem and using tools from center manifold theory, we provide necessary and sufficient conditions both for an optimization algorithm to achieve exact asymptotic tracking and for such an algorithm to exist. We illustrate the applicability of the approach numerically on both synthetic problems as well as practical problems in transportation.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e89b2b8bdad2c98d764f8c828e40b1065ff7464d" target='_blank'>
-              Physics-Informed Geometric Operators to Support Surrogate, Dimension Reduction and Generative Models for Engineering Design
+          <td><a href="https://www.semanticscholar.org/paper/8aee1c4d1d9bfe7e68a03ee2eb770d81f18d112d" target='_blank'>
+              The Internal Model Principle of Time-Varying Optimization
               </a>
             </td>
           <td>
-            Shahroz Khan, Zahid Masood, Muhammad Usama, Konstantinos V. Kostas, P. Kaklis, Wei Chen
+            G. Bianchin, Bryan Van Scoy
           </td>
           <td>2024-07-10</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>21</td>
+          <td>11</td>
         </tr>
 
-        <tr id="We discuss an approach to mathematically modelling systems made of objects that are coupled together, using generative models of the dependence relationships between states (or trajectories) of the things comprising such systems. This broad class includes open or non-equilibrium systems and is especially relevant to self-organising systems. The ensuing variational free energy principle (FEP) has certain advantages over using random dynamical systems explicitly, notably, by being more tractable and offering a parsimonious explanation of why the joint system evolves in the way that it does, based on the properties of the coupling between system components. Using the FEP allows us to model the dynamics of an object as if it were a process of variational inference, because variational free energy (or surprisal) is a Lyapunov function for its dynamics. In short, we argue that using generative models to represent and track relations among subsystems leads us to a particular statistical theory of interacting systems. Conversely, this theory enables us to construct nested models that respect the known relations among subsystems. We point out that the fact that a physical object conforms to the FEP does not necessarily imply that this object performs inference in the literal sense; rather, it is a useful explanatory fiction which replaces the 'explicit' dynamics of the object with an 'implicit' flow on free energy gradients - a fiction that may or may not be entertained by the object itself.">
+        <tr id="Modeling atmospheric chemistry is complex and computationally intense. Given the recent success of Deep neural networks in digital signal processing, we propose a Neural Network Emulator for fast chemical concentration modeling. We consider atmospheric chemistry as a time-dependent Ordinary Differential Equation. To extract the hidden correlations between initial states and future time evolution, we propose ChemNNE, an Attention based Neural Network Emulator (NNE) that can model the atmospheric chemistry as a neural ODE process. To efficiently simulate the chemical changes, we propose the sinusoidal time embedding to estimate the oscillating tendency over time. More importantly, we use the Fourier neural operator to model the ODE process for efficient computation. We also propose three physical-informed losses to supervise the training optimization. To evaluate our model, we propose a large-scale chemical dataset that can be used for neural network training and evaluation. The extensive experiments show that our approach achieves state-of-the-art performance in modeling accuracy and computational speed.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7d9000095cab2d2187f9dc3eb5aeba6fe5752a46" target='_blank'>
-              An approach to non-equilibrium statistical physics using variational Bayesian inference
+          <td><a href="https://www.semanticscholar.org/paper/803f6e09980225170873259886d0fd771d2085f8" target='_blank'>
+              Neural Network Emulator for Atmospheric Chemical ODE
               </a>
             </td>
           <td>
-            M. Ramstead, D. A. R. Sakthivadivel, K. Friston
+            Zhi-Song Liu, Petri S. Clusius, Michael Boy
           </td>
-          <td>2024-06-17</td>
+          <td>2024-08-03</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>23</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we improve the convergence of the loss during training in most practical scenarios. This work analyzes the computational cost of the resulting hybrid Least-Squares/Gradient-Descent optimizer and explains how to implement it efficiently. In particular, we show that a traditional implementation based on backward-mode automatic differentiation leads to a prohibitively expensive algorithm. To remedy this, we propose using either forward-mode automatic differentiation or an ultraweak-type scheme that avoids the differentiation of trial functions in the discrete weak formulation. The proposed alternatives are up to 100 times faster than the traditional one, recovering a computational cost-per-iteration similar to that of a conventional gradient-descent-based optimizer alone. To support our analysis, we derive computational estimates and conduct numerical experiments in one- and two-dimensional problems.">
+        <tr id="In this work, we discuss the use of a recently introduced machine learning (ML) technique known as Fourier neural operators (FNO) as an efficient alternative to the traditional solution of the time-dependent Schrödinger equation (TDSE). FNOs are ML models which are employed in the approximated solution of partial differential equations. For a wavepacket propagating in an anharmonic potential and for a tunneling system, we show that the FNO approach can accurately and faithfully model wavepacket propagation via the density. Additionally, we demonstrate that FNOs can be a suitable replacement for traditional TDSE solvers in cases where the results of the quantum dynamical simulation are required repeatedly such as in the case of parameter optimization problems (e.g., control). The speed-up from the FNO method allows for its combination with the Markov-chain Monte Carlo approach in applications that involve solving inverse problems such as optimal and coherent laser control of the outcome of dynamical processes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/17eda77a3cdea99de9f795c5bb3e5312a9f5c667" target='_blank'>
-              Optimizing Variational Physics-Informed Neural Networks Using Least Squares
+          <td><a href="https://www.semanticscholar.org/paper/e9adc38ac192d36f40f2d38abb968ebc1c04c08b" target='_blank'>
+              Accelerating wavepacket propagation with machine learning.
               </a>
             </td>
           <td>
-            C. Uriarte, Manuela Bastidas, David Pardo, Jamie M. Taylor, Sergio Rojas
+            Kanishka Singh, Ka Hei Lee, Daniel Peláez, A. Bande
           </td>
-          <td>2024-07-29</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
-        </tr>
-
-        <tr id="Time-delay fractional optimal control problems (OCPs) are an important research area for developing effective control and optimization strategies to address complex phenomena occurring in various natural sciences, such as physics, chemistry, biology, and engineering. By considering fractional OCPs with time delays, we can design control strategies that take into account the system's history and optimize its behavior over a given time horizon. However, applying the Pontryagin principle of maximization to solve these problems leads to a boundary value problem (BVP) that includes delay and advance terms, making analytical solutions difficult and demanding. To address this issue, this paper presents a precise finite difference formula to solve the aforementioned advance-delay BVP numerically. The suggested approximate method's error analysis and convergence properties are provided, and several illustrative examples demonstrate the applicability, validity, and accuracy of the proposed approach. Simulation results confirm the proposed technique's advantages for the optimal control of delay fractional dynamical equations.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a596cb9b8d036a751e9996eea24f4510663c8a7c" target='_blank'>
-              An accurate finite difference formula for the numerical solution of delay-dependent fractional optimal control problems
-              </a>
-            </td>
-          <td>
-            D. Băleanu, M. Hajipour, A. Jajarmi
-          </td>
-          <td>2024-07-12</td>
-          <td>An International Journal of Optimization and Control: Theories &amp; Applications (IJOCTA)</td>
-          <td>0</td>
-          <td>40</td>
-        </tr>
-
-        <tr id="Time-varying optimization problems are central to many engineering applications, where performance metrics and system constraints evolve dynamically with time. A number of algorithms have been proposed in recent years to solve such problems; a common feature of all these methods is that they implicitly require precise knowledge of the temporal variability of the solutions in order to exactly track the optimizers. In this paper, we seek to lift these stringent assumptions. Our main result is a fundamental characterization, showing that an algorithm can track an optimal trajectory if and only if it contains a model of the temporal variability of the problem. We refer to this concept to as the internal model principle of time-varying optimization. By recasting the optimization objective as a nonlinear regulation problem and using tools from center manifold theory, we provide necessary and sufficient conditions both for an optimization algorithm to achieve exact asymptotic tracking and for such an algorithm to exist. We illustrate the applicability of the approach numerically on both synthetic problems as well as practical problems in transportation.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8aee1c4d1d9bfe7e68a03ee2eb770d81f18d112d" target='_blank'>
-              The Internal Model Principle of Time-Varying Optimization
-              </a>
-            </td>
-          <td>
-            G. Bianchin, Bryan Van Scoy
-          </td>
-          <td>2024-07-10</td>
-          <td>ArXiv</td>
+          <td>2024-06-21</td>
+          <td>Journal of computational chemistry</td>
           <td>0</td>
-          <td>11</td>
+          <td>12</td>
         </tr>
 
-        <tr id="We introduce COBRA (Cosmology with Optimally factorized Bases of Radial Approximants), a novel framework for rapid computation of large-scale structure observables. COBRA separates scale dependence from cosmological parameters in the linear matter power spectrum while also minimising the number of necessary basis terms $N_b$, thus enabling direct and efficient computation of derived and nonlinear observables. Moreover, the dependence on cosmological parameters is efficiently approximated using radial basis function interpolation. We apply our framework to decompose the linear matter power spectrum in the standard $\Lambda$CDM scenario, as well as by adding curvature, dynamical dark energy and massive neutrinos, covering all redshifts relevant for Stage IV surveys. With only a dozen basis terms $N_b$, COBRA reproduces exact Boltzmann solver calculations to $\sim 0.1\%$ precision, which improves further to $0.02\%$ in the pure $\Lambda$CDM scenario. Using our decomposition, we recast the one-loop redshift space galaxy power spectrum in a separable minimal-basis form, enabling $\sim 4000$ model evaluations per second at $0.02\%$ precision on a single thread. This constitutes a considerable improvement over previously existing methods (e.g., FFTLog) opening a window for efficient computations of higher loop and higher order correlators involving multiple powers of the linear matter power spectra. The resulting factorisation can also be utilised in clustering, weak lensing and CMB analyses. Our implementation will be made public upon publication.">
+        <tr id="Inverse stochastic resonance (ISR) is a phenomenon where noise reduces rather than increases the firing rate of a neuron, sometimes leading to complete quiescence. ISR was first experimentally verified with cerebellar Purkinje neurons. These experiments showed that ISR enables optimal information transfer between the input and output spike train of neurons. Subsequent studies demonstrated the efficiency of information processing and transfer in neural networks with small-world topology. We conducted a numerical investigation into the impact of adaptivity on ISR in a small-world network of noisy FitzHugh-Nagumo (FHN) neurons, operating in a bistable regime with a stable fixed point and a limit cycle -- a prerequisite for ISR. Our results show that the degree of ISR is highly dependent on the FHN model's timescale separation parameter $\epsilon$. The network structure undergoes dynamic adaptation via mechanisms of either spike-time-dependent plasticity (STDP) with potentiation-/depression-domination parameter $P$, or homeostatic structural plasticity (HSP) with rewiring frequency $F$. We demonstrate that both STDP and HSP amplify ISR when $\epsilon$ lies within the bistability region of FHN neurons. Specifically, at larger values of $\epsilon$ within the bistability regime, higher rewiring frequencies $F$ enhance ISR at intermediate (weak) synaptic noise intensities, while values of $P$ consistent with depression-domination (potentiation-domination) enhance (deteriorate) ISR. Moreover, although STDP and HSP parameters may jointly enhance ISR, $P$ has a greater impact on ISR compared to $F$. Our findings inform future ISR enhancement strategies in noisy artificial neural circuits, aiming to optimize information transfer between input and output spike trains in neuromorphic systems, and prompt venues for experiments in neural networks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b3dbca5211f988f8e52a21fdea5bf0a183d346ba" target='_blank'>
-              COBRA: Optimal Factorization of Cosmological Observables
+          <td><a href="https://www.semanticscholar.org/paper/d7c658287ef239a4055ba2bf2436639fd02518af" target='_blank'>
+              Inverse stochastic resonance in adaptive small-world neural networks
               </a>
             </td>
           <td>
-            Thomas Bakx, N. E. Chisari, Z. Vlah
+            Marius E. Yamakou, Jinjie Zhu, Erik A. Martens
           </td>
-          <td>2024-07-05</td>
+          <td>2024-07-03</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>25</td>
+          <td>1</td>
+          <td>9</td>
         </tr>
 
-        <tr id="It has recently been realized that many theories of physics beyond the Standard Model give rise to cosmological histories exhibiting extended epochs of cosmological stasis. During such epochs, the abundances of different energy components such as matter, radiation, and vacuum energy each remain fixed despite cosmological expansion. In previous analyses of the stasis phenomenon, these different energy components were modeled as fluids with fixed, unchanging equations of state. In this paper, by contrast, we consider more realistic systems involving dynamical scalars which pass through underdamping transitions as the universe expands. Indeed, such systems might be highly relevant for BSM scenarios involving higher-dimensional bulk moduli and inflatons. Remarkably, we find that stasis emerges even in such situations, despite the appearance of time-varying equations of state. Moreover, this stasis includes several new features which might have important phenomenological implications and applications. For example, in the presence of an additional"background"energy component, we find that the scalars evolve into a"tracking"stasis in which the stasis equation of state automatically tracks that of the background. This phenomenon exists even if the background has only a small initial abundance. We also discuss the intriguing possibility that our results might form the basis of a new"Stasis Inflation"scenario in which no ad-hoc inflaton potential is needed and in which there is no graceful-exit problem. Within such a scenario, the number of e-folds of cosmological expansion produced is directly related to the hierarchies between physical BSM mass scales. Moreover, non-zero matter and radiation abundances can be sustained throughout the inflationary epoch.">
+        <tr id="Transformations are a key tool in the qualitative study of dynamical systems: transformations to a normal form, for example, underpin the study of instabilities and bifurcations. In this work, we test, and when possible establish, an equivalence between two different artificial neural networks by attempting to construct a data-driven transformation between them, using diffusion maps with a Mahalanobis-like metric. If the construction succeeds, the two networks can be thought of as belonging to the same equivalence class. We first discuss transformation functions between only the outputs of the two networks; we then also consider transformations that take into account outputs (activations) of a number of internal neurons from each network. Whitney's theorem dictates the number of (generic) measurements from one of the networks required to reconstruct each and every feature of the second network. The construction of the transformation function relies on a consistent, intrinsic representation of the network input space. We illustrate our algorithm by matching neural network pairs trained to learn (a) observations of scalar functions, (b) observations of two-dimensional vector fields, and (c) representations of images of a moving three-dimensional object (a rotating horse). We also demonstrate reconstruction of a network's input (and output) from minimal partial observations of intermediate neuron activations. The construction of equivalences across different network instantiations clearly relates to transfer learning and will also be valuable in establishing equivalence between different machine learning-based tools.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d2fb6599d1f8077e14afa3e54fb4855ccc7ef62c" target='_blank'>
-              Cosmological Stasis from Dynamical Scalars: Tracking Solutions and the Possibility of a Stasis-Induced Inflation
+          <td><a href="https://www.semanticscholar.org/paper/e0effe6704619a849e7613b7f6a123884ce613df" target='_blank'>
+              Transformations establishing equivalence across neural networks: When have two networks learned the same task?
               </a>
             </td>
           <td>
-            K. Dienes, L. Heurtier, Fei Huang, T. Tait, B. Thomas
+            Tom S. Bertalan, Felix Dietrich, I. Kevrekidis
           </td>
-          <td>2024-06-10</td>
-          <td>ArXiv</td>
+          <td>2024-07-01</td>
+          <td>Chaos</td>
           <td>0</td>
-          <td>37</td>
+          <td>15</td>
         </tr>
 
         <tr id="Areas of computational mechanics such as uncertainty quantification and optimization usually involve repeated evaluation of numerical models that represent the behavior of engineering systems. In the case of complex nonlinear systems however, these models tend to be expensive to evaluate, making surrogate models quite valuable. Artificial neural networks approximate systems very well by taking advantage of the inherent information of its given training data. In this context, this paper investigates the improvement of the training process by including sensitivity information, which are partial derivatives w.r.t. inputs, as outlined by Sobolev training. In computational mechanics, sensitivities can be applied to neural networks by expanding the training loss function with additional loss terms, thereby improving training convergence resulting in lower generalisation error. This improvement is shown in two examples of linear and non-linear material behavior. More specifically, the Sobolev designed loss function is expanded with residual weights adjusting the effect of each loss on the training step. Residual weighting is the given scaling to the different training data, which in this case are response and sensitivities. These residual weights are optimized by an adaptive scheme, whereby varying objective functions are explored, with some showing improvements in accuracy and precision of the general training convergence.">
@@ -3955,52 +4046,22 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>2024-07-23</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>23</td>
-        </tr>
-
-        <tr id="The brain needs to perform time-critical computations to ensure survival. A potential solution lies in the non-local, distributed computation at the whole-brain level made possible by criticality and amplified by the rare long-range connections found in the brain’s unique anatomical structure. This non-locality can be captured by the mathematical structure of Schrödinger’s wave equation, which is at the heart of the novel CHARM (Complex Harmonics decomposition) framework that performs the necessary dimensional manifold reduction able to extract non-locality in critical spacetime brain dynamics. Using a large neuroimaging dataset of over 1,000 people, CHARM captured the critical, non-local/long-range nature of brain dynamics and the underlying mechanisms were established using a precise whole-brain model. Equally, CHARM revealed the significantly different critical dynamics of wakefulness and sleep. Overall, CHARM is a promising theoretical framework for capturing the low-dimensionality of the complex network dynamics observed in neuroscience and provides evidence that networks of brain regions rather than individual brain regions are the key computational engines of critical brain dynamics.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/79c92bde562ae0356acda295ead7128e8c11928b" target='_blank'>
-              Complex harmonics reveal low-dimensional manifolds of critical brain dynamics
-              </a>
-            </td>
-          <td>
-            G. Deco, Y. Perl, M. Kringelbach
-          </td>
-          <td>2024-06-16</td>
-          <td>bioRxiv</td>
-          <td>0</td>
-          <td>13</td>
-        </tr>
-
-        <tr id="A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced with theoretical ground, algorithm design and experimental validation. This method simulates an interacting particle system (IPS) where particles, i.e. the freely-moving negative charges and spatially-fixed positive charges with magnitudes proportional to the target distribution, interact with each other via attraction and repulsion induced by the resulting electric fields described by Poisson's equation. The IPS evolves towards a steady-state where the distribution of negative charges conforms to the target distribution. This physics-inspired method offers deterministic, gradient-free sampling and inference, achieving comparable performance as other particle-based and MCMC methods in benchmark tasks of inferring complex densities, Bayesian logistic regression and dynamical system identification. A discrete-time, discrete-space algorithmic design, readily extendable to continuous time and space, is provided for usage in more general inference problems occurring in probabilistic machine learning scenarios such as Bayesian inference, generative modelling, and beyond.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f084ff68562acff79ea7b538f61a3d7bacd36009" target='_blank'>
-              Electrostatics-based particle sampling and approximate inference
-              </a>
-            </td>
-          <td>
-            Yongchao Huang
-          </td>
-          <td>2024-06-28</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>0</td>
+          <td>24</td>
         </tr>
 
-        <tr id="In this work, we first show that the problem of parameter identification is often ill-conditioned and lacks the persistence of excitation required for the convergence of online learning schemes. To tackle these challenges, we introduce the notion of optimal and greedy excitation sets which contain data points with sufficient richness to aid in the identification task. We then present the greedy excitation set-based recursive least squares algorithm to alleviate the problem of the lack of persistent excitation, and prove that the iterates generated by the proposed algorithm minimize an auxiliary weighted least squares cost function. When data points are generated from time-varying parameters, online estimators tend to underfit the true parameter trajectory, and their predictability deteriorates. To tackle this problem, we propose a memory resetting scheme leveraging change point detection techniques. Finally, we illustrate the performance of the proposed algorithms via several numerical case studies to learn the (time-varying) parameters of networked epidemic dynamics, and compare it with results obtained using conventional approaches.">
+        <tr id="Skilful Machine Learned weather forecasts have challenged our approach to numerical weather prediction, demonstrating competitive performance compared to traditional physics-based approaches. Data-driven systems have been trained to forecast future weather by learning from long historical records of past weather such as the ECMWF ERA5. These datasets have been made freely available to the wider research community, including the commercial sector, which has been a major factor in the rapid rise of ML forecast systems and the levels of accuracy they have achieved. However, historical reanalyses used for training and real-time analyses used for initial conditions are produced by data assimilation, an optimal blending of observations with a physics-based forecast model. As such, many ML forecast systems have an implicit and unquantified dependence on the physics-based models they seek to challenge. Here we propose a new approach, training a neural network to predict future weather purely from historical observations with no dependence on reanalyses. We use raw observations to initialise a model of the atmosphere (in observation space) learned directly from the observations themselves. Forecasts of crucial weather parameters (such as surface temperature and wind) are obtained by predicting weather parameter observations (e.g. SYNOP surface data) at future times and arbitrary locations. We present preliminary results on forecasting observations 12-hours into the future. These already demonstrate successful learning of time evolutions of the physical processes captured in real observations. We argue that this new approach, by staying purely in observation space, avoids many of the challenges of traditional data assimilation, can exploit a wider range of observations and is readily expanded to simultaneous forecasting of the full Earth system (atmosphere, land, ocean and composition).">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f77ed1877cc1126478cecdbf4ca3316c240db17e" target='_blank'>
-              Online Identification of Time-Varying Systems Using Excitation Sets and Change Point Detection
+          <td><a href="https://www.semanticscholar.org/paper/f12110407568e11614a4bec8a9d4a303c2c72458" target='_blank'>
+              Data driven weather forecasts trained and initialised directly from observations
               </a>
             </td>
           <td>
-            Chi Ho Leung, Ashish R. Hota, Philip E. Par'e
+            Anthony McNally, Christian Lessig, Peter Lean, Eulalie Boucher, Mihai Alexe, E. Pinnington, M. Chantry, Simon Lang, Chris Burrows, Marcin Chrust, F. Pinault, Ethel Villeneuve, Niels Bormann, Sean Healy
           </td>
-          <td>2024-06-14</td>
+          <td>2024-07-22</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>15</td>
         </tr>
 
         <tr id="The Path-dependent Neural Jump ODE (PD-NJ-ODE) is a model for online prediction of generic (possibly non-Markovian) stochastic processes with irregular (in time) and potentially incomplete (with respect to coordinates) observations. It is a model for which convergence to the $L^2$-optimal predictor, which is given by the conditional expectation, is established theoretically. Thereby, the training of the model is solely based on a dataset of realizations of the underlying stochastic process, without the need of knowledge of the law of the process. In the case where the underlying process is deterministic, the conditional expectation coincides with the process itself. Therefore, this framework can equivalently be used to learn the dynamics of ODE or PDE systems solely from realizations of the dynamical system with different initial conditions. We showcase the potential of our method by applying it to the chaotic system of a double pendulum. When training the standard PD-NJ-ODE method, we see that the prediction starts to diverge from the true path after about half of the evaluation time. In this work we enhance the model with two novel ideas, which independently of each other improve the performance of our modelling setup. The resulting dynamics match the true dynamics of the chaotic system very closely. The same enhancements can be used to provably enable the PD-NJ-ODE to learn long-term predictions for general stochastic datasets, where the standard model fails. This is verified in several experiments.">
@@ -4018,751 +4079,706 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
           <td>13</td>
         </tr>
 
-        <tr id="We present a knowledge-guided machine learning (KGML) framework for modeling multi-scale processes, and study its performance in the context of streamflow forecasting in hydrology. Specifically, we propose a novel hierarchical recurrent neural architecture that factorizes the system dynamics at multiple temporal scales and captures their interactions. This framework consists of an inverse and a forward model. The inverse model is used to empirically resolve the system's temporal modes from data (physical model simulations, observed data, or a combination of them from the past), and these states are then used in the forward model to predict streamflow. In a hydrological system, these modes can represent different processes, evolving at different temporal scales (e.g., slow: groundwater recharge and baseflow vs. fast: surface runoff due to extreme rainfall). A key advantage of our framework is that once trained, it can incorporate new observations into the model's context (internal state) without expensive optimization approaches (e.g., EnKF) that are traditionally used in physical sciences for data assimilation. Experiments with several river catchments from the NWS NCRFC region show the efficacy of this ML-based data assimilation framework compared to standard baselines, especially for basins that have a long history of observations. Even for basins that have a shorter observation history, we present two orthogonal strategies of training our FHNN framework: (a) using simulation data from imperfect simulations and (b) using observation data from multiple basins to build a global model. We show that both of these strategies (that can be used individually or together) are highly effective in mitigating the lack of training data. The improvement in forecast accuracy is particularly noteworthy for basins where local models perform poorly because of data sparsity.">
+        <tr id="The interdisciplinary time-series analysis literature encompasses thousands of statistical features for quantifying interpretable properties of dynamical data. But for any given application, it is likely that just a small subset of informative time-series features is required to capture the dynamical quantities of interest. So, while comprehensive libraries of time-series features have been developed, it is useful to construct reduced and computationally efficient subsets for specific applications. In this work, we demonstrate a systematic process to deduce such a reduced set, focused on the problem of distinguishing changes to functional Magnetic Resonance Imaging (fMRI) time series caused by a range of experimental manipulations of excitatory and inhibitory neural activity in mouse cortical circuits. We reduce a comprehensive library of over 7000 candidate time-series features down to a subset of 16 features, which we call catchaMouse16, that aims to both: (i) accurately characterize biologically relevant properties of fMRI time series; and (ii) minimize inter-feature redundancy. The catchaMouse16 feature set accurately classifies experimental perturbations of neuronal activity from fMRI recordings, and also shows strong generalization performance on an unseen mouse and human resting-state fMRI data where it tracks spatial variations in excitatory and inhibitory cortical cell densities, often with greater statistical power than the full hctsa feature set. We provide an efficient, open-source implementation of the catchaMouse16 feature set in C (achieving an approximately 60 times speed-up relative to the native Matlab code of the same features), with wrappers for Python and Matlab. This work demonstrates a procedure to reduce a large candidate time-series feature set down to the key statistical properties of mouse fMRI dynamics that can be used to efficiently quantify and interpret informative dynamical patterns in neural time series.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/520332f72d1a6deaabdd7dd965c0cf76e89053b5" target='_blank'>
-              Hierarchically Disentangled Recurrent Network for Factorizing System Dynamics of Multi-scale Systems
+          <td><a href="https://www.semanticscholar.org/paper/e685be5f1377cb0acf6421ed0e2a179e1e4372df" target='_blank'>
+              Canonical time-series features for characterizing biologically informative dynamical patterns in fMRI
               </a>
             </td>
           <td>
-            Rahul Ghosh, Zac McEachran, Arvind Renganathan, Kelly Lindsay, Somya Sharma, M. Steinbach, John L. Nieber, Christopher J. Duffy, Vipin Kumar
+            Imran Alam, Brendan Harris, Patrick Cahill, Oliver Cliff, M. Markicevic, Valerio Zerbi, BD Fulcher
           </td>
-          <td>2024-07-29</td>
-          <td>ArXiv</td>
+          <td>2024-07-17</td>
+          <td>bioRxiv</td>
           <td>0</td>
-          <td>44</td>
+          <td>10</td>
         </tr>
 
-        <tr id="Skilful Machine Learned weather forecasts have challenged our approach to numerical weather prediction, demonstrating competitive performance compared to traditional physics-based approaches. Data-driven systems have been trained to forecast future weather by learning from long historical records of past weather such as the ECMWF ERA5. These datasets have been made freely available to the wider research community, including the commercial sector, which has been a major factor in the rapid rise of ML forecast systems and the levels of accuracy they have achieved. However, historical reanalyses used for training and real-time analyses used for initial conditions are produced by data assimilation, an optimal blending of observations with a physics-based forecast model. As such, many ML forecast systems have an implicit and unquantified dependence on the physics-based models they seek to challenge. Here we propose a new approach, training a neural network to predict future weather purely from historical observations with no dependence on reanalyses. We use raw observations to initialise a model of the atmosphere (in observation space) learned directly from the observations themselves. Forecasts of crucial weather parameters (such as surface temperature and wind) are obtained by predicting weather parameter observations (e.g. SYNOP surface data) at future times and arbitrary locations. We present preliminary results on forecasting observations 12-hours into the future. These already demonstrate successful learning of time evolutions of the physical processes captured in real observations. We argue that this new approach, by staying purely in observation space, avoids many of the challenges of traditional data assimilation, can exploit a wider range of observations and is readily expanded to simultaneous forecasting of the full Earth system (atmosphere, land, ocean and composition).">
+        <tr id="Deep Gaussian Processes (DGPs) leverage a compositional structure to model non-stationary processes. DGPs typically rely on local inducing point approximations across intermediate GP layers. Recent advances in DGP inference have shown that incorporating global Fourier features from Reproducing Kernel Hilbert Space (RKHS) can enhance the DGPs' capability to capture complex non-stationary patterns. This paper extends the use of these features to compositional GPs involving linear transformations. In particular, we introduce Ordinary Differential Equation (ODE) -based RKHS Fourier features that allow for adaptive amplitude and phase modulation through convolution operations. This convolutional formulation relates our work to recently proposed deep latent force models, a multi-layer structure designed for modelling nonlinear dynamical systems. By embedding these adjustable RKHS Fourier features within a doubly stochastic variational inference framework, our model exhibits improved predictive performance across various regression tasks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f12110407568e11614a4bec8a9d4a303c2c72458" target='_blank'>
-              Data driven weather forecasts trained and initialised directly from observations
+          <td><a href="https://www.semanticscholar.org/paper/6828a61a888094de685450ee2ce84e8f6bcfb2a8" target='_blank'>
+              Adaptive RKHS Fourier Features for Compositional Gaussian Process Models
               </a>
             </td>
           <td>
-            Anthony McNally, Christian Lessig, Peter Lean, Eulalie Boucher, Mihai Alexe, E. Pinnington, M. Chantry, Simon Lang, Chris Burrows, Marcin Chrust, F. Pinault, Ethel Villeneuve, Niels Bormann, Sean Healy
+            Xinxing Shi, Thomas Baldwin-McDonald, Mauricio A. 'Alvarez
           </td>
-          <td>2024-07-22</td>
+          <td>2024-07-01</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>15</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Training neural networks involves optimizing parameters to minimize a loss function, where the nature of the loss function and the optimization strategy are crucial for effective training. Hyperparameter choices, such as the learning rate in gradient descent (GD), significantly affect the success and speed of convergence. Recent studies indicate that the boundary between bounded and divergent hyperparameters can be fractal, complicating reliable hyperparameter selection. However, the nature of this fractal boundary and methods to avoid it remain unclear. In this study, we focus on GD to investigate the loss landscape properties that might lead to fractal trainability boundaries. We discovered that fractal boundaries can emerge from simple non-convex perturbations, i.e., adding or multiplying cosine type perturbations to quadratic functions. The observed fractal dimensions are influenced by factors like parameter dimension, type of non-convexity, perturbation wavelength, and perturbation amplitude. Our analysis identifies"roughness of perturbation", which measures the gradient's sensitivity to parameter changes, as the factor controlling fractal dimensions of trainability boundaries. We observed a clear transition from non-fractal to fractal trainability boundaries as roughness increases, with the critical roughness causing the perturbed loss function non-convex. Thus, we conclude that fractal trainability boundaries can arise from very simple non-convexity. We anticipate that our findings will enhance the understanding of complex behaviors during neural network training, leading to more consistent and predictable training strategies.">
+        <tr id="Understanding the dynamics of open quantum systems in strong coupling and non-Markovian regimes remains a formidable theoretical challenge. One popular and well-established method of approximation in these circumstances is provided by the polaron master equation (PME). In this work we reevaluate and extend the validity of the PME to capture the impact of non-Markovian polaron dressing, induced by non-equilibrium open system dynamics. By comparing with numerically exact techniques, we confirm that while the standard PME successfully predicts the dynamics of system observables that commute with the polaron transformation (e.g. populations in the Pauli z-basis), it can struggle to fully capture those that do not (e.g. coherences). This limitation stems from the mixing of system and environment degrees of freedom inherent to the polaron transformation, which affects the accuracy of calculated expectation values within the polaron frame. Employing the Nakajima-Zwanzig projection operator formalism, we introduce correction terms that provide an accurate description of observables that do not commute with the transformation. We demonstrate the significance of the correction terms in two cases, the canonical spin-boson model and a dissipative time-dependent Landau-Zener protocol, where they are shown to impact the system dynamics on both short and long timescales.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/da89cee139251ba0fe289fb5dd11c8d576adca50" target='_blank'>
-              Complex fractal trainability boundary can arise from trivial non-convexity
+          <td><a href="https://www.semanticscholar.org/paper/97eb69ef1b908a5b349cac016b071bc744ed7afd" target='_blank'>
+              Capturing non-Markovian polaron dressing with the master equation formalism
               </a>
             </td>
           <td>
-            Yizhou Liu
+            Jake Iles-Smith, Owen Diba, A. Nazir
           </td>
-          <td>2024-06-20</td>
+          <td>2024-07-15</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>30</td>
         </tr>
 
-        <tr id="Predictive models are a crucial component of many robotic systems. Yet, constructing accurate predictive models for a variety of deformable objects, especially those with unknown physical properties, remains a significant challenge. This paper introduces AdaptiGraph, a learning-based dynamics modeling approach that enables robots to predict, adapt to, and control a wide array of challenging deformable materials with unknown physical properties. AdaptiGraph leverages the highly flexible graph-based neural dynamics (GBND) framework, which represents material bits as particles and employs a graph neural network (GNN) to predict particle motion. Its key innovation is a unified physical property-conditioned GBND model capable of predicting the motions of diverse materials with varying physical properties without retraining. Upon encountering new materials during online deployment, AdaptiGraph utilizes a physical property optimization process for a few-shot adaptation of the model, enhancing its fit to the observed interaction data. The adapted models can precisely simulate the dynamics and predict the motion of various deformable materials, such as ropes, granular media, rigid boxes, and cloth, while adapting to different physical properties, including stiffness, granular size, and center of pressure. On prediction and manipulation tasks involving a diverse set of real-world deformable objects, our method exhibits superior prediction accuracy and task proficiency over non-material-conditioned and non-adaptive models. The project page is available at https://robopil.github.io/adaptigraph/ .">
+        <tr id="Following the discovery of the least squares method in 1805 by Legendre and later in 1809 by Gauss, surrogate modeling and machine learning have come a long way. From identifying patterns and trends in process data to predictive modeling, optimization, fault detection, reaction network discovery, and process operations, machine learning became an integral part of all aspects of process design and process systems engineering. This is enabled, at the same time necessitated, by the vast amounts of data that are readily available from processes, increased digitalization, automation, increasing computation power, and simulation software that can model complex phenomena that span over several temporal and spatial scales. Although this paper is not a comprehensive review, it gives an overview of the recent history of machine learning models that we use every day and how they shaped process design problems from the recent advances to the exploration of their prospects.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/06d79953e85f7981f8a2cabad2165ca739af35af" target='_blank'>
-              AdaptiGraph: Material-Adaptive Graph-Based Neural Dynamics for Robotic Manipulation
+          <td><a href="https://www.semanticscholar.org/paper/4ca2456c9116fb14b2abeebf2076d63a64574d2d" target='_blank'>
+              From Then to Now and Beyond: Exploring How Machine Learning Shapes Process Design Problems
               </a>
             </td>
           <td>
-            Kaifeng Zhang, Baoyu Li, Kris Hauser, Yunzhu Li
+            Burcu Beykal
           </td>
-          <td>2024-07-10</td>
-          <td>ArXiv</td>
+          <td>2024-07-09</td>
+          <td>Systems and Control Transactions</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="A recent study in turbulent flow simulation demonstrated the potential of generative diffusion models for fast 3D surrogate modeling. This approach eliminates the need for specifying initial states or performing lengthy simulations, significantly accelerating the process. While adept at sampling individual frames from the learned manifold of turbulent flow states, the previous model lacks the capability to generate sequences, hindering analysis of dynamic phenomena. This work addresses this limitation by introducing a 4D generative diffusion model and a physics-informed guidance technique that enables the generation of realistic sequences of flow states. Our findings indicate that the proposed method can successfully sample entire subsequences from the turbulent manifold, even though generalizing from individual frames to sequences remains a challenging task. This advancement opens doors for the application of generative modeling in analyzing the temporal evolution of turbulent flows, providing valuable insights into their complex dynamics.">
+        <tr id="Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computational costs. On the other hand, recent deep learning and reinforcement learning-based approaches often struggle to optimize long-term control sequences under the constraints of system dynamics. In this work, we introduce Diffusion Physical systems Control (DiffPhyCon), a new class of method to address the physical systems control problem. DiffPhyCon excels by simultaneously minimizing both the learned generative energy function and the predefined control objectives across the entire trajectory and control sequence. Thus, it can explore globally and identify near-optimal control sequences. Moreover, we enhance DiffPhyCon with prior reweighting, enabling the discovery of control sequences that significantly deviate from the training distribution. We test our method in 1D Burgers' equation and 2D jellyfish movement control in a fluid environment. Our method outperforms widely applied classical approaches and state-of-the-art deep learning and reinforcement learning methods. Notably, DiffPhyCon unveils an intriguing fast-close-slow-open pattern observed in the jellyfish, aligning with established findings in the field of fluid dynamics.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/dc78763ae5036e70c9aea5f2b3c74d7a5cb9b6e2" target='_blank'>
-              Unfolding Time: Generative Modeling for Turbulent Flows in 4D
+          <td><a href="https://www.semanticscholar.org/paper/2ed151b432bd4c9d4bafa7399dadc48d42ebe3d6" target='_blank'>
+              A Generative Approach to Control Complex Physical Systems
               </a>
             </td>
           <td>
-            Abdullah Saydemir, Marten Lienen, Stephan Gunnemann
+            Long Wei, Peiyan Hu, Ruiqi Feng, Haodong Feng, Yixuan Du, Tao Zhang, Rui Wang, Yue Wang, Zhi-Ming Ma, Tailin Wu
           </td>
-          <td>2024-06-17</td>
+          <td>2024-07-09</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>5</td>
+          <td>1</td>
+          <td>3</td>
         </tr>
 
-        <tr id="We present a new step in our systematic effort to develop self-consistent dynamical models with a finite radial extent. The focus is on models with simple analytical density profiles allowing for analytical calculations of many dynamical properties. In this paper, we introduce a family of models, termed Wendland models, based on compactly supported radial basis functions. The family of models is characterised by a parameter $k$ that controls the smoothness of the transition at the truncation radius. In the limit $k\to\infty$, the Wendland model reduces to a non-truncated model with a Gaussian density profile. For each Wendland model, the density, mass and gravitational potential are simple truncated polynomial functions of radius. Via the SpheCow tool we demonstrate that all Wendland models can be supported by isotropic distribution functions. Surprisingly, the isotropic distribution function exhibits varied behaviour across different Wendland models. Additionally, each model can be supported by a continuum of Osipkov--Merritt orbital structures, ranging from radially anisotropic to completely tangential at the truncation radius. To the best of our knowledge, the Wendland models presented here are the first family of models accommodating both radial and tangential Osipkov--Merritt distribution functions. Using linear superposition, these models can easily be combined to generate Wendland models with even more diverse orbital structures. While the Wendland models are not fully representative of real dynamical systems due to their Gaussian-like density profile, this study lays important groundwork for constructing more realistic models with truncated density profiles that can be supported by a range of orbital structures.">
+        <tr id="Verification of uncertain, complex dynamical systems is crucial in the modern day world. An increasingly common method to verify complex logic specifications for dynamical systems involves symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. By sampling trajectories of the concrete, unknown system and via robust analysis, we build a data-driven abstraction, related to the underlying model through a probabilistic behavioural inclusion relation. As the distribution from which the trajectories are drawn is unknown, we adopt two distinct distribution-free theories, namely scenario optimization and conformal prediction. We compare and discuss the differences between the two approaches in terms of the type of guarantees that they are able to provide. Furthermore, via experimental benchmarks we outline the efficiency of the two methods with respect to the number of samples available and the tightness of the guarantees.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/602e48b057ea8900fb3ce6dcced4d37b2035392e" target='_blank'>
-              Self-consistent dynamical models with a finite extent -- IV. Wendland models based on compactly supported radial basis functions
+          <td><a href="https://www.semanticscholar.org/paper/a4bc6fac276ef549b5a06e10e0b424eaf5ed1fd7" target='_blank'>
+              Scenario Approach and Conformal Prediction for Verification of Unknown Systems via Data-Driven Abstractions
               </a>
             </td>
           <td>
-            Maarten Baes
+            Rudi Coppola, Andrea Peruffo, Lars Lindemann, Manuel Mazo
           </td>
-          <td>2024-06-15</td>
-          <td>ArXiv</td>
-          <td>0</td>
+          <td>2024-06-25</td>
+          <td>2024 European Control Conference (ECC)</td>
           <td>0</td>
+          <td>9</td>
         </tr>
 
-        <tr id="Hybrid modeling aims to augment traditional theory-driven models with machine learning components that learn unknown parameters, sub-models or correction terms from data. In this work, we build on FluxRGNN, a recently developed hybrid model of continental-scale bird migration, which combines a movement model inspired by fluid dynamics with recurrent neural networks that capture the complex decision-making processes of birds. While FluxRGNN has been shown to successfully predict key migration patterns, its spatial resolution is constrained by the typically sparse observations obtained from weather radars. Additionally, its trainable components lack explicit incentives to adequately predict take-off and landing events. Both aspects limit our ability to interpret model results ecologically. To address this, we propose two major modifications that allow for more detailed predictions on any desired tessellation while providing control over the interpretability of model components. In experiments on the U.S. weather radar network, the enhanced model effectively leverages the underlying movement model, resulting in strong extrapolation capabilities to unobserved locations.">
+        <tr id="Encoding frequency stability constraints in the operation problem is challenging due to its complex dynamics. Recently, data-driven approaches have been proposed to learn the stability criteria offline with the trained model embedded as a constraint of online optimization. However, random sampling of stationary operation points is less efficient in generating balanced stable and unstable samples. Meanwhile, the performance of such a model is strongly dependent on the quality of the training dataset. Observing this research gap, we propose a gradient-based data generation method via forward-mode automatic differentiation. In this method, the original dynamic system is augmented with new states that represent the dynamic of sensitivities of the original states, which can be solved by invoking any ODE solver for a single time. To compensate for the contradiction between the gradient of various frequency stability criteria, gradient surgery is proposed by projecting the gradient on the normal plane of the other. In the end, we demonstrate the superior performance of the proposed sampling algorithm, compared with the unrolling differentiation and finite difference. All codes are available at https://github.com/xuwkk/frequency_sample_ad.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/db8ecd0f823bc56c0fe6b87a31bdeea470304f59" target='_blank'>
-              Towards detailed and interpretable hybrid modeling of continental-scale bird migration
+          <td><a href="https://www.semanticscholar.org/paper/c2a8a10d25fc8962321b615ea83477e1fb4d6310" target='_blank'>
+              Efficient Sampling for Data-Driven Frequency Stability Constraint via Forward-Mode Automatic Differentiation
               </a>
             </td>
           <td>
-            Fiona Lippert, Bart Kranstauber, Patrick Forr'e, E. E. V. Loon
+            Wangkun Xu, Qian Chen, Pudong Ge, Zhongda Chu, Fei Teng
           </td>
-          <td>2024-07-14</td>
+          <td>2024-07-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>5</td>
+          <td>7</td>
         </tr>
 
-        <tr id="Scientific computing has been an indispensable tool in applied sciences and engineering, where traditional numerical methods are often employed due to their superior accuracy guarantees. However, these methods often encounter challenges when dealing with problems involving complex geometries. Machine learning-based methods, on the other hand, are mesh-free, thus providing a promising alternative. In particular, operator learning methods have been proposed to learn the mapping from the input space to the solution space, enabling rapid inference of solutions to partial differential equations (PDEs) once trained. In this work, we address the parametric elliptic interface problem. Building upon the deep operator network (DeepONet), we propose an extended interface deep operator network (XI-DeepONet). XI-DeepONet exhibits three unique features: (1) The interface geometry is incorporated into the neural network as an additional input, enabling the network to infer solutions for new interface geometries once trained; (2) The level set function associated with the interface geometry is treated as the input, on which the solution mapping is continuous and can be effectively approximated by the deep operator network; (3) The network can be trained without any input-output data pairs, thus completely avoiding the need for meshes of any kind, directly or indirectly. We conduct a comprehensive series of numerical experiments to demonstrate the accuracy and robustness of the proposed method.">
+        <tr id="Deep learning-based partial differential equation(PDE) solvers have received much attention in the past few years. Methods of this category can solve a wide range of PDEs with high accuracy, typically by transforming the problems into highly nonlinear optimization problems of neural network parameters. This work reviews several deep learning solvers proposed a few years ago, including PINN, WAN, DRM, and VPINN. Numerical results are provided to make comparisons amongst them and address the importance of loss formulation and the optimization method. A rigorous error analysis for PINN is also presented. Finally, we discuss the current limitations and bottlenecks of these methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/649bca2a52c735c23a301cc270501ada4e4462c2" target='_blank'>
-              XI-DeepONet: An operator learning method for elliptic interface problems
+          <td><a href="https://www.semanticscholar.org/paper/e8ab3da28291cf15c3b44c4f064373f4597eb015" target='_blank'>
+              A Review of Neural Network Solvers for Second-order Boundary Value Problems
               </a>
             </td>
           <td>
-            Ran Bi, Jingrun Chen, Weibing Deng
+            Ramesh Chandra Sau, Luowei Yin
           </td>
-          <td>2024-07-21</td>
+          <td>2024-06-29</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="The dynamics of supercooled liquids slow down and become increasingly heterogeneous as they are cooled. Recently, local structural variables identified using machine learning, such as"softness", have emerged as predictors of local dynamics. Here we construct a model using softness to describe the structural origins of dynamical heterogeneity in supercooled liquids. In our model, the probability of particles to rearrange is determined by their softness, and each rearrangement induces changes in the softness of nearby particles, describing facilitation. We show how to ensure that these changes respect the underlying time-reversal symmetry of the liquid's dynamics. The model reproduces the salient features of dynamical heterogeneity, and demonstrates how long-ranged dynamical correlations can emerge at long time scales from a relatively short softness correlation length.">
+        <tr id="Symmetries play a pivotal role in our understanding of the properties of quantum many-body systems. While there are theorems and a well-established toolbox for systems in thermal equilibrium, much less is known about the role of symmetries and their connection to dynamics out of equilibrium. This arises due to the direct link between a system's thermal state and its Hamiltonian, which is generally not the case for nonequilibrium dynamics. Here we present a pathway to identify the effective symmetries and to extract them from data in nonequilibrium quantum many-body systems. Our approach is based on exact relations between correlation functions involving different numbers of spatial points, which can be viewed as nonequilibrium versions of (equal-time) Ward identities encoding the symmetries of the system. We derive symmetry witnesses, which are particularly suitable for the analysis of measured or simulated data at different snapshots in time. To demonstrate the potential of the approach, we apply our method to numerical and experimental data for a spinor Bose gas. We investigate the important question of a dynamical restoration of an explicitly broken symmetry of the Hamiltonian by the initial state. Remarkably, it is found that effective symmetry restoration can occur long before the system equilibrates. We also use the approach to define and identify spontaneous symmetry breaking far from equilibrium, which is of great relevance for applications to nonequilibrium phase transitions. Our work opens new avenues for the classification and analysis of quantum as well as classical many-body dynamics in a large variety of systems, ranging from ultracold quantum gases to cosmology.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d32819cfd5ee45a8ac43a269f5f4b86638fff470" target='_blank'>
-              The dynamics of machine-learned"softness"in supercooled liquids describe dynamical heterogeneity
+          <td><a href="https://www.semanticscholar.org/paper/8a8950d1ce041653ba3716007a86405364e34167" target='_blank'>
+              Extracting the symmetries of nonequilibrium quantum many-body systems
               </a>
             </td>
           <td>
-            S. Ridout, Andrea J. Liu
+            A. Mikheev, Viktoria Noel, Ido Siovitz, H. Strobel, M. Oberthaler, Jurgen Berges
           </td>
-          <td>2024-06-09</td>
+          <td>2024-07-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>8</td>
+          <td>48</td>
         </tr>
 
-        <tr id="Verification of uncertain, complex dynamical systems is crucial in the modern day world. An increasingly common method to verify complex logic specifications for dynamical systems involves symbolic abstractions: simpler, finite-state models whose behaviour mimics the one of the systems of interest. By sampling trajectories of the concrete, unknown system and via robust analysis, we build a data-driven abstraction, related to the underlying model through a probabilistic behavioural inclusion relation. As the distribution from which the trajectories are drawn is unknown, we adopt two distinct distribution-free theories, namely scenario optimization and conformal prediction. We compare and discuss the differences between the two approaches in terms of the type of guarantees that they are able to provide. Furthermore, via experimental benchmarks we outline the efficiency of the two methods with respect to the number of samples available and the tightness of the guarantees.">
+        <tr id="We consider quantum or classical many-body Hamiltonian systems, whose dynamics is given by an integrable, contact interactions, plus another, possibly long-range, generic two-body potential. We show how the dynamics of local observables is given in terms of a generalised version of Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, which we denote as gBBGKY, which is built for the densities, and their correlations, of the quasiparticles of the underlying integrable model. Unlike the usual cases of perturbation theory from free gases, the presence of local interactions in the integrable model"lifts"the so-called kinetic blocking, and the second layer of the hierarchy reproduces the dynamics at all time-scales. The latter consists of a fast pre-equilibration to a non-thermal steady state, and its subsequent thermalisation to a Gibbs ensemble. We show how the final relaxation is encoded into a Boltzmann scattering integral involving three or higher body-scatterings, and which, remarkably, is entirely determined by the diffusion constants of the underlying integrable model. We check our results with exact molecular dynamics simulations, finding perfect agreement. Our results show how gBBGKY can be successfully employed in quantum systems to compute scattering integrals and Fermi's golden rule transition rates.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a4bc6fac276ef549b5a06e10e0b424eaf5ed1fd7" target='_blank'>
-              Scenario Approach and Conformal Prediction for Verification of Unknown Systems via Data-Driven Abstractions
+          <td><a href="https://www.semanticscholar.org/paper/e0ea32035f5732ebc13f1df5f3d70be5820746ea" target='_blank'>
+              Generalised BBGKY hierarchy for near-integrable dynamics
               </a>
             </td>
           <td>
-            Rudi Coppola, Andrea Peruffo, Lars Lindemann, Manuel Mazo
+            Leonardo Biagetti, Maciej Lebek, M. Panfil, J. D. Nardis
           </td>
-          <td>2024-06-25</td>
-          <td>2024 European Control Conference (ECC)</td>
+          <td>2024-08-01</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>9</td>
+          <td>19</td>
         </tr>
 
-        <tr id="This work introduces a novel, simple, and flexible method to quantify irreversibility in generic high-dimensional time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting for estimation, providing a model-free, nonlinear analysis able to handle large-dimensional systems while requiring minimal or no calibration. Our procedure is divided into three phases: trajectory encoding, Markovian order identification, and hypothesis testing for variable interactions. The latter is the key innovation that allows us to selectively switch off variable interactions to discern their specific contribution to irreversibility. When applied to financial markets, our findings reveal a distinctive shift: during stable periods, irreversibility is mainly related to short-term patterns, whereas in unstable periods, these short-term patterns are disrupted, leaving only contributions from stable long-term ones. This observed transition underscores the crucial importance of high-order variable interactions in understanding the dynamics of financial markets, especially in times of turbulence.">
+        <tr id="We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity and, by leveraging the Kolosov-Muskhelishvili representation of the solution in terms of holomorphic potentials, we train a complex-valued neural network to fulfill stress and displacement boundary conditions while automatically satisfying the governing equations. This is achieved by designing the network to return only approximations that inherently satisfy the Cauchy-Riemann conditions through specific choices of layers and activation functions. To ensure generality, we provide a universal approximation theorem guaranteeing that, under basic assumptions, the proposed holomorphic neural networks can approximate any holomorphic function. Furthermore, we suggest a new tailored weight initialization technique to mitigate the issue of vanishing/exploding gradients. Compared to the standard PINN approach, noteworthy benefits of the proposed method for the linear elasticity problem include a more efficient training, as evaluations are needed solely on the boundary of the domain, lower memory requirements, due to the reduced number of training points, and $C^\infty$ regularity of the learned solution. Several benchmark examples are used to verify the correctness of the obtained PIHNN approximations, the substantial benefits over traditional PINNs, and the possibility to deal with non-trivial, multiply-connected geometries via a domain-decomposition strategy.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/13af2b3fdfb1da693055642a783d2277f03dfeab" target='_blank'>
-              Functional Decomposition and Estimation of Irreversibility in Time Series via Machine Learning
+          <td><a href="https://www.semanticscholar.org/paper/1e71714f3dda61e6e50ace4788915467f7d4f810" target='_blank'>
+              Physics-Informed Holomorphic Neural Networks (PIHNNs): Solving Linear Elasticity Problems
               </a>
             </td>
           <td>
-            Michele Vodret, Cristiano Pacini, Christian Bongiorno
+            Matteo Calafa, Emil Hovad, A. Engsig-Karup, T. Andriollo
           </td>
-          <td>2024-07-08</td>
+          <td>2024-07-01</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>20</td>
         </tr>
 
-        <tr id="Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computational costs. On the other hand, recent deep learning and reinforcement learning-based approaches often struggle to optimize long-term control sequences under the constraints of system dynamics. In this work, we introduce Diffusion Physical systems Control (DiffPhyCon), a new class of method to address the physical systems control problem. DiffPhyCon excels by simultaneously minimizing both the learned generative energy function and the predefined control objectives across the entire trajectory and control sequence. Thus, it can explore globally and identify near-optimal control sequences. Moreover, we enhance DiffPhyCon with prior reweighting, enabling the discovery of control sequences that significantly deviate from the training distribution. We test our method in 1D Burgers' equation and 2D jellyfish movement control in a fluid environment. Our method outperforms widely applied classical approaches and state-of-the-art deep learning and reinforcement learning methods. Notably, DiffPhyCon unveils an intriguing fast-close-slow-open pattern observed in the jellyfish, aligning with established findings in the field of fluid dynamics.">
+        <tr id="We present an expansion of a many-body correlation function in a sum of pseudomodes - exponents with complex frequencies that encompass both decay and oscillations. We demonstrate that, typically, it is enough to take a few first terms of this infinite sum to obtain an excellent approximation to the correlation function at any time, with the large time behavior being determined solely by the first pseudomode. The pseudomode expansion emerges in the framework of the Heisenberg version of the recursion method. This method essentially solves Heisenberg equations in a Lanczos tridiagonal basis constructed in the Krylov space of a given observable. To obtain pseudomodes, we first add artificial dissipation satisfying the dissipative generalization of the universal operator growth hypothesis, and then take the limit of the vanishing dissipation strength. Fast convergence of the pseudomode expansion is facilitated by the localization in the Krylov space, which is generic in the presence of dissipation and can survive the limit of the vanishing dissipation strength. As an illustration, we apply the pseudomode expansion to calculate infinite-temperature autocorrelation functions in the quantum Ising and $XX$ spin-$1/2$ models on the square lattice.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2ed151b432bd4c9d4bafa7399dadc48d42ebe3d6" target='_blank'>
-              A Generative Approach to Control Complex Physical Systems
+          <td><a href="https://www.semanticscholar.org/paper/8c0e1c45eedb9a16b0066dded4a252c6974da710" target='_blank'>
+              Pseudomode expansion of many-body correlation functions
               </a>
             </td>
           <td>
-            Long Wei, Peiyan Hu, Ruiqi Feng, Haodong Feng, Yixuan Du, Tao Zhang, Rui Wang, Yue Wang, Zhi-Ming Ma, Tailin Wu
+            Alexander Teretenkov, F. Uskov, Oleg Lychkovskiy
           </td>
-          <td>2024-07-09</td>
+          <td>2024-07-17</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>3</td>
         </tr>
 
-        <tr id="Although optimal control (OC) has been studied in stochastic thermodynamics for systems with continuous state variables, less is known in systems with discrete state variables, such as Chemical Reaction Networks (CRNs). Here, we develop a general theoretical framework to study OC of CRNs for changing the system from an initial distribution of states to a final distribution with minimum dissipation. We derive a ``Kirchhoff's law"for the probability current in the adiabatic limit, from which the optimal kinetic rates are determined analytically for any given probability trajectory. By using the optimal rates, we show that the total dissipation is determined by a $L_2$-distance measure in the probability space and derive an analytical expression for the metric tensor that depends on the probability distribution, network topology, and capacity of each link. Minimizing the total dissipation leads to the geodesic trajectory in the probability space and the corresponding OC protocol is determined by the Kirchhoff's law. To demonstrate our general approach, we use it to find a lower bound for the minimum dissipation that is tighter than existing bounds obtained with only global constraints. We also apply it to simple networks, e.g., fully connected 3-state CRNs with different local constraints and show that indirect pathway and non-functional transient state can play a crucial role in switching between different probability distributions efficiently. Future directions in studying OC in CRNs by using our general framework are discussed.">
+        <tr id="Studying the temporal evolution of complex systems requires tools able to detect the presence and quantify the strength of predictable dynamics within their output signals. Information theory aids in such a description, particularly through information storage (IS), which reflects the regularity of system dynamics by measuring the information shared between the present and the past system states. While the conventional IS computation provides an overall measure of predictable information, transient behaviors of predictability occurring during system transitions can be assessed by time-resolved measures such as the local information storage (L-IS), assuming stationarity, and the time-varying information storage (TV-IS), without stationarity assumptions. In this work, through a comparative analysis in simulated and real contexts, we aim to demonstrate how these methods complement each other and reveal dynamic changes of the system behavior associated to state transitions. In simulations, we show that the TV-IS can effectively track sudden changes of the information stored in the system, which is reflected in its average value computed over specific time intervals; on the other hand, the surprise originated by the emergence of a change in the predictability of the system is reflected in the variance of the L-IS computed within specific time intervals. In neurophysiological applications, the distinct phenomena of respiratory activity in sleep apnea and brain activity during somatosensory stimulation both reveal a significant decrease of IS evoked by state transitions, highlighting how such transitions can inject new information in physiological systems, affecting significantly their internal dynamics. Overall, TV-IS and L-IS appear to provide different and complementary information about the behavior of the systems under investigation, thereby offering valuable tools for the study of complex physiological systems where both stationary and non-stationary conditions may be present.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/10b37de358ef271ea50059678271fca729dce156" target='_blank'>
-              Geometry of optimal control in chemical reaction networks
+          <td><a href="https://www.semanticscholar.org/paper/7c3b648f9e9d48cea5dda06ced2a7fa4a474d58a" target='_blank'>
+              Exploring transient neurophysiological states through local and time-varying measures of Information Dynamics
               </a>
             </td>
           <td>
-            Yikuan Zhang, Ouyang Qi, Yuhai Tu
+            Y. Antonacci, C. Barà, G. De Felice, A. Sferlazza, R. Pernice, L. Faes
           </td>
-          <td>2024-07-08</td>
-          <td>ArXiv</td>
+          <td>2024-06-24</td>
+          <td>bioRxiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>21</td>
         </tr>
 
-        <tr id="This paper presents a methodical dynamical analysis of the Big Bang model, taking into account dark matter and an arbitrary form of dark energy. Nevertheless, why dynamic analysis? The primary advantage of the dynamical analysis approach is that it obviates the necessity to precisely solve the system for every individual dependent variable. Instead, it enables the prediction of the overall evolutions. In this regard, there are some powerful tools of non-dynamical systems (theorems, perturbation, etc.) which can help us a lot. The model under consideration is a nonlinear system with two dimensions (2D). In order to investigate this, we employ a sophisticated form of nonlinear dynamical systems theory in our research. We have delved into the full potential of nonlinear dynamical system theory known until now in our work. This analysis has produced very interesting solutions, which are in quite a contrast with the linear analysis approach. The stability of the system is considered at length, and the corresponding evolutions of the universe are also discussed consequently. A handful number of figures are given to visualize the behavior of the evolutions. The plots that are presented here are vector field plots and a new plotting technique initiated by us and used in our earlier papers. Interestingly, our work indicates the universe might resemble “phantom” evolution. Also, among the fixed points of our model, one is able to escape the singular situation called “Big Rip”.">
+        <tr id="In the central nervous system, sequences of neural activity form trajectories on low dimensional neural manifolds. The neural computation underlying flexible cognition and behavior relies on dynamic control of these structures. For example different tasks or behaviors are represented on different subspaces, requiring fast timescale subspace rotation to move from one behavior to the next. For flexibility in a particular behavior, the neural trajectory must be dynamically controllable within that behaviorally determined subspace. To understand how dynamic control of neural trajectories and their underlying subspaces may be implemented in neural circuits, we first characterized the relationship between features of neural activity sequences and aspects of the low dimensional projection. Based on this, we propose neural mechanisms that can act within local circuits to modulate activity sequences thereby controlling neural trajectories in low dimensional subspaces. In particular, we show that gain modulation and transient synaptic currents control the speed and path of neural trajectories and clustered inhibition determines manifold orientation. Together, these neural mechanisms may enable a substrate for fast timescale computation on neural manifolds.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9649042fb8c1c032aa5bd8ad6a4249c0234e8a63" target='_blank'>
-              Dark energy and dark matter interaction: A nonlinear dynamical system study
+          <td><a href="https://www.semanticscholar.org/paper/0a6120a5f2c70336b63e76de5fc920ea9b4af59d" target='_blank'>
+              Dynamic control of neural manifolds
               </a>
             </td>
           <td>
-            Jyotirmay Das Mandal, U. Debnath, Anirudh Pradhan
+            Andrew B. Lehr, Arvind Kumar, Christian Tetzlaff
           </td>
-          <td>2024-06-27</td>
-          <td>International Journal of Geometric Methods in Modern Physics</td>
+          <td>2024-07-11</td>
+          <td>bioRxiv</td>
           <td>0</td>
-          <td>25</td>
-        </tr>
-
-        <tr id="Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the neural network, and they scale to large models and datasets. While the choice of prior strongly affects the resulting posterior distribution, computational tractability and lack of interpretability of weight space typically limit the Laplace approximation to isotropic Gaussian priors, which are known to cause pathological behavior as depth increases. As a remedy, we directly place a prior on function space. More precisely, since Lebesgue densities do not exist on infinite-dimensional function spaces, we have to recast training as finding the so-called weak mode of the posterior measure under a Gaussian process (GP) prior restricted to the space of functions representable by the neural network. Through the GP prior, one can express structured and interpretable inductive biases, such as regularity or periodicity, directly in function space, while still exploiting the implicit inductive biases that allow deep networks to generalize. After model linearization, the training objective induces a negative log-posterior density to which we apply a Laplace approximation, leveraging highly scalable methods from matrix-free linear algebra. Our method provides improved results where prior knowledge is abundant, e.g., in many scientific inference tasks. At the same time, it stays competitive for black-box regression and classification tasks where neural networks typically excel.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c1a0555187db175d6e1fb7be3e3ea84e032a4d7c" target='_blank'>
-              FSP-Laplace: Function-Space Priors for the Laplace Approximation in Bayesian Deep Learning
-              </a>
-            </td>
-          <td>
-            Tristan Cinquin, Marvin Pfortner, Vincent Fortuin, Philipp Hennig, Robert Bamler
-          </td>
-          <td>2024-07-18</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>14</td>
+          <td>6</td>
         </tr>
 
-        <tr id="We consider quantum or classical many-body Hamiltonian systems, whose dynamics is given by an integrable, contact interactions, plus another, possibly long-range, generic two-body potential. We show how the dynamics of local observables is given in terms of a generalised version of Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, which we denote as gBBGKY, which is built for the densities, and their correlations, of the quasiparticles of the underlying integrable model. Unlike the usual cases of perturbation theory from free gases, the presence of local interactions in the integrable model"lifts"the so-called kinetic blocking, and the second layer of the hierarchy reproduces the dynamics at all time-scales. The latter consists of a fast pre-equilibration to a non-thermal steady state, and its subsequent thermalisation to a Gibbs ensemble. We show how the final relaxation is encoded into a Boltzmann scattering integral involving three or higher body-scatterings, and which, remarkably, is entirely determined by the diffusion constants of the underlying integrable model. We check our results with exact molecular dynamics simulations, finding perfect agreement. Our results show how gBBGKY can be successfully employed in quantum systems to compute scattering integrals and Fermi's golden rule transition rates.">
+        <tr id="Piecewise-deterministic Markov processes (PDMPs) are often used to model abrupt changes in the global environment or capabilities of a controlled system. This is typically done by considering a set of"operating modes"(each with its own system dynamics and performance metrics) and assuming that the mode can switch stochastically while the system state evolves. Such models have a broad range of applications in engineering, economics, manufacturing, robotics, and biological sciences. Here, we introduce and analyze an"occasionally observed"version of mode-switching PDMPs. We show how such systems can be controlled optimally if the planner is not alerted to mode-switches as they occur but may instead have access to infrequent mode observations. We first develop a general framework for handling this through dynamic programming on a higher-dimensional mode-belief space. While quite general, this method is rarely practical due to the curse of dimensionality. We then discuss assumptions that allow for solving the same problem much more efficiently, with the computational costs growing linearly (rather than exponentially) with the number of modes. We use this approach to derive Hamilton-Jacobi-Bellman PDEs and quasi-variational inequalities encoding the optimal behavior for a variety of planning horizons (fixed, infinite, indefinite, random) and mode-observation schemes (at fixed times or on-demand). We discuss the computational challenges associated with each version and illustrate the resulting methods on test problems from surveillance-evading path planning. We also include an example based on robotic navigation: a Mars rover that minimizes the expected time to target while accounting for the possibility of unobserved/incremental damages and dynamics-altering breakdowns.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e0ea32035f5732ebc13f1df5f3d70be5820746ea" target='_blank'>
-              Generalised BBGKY hierarchy for near-integrable dynamics
+          <td><a href="https://www.semanticscholar.org/paper/96c947b88c4459fcab4ac11d8b03e77f99a42182" target='_blank'>
+              Occasionally Observed Piecewise-deterministic Markov Processes
               </a>
             </td>
           <td>
-            Leonardo Biagetti, Maciej Lebek, M. Panfil, J. D. Nardis
+            Marissa Gee, Alexander Vladimirsky
           </td>
-          <td>2024-08-01</td>
+          <td>2024-08-02</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>19</td>
-        </tr>
-
-        <tr id="Symmetries play a pivotal role in our understanding of the properties of quantum many-body systems. While there are theorems and a well-established toolbox for systems in thermal equilibrium, much less is known about the role of symmetries and their connection to dynamics out of equilibrium. This arises due to the direct link between a system's thermal state and its Hamiltonian, which is generally not the case for nonequilibrium dynamics. Here we present a pathway to identify the effective symmetries and to extract them from data in nonequilibrium quantum many-body systems. Our approach is based on exact relations between correlation functions involving different numbers of spatial points, which can be viewed as nonequilibrium versions of (equal-time) Ward identities encoding the symmetries of the system. We derive symmetry witnesses, which are particularly suitable for the analysis of measured or simulated data at different snapshots in time. To demonstrate the potential of the approach, we apply our method to numerical and experimental data for a spinor Bose gas. We investigate the important question of a dynamical restoration of an explicitly broken symmetry of the Hamiltonian by the initial state. Remarkably, it is found that effective symmetry restoration can occur long before the system equilibrates. We also use the approach to define and identify spontaneous symmetry breaking far from equilibrium, which is of great relevance for applications to nonequilibrium phase transitions. Our work opens new avenues for the classification and analysis of quantum as well as classical many-body dynamics in a large variety of systems, ranging from ultracold quantum gases to cosmology.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8a8950d1ce041653ba3716007a86405364e34167" target='_blank'>
-              Extracting the symmetries of nonequilibrium quantum many-body systems
-              </a>
-            </td>
-          <td>
-            A. Mikheev, Viktoria Noel, Ido Siovitz, H. Strobel, M. Oberthaler, Jurgen Berges
-          </td>
-          <td>2024-07-25</td>
-          <td>ArXiv</td>
           <td>0</td>
-          <td>48</td>
         </tr>
 
-        <tr id="Large matrices arise in many machine learning and data analysis applications, including as representations of datasets, graphs, model weights, and first and second-order derivatives. Randomized Numerical Linear Algebra (RandNLA) is an area which uses randomness to develop improved algorithms for ubiquitous matrix problems. The area has reached a certain level of maturity; but recent hardware trends, efforts to incorporate RandNLA algorithms into core numerical libraries, and advances in machine learning, statistics, and random matrix theory, have lead to new theoretical and practical challenges. This article provides a self-contained overview of RandNLA, in light of these developments.">
+        <tr id="In this article we study if a Deep Learning technique can be used to obtain an approximated value of the Lyapunov exponents of a dynamical system. Moreover, we want to know if Machine Learning techniques are able, once trained, to provide the complete Lyapunov exponents spectrum with just single-variable time series. We train a Convolutional Neural Network and we use the resulting network to approximate the complete spectrum using the time series of just one variable from the studied systems (Lorenz system and coupled Lorenz system). The results are quite stunning as all the values are well approximated with only partial data. This strategy permits to speed up the complete analysis of the systems and also to study the hyperchaotic dynamics in the coupled Lorenz system.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/87ba4c0a0658c3c635c4a84120e5a3c8cd322fdd" target='_blank'>
-              Recent and Upcoming Developments in Randomized Numerical Linear Algebra for Machine Learning
+          <td><a href="https://www.semanticscholar.org/paper/09290aec6c4160820790c56611a3f3eca51095dc" target='_blank'>
+              Full Lyapunov Exponents spectrum with Deep Learning from single-variable time series
               </a>
             </td>
           <td>
-            Michal Derezi'nski, Michael W. Mahoney
+            C. Mayora-Cebollero, A. Mayora-Cebollero, 'Alvaro Lozano, Roberto Barrio
           </td>
-          <td>2024-06-17</td>
+          <td>2024-06-23</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
+          <td>1</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Motivated by the recent successful application of physics-informed neural networks (PINNs) to solve Boltzmann-type equations [S. Jin, Z. Ma, and K. Wu, J. Sci. Comput., 94 (2023), pp. 57], we provide a rigorous error analysis for PINNs in approximating the solution of the Boltzmann equation near a global Maxwellian. The challenge arises from the nonlocal quadratic interaction term defined in the unbounded domain of velocity space. Analyzing this term on an unbounded domain requires the inclusion of a truncation function, which demands delicate analysis techniques. As a generalization of this analysis, we also provide proof of the asymptotic preserving property when using micro-macro decomposition-based neural networks.">
+        <tr id="
+ Reservoir computing is an efficient artificial neural network for model-free prediction and analysis of dynamical systems time series. As a data-based method, the capacity of reservoir computing is stongly affected by the time sampling interval of training data. In this paper, taking Lorenz system as an example, we explore the influence of this sampling interval on the performance of reservoir computing in predicting chaotic sequences. When the sampling interval increases, the prediction capacity of reservoir computing is first enhanced then weakened, presenting a bell-shaped curve. By slightly revising the calculation method of the output matrix, the prediction performance of reservoir computing with small sampling interval can be improved. Furthermore, reservoir computing can learn and reproduce the state of chaotic system with a large time interval, which is almost five times larger than that of the classic fourth-order Runge-Kutta method. Our results show the capacity of reservoir computing in the applications where the time sampling intervals are constrained and laid the foundation for building a fast algorithm with larger time iteration steps.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/964863128ad956abcbc31dbcdc5eb8086a24f70d" target='_blank'>
-              Error estimates of physics-informed neural networks for approximating Boltzmann equation
+          <td><a href="https://www.semanticscholar.org/paper/2299dd61e3d42dbb604ec45370f99d03bbd6e6f9" target='_blank'>
+              Large sampling intervals for learning and predicting chaotic systems with reservoir computing
               </a>
             </td>
           <td>
-            E. Abdo, Lihui Chai, Ruimeng Hu, Xu Yang
+            Qingyan Xie, Zixiang Yan, Hui Zhao, Jian Gao, Jinghua Xiao
           </td>
-          <td>2024-07-11</td>
-          <td>ArXiv</td>
+          <td>2024-06-28</td>
+          <td>Journal of Physics A: Mathematical and Theoretical</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="None">
+        <tr id="Many problems in Physics and Chemistry are formulated as the minimization of a functional. Therefore, methods for solving these problems typically require differentiating maps whose input and/or output are functions -- commonly referred to as variational differentiation. Such maps are not addressed at the mathematical level by the chain rule, which underlies modern symbolic and algorithmic differentiation (AD) systems. Although there are algorithmic solutions such as tracing and reverse accumulation, they do not provide human readability and introduce strict programming constraints that bottleneck performance, especially in high-performance computing (HPC) environments. In this manuscript, we propose a new computer theoretic model of differentiation by combining the pullback of the $\mathbf{B}$ and $\mathbf{C}$ combinators from the combinatory logic. Unlike frameworks based on the chain rule, this model differentiates a minimal complete basis for the space of computable functions. Consequently, the model is capable of analytic backpropagation and variational differentiation while supporting complex numbers. To demonstrate the generality of this approach we build a system named CombDiff, which can differentiate nontrivial variational problems such as Hartree-Fock (HF) theory and multilayer perceptrons.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/57132863d898425b060495280068009b30321f05" target='_blank'>
-              A dynamical system analysis of bouncing cosmology with spatial curvature
+          <td><a href="https://www.semanticscholar.org/paper/4c640b0ba0b06a2a81e8f349b2681297670ab04e" target='_blank'>
+              Automating Variational Differentiation
               </a>
             </td>
           <td>
-            Soumya Chakraborty, Sudip Mishra, S. Chakraborty
+            Kangbo Li, Anil Damle
           </td>
-          <td>2024-07-01</td>
-          <td>General Relativity and Gravitation</td>
+          <td>2024-06-23</td>
+          <td>ArXiv</td>
+          <td>0</td>
           <td>0</td>
-          <td>29</td>
         </tr>
 
-        <tr id="The view that the laws of nature produce later states of the universe from earlier ones (prominently defended by Maudlin) faces difficult questions as to how the laws produce the future and whether that production is compatible with special relativity. This article grapples with those questions, arguing that the concerns can be overcome through a close analysis of the laws of classical mechanics and electromagnetism. The view that laws produce the future seems to require that the laws of nature take a certain form, fitting what Adlam has called"the time evolution paradigm."Making that paradigm precise, we might demand that there be temporally local dynamical laws that take properties of the present and the arbitrarily-short past as input, returning as output changes in such properties into the arbitrarily-short future. In classical mechanics, Newton's second law can be fit into this form if we follow a proposal from Easwaran and understand the acceleration that appears in the law to capture how velocity (taken to be a property of the present and the arbitrarily-short past) changes into the arbitrarily-short future. The dynamical laws of electromagnetism can be fit into this form as well, though because electromagnetism is a special relativistic theory we might require that the laws meet a higher standard: linking past light-cone to future light-cone. With some work, the laws governing the evolution of the vector and scalar potentials, as well as the evolution of charged matter, can be put in a form that meets this higher standard.">
+        <tr id="Stochastic systems are used to model a variety of phenomena in which noise plays an essential role. In these models, one potential goal is to determine if noise can induce transitions between states, and if so, to calculate the most probable escape path from an attractor. In the small noise limit, the Freidlin-Wentzell theory of large deviations provides a variational framework to calculate these paths. This work focuses on using large deviation theory to calculate such paths for stochastic gradient systems with non-gradient perturbations. While for gradient systems the most probable escape paths consist of time-reversed heteroclinic orbits, for general systems it can be a challenging calculation. By applying Melnikov theory to the resulting Euler-Lagrange equations recast in Hamiltonian form, we determine a condition for when the optimal escape path is the heteroclinic orbit for the perturbed system. We provide a numerical example to illustrate how the computed most probable escape path compares with the theoretical result.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c45f0f4e7ef06ebe118ead2656895ec1a436690e" target='_blank'>
-              How do Laws Produce the Future?
+          <td><a href="https://www.semanticscholar.org/paper/330a794bfa885f5551f29fba1960f92ebc6ccf55" target='_blank'>
+              Most probable escape paths in perturbed gradient systems
               </a>
             </td>
           <td>
-            C. Sebens
+            Katherine Slyman, Mackenzie Simper, John A Gemmer, Bjorn Sandstede
           </td>
-          <td>2024-06-28</td>
+          <td>2024-07-25</td>
           <td>ArXiv</td>
-          <td>1</td>
-          <td>9</td>
+          <td>0</td>
+          <td>7</td>
         </tr>
 
-        <tr id="The class of Constitutive Artificial Neural Networks (CANNs) represents a new approach of neural networks in the field of constitutive modeling. So far, CANNs have proven to be a powerful tool in predicting elastic and inelastic material behavior. However, the specification of inelastic constitutive artificial neural networks (iCANNs) to capture plasticity remains to be discussed. We present the extension and application of an iCANN to the inelastic phenomena of plasticity. This includes the prediction of a formulation for the elastic and plastic Helmholtz free energies, the inelastic flow rule, and the yield condition that defines the onset of plasticity. Thus, we learn four feed-forward networks in combination with a recurrent neural network and use the second Piola-Kirchhoff stress measure for training. The presented formulation captures both, associative and non-associative plasticity. In addition, the formulation includes kinematic hardening effects by introducing the plastic Helmholtz free energy. This opens the range of application to a wider class of materials. The capabilities of the presented framework are demonstrated by training on artificially generated data of models for perfect plasticity of von-Mises type, tension-compression asymmetry, and kinematic hardening. We observe already satisfactory results for training on one load case only while extremely precise agreement is found for an increase in load cases. In addition, the performance of the specified iCANN was validated using experimental data of X10CrMoVNb9-1 steel. Training has been performed on both, uniaxial tension and cyclic loading, separately and the predicted results are then validated on the opposing set. The results underline that the autonomously discovered material model is capable to describe and predict the underlying experimental data.">
+        <tr id="Overparameterized stochastic differential equation (SDE) models have achieved remarkable success in various complex environments, such as PDE-constrained optimization, stochastic control and reinforcement learning, financial engineering, and neural SDEs. These models often feature system evolution coefficients that are parameterized by a high-dimensional vector $\theta \in \mathbb{R}^n$, aiming to optimize expectations of the SDE, such as a value function, through stochastic gradient ascent. Consequently, designing efficient gradient estimators for which the computational complexity scales well with $n$ is of significant interest. This paper introduces a novel unbiased stochastic gradient estimator--the generator gradient estimator--for which the computation time remains stable in $n$. In addition to establishing the validity of our methodology for general SDEs with jumps, we also perform numerical experiments that test our estimator in linear-quadratic control problems parameterized by high-dimensional neural networks. The results show a significant improvement in efficiency compared to the widely used pathwise differentiation method: Our estimator achieves near-constant computation times, increasingly outperforms its counterpart as $n$ increases, and does so without compromising estimation variance. These empirical findings highlight the potential of our proposed methodology for optimizing SDEs in contemporary applications.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c789f65f0c019bfe98255a7c00f1555dc262f7ca" target='_blank'>
-              Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/6fc1545e20fb78c9271560d34a3512c20ad26286" target='_blank'>
+              An Efficient High-dimensional Gradient Estimator for Stochastic Differential Equations
               </a>
             </td>
           <td>
-            Birte Boes, Jaan‐Willem Simon, H. Holthusen
+            Shengbo Wang, Jose Blanchet, Peter Glynn
           </td>
-          <td>2024-07-27</td>
+          <td>2024-07-14</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>9</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Pretraining for partial differential equation (PDE) modeling has recently shown promise in scaling neural operators across datasets to improve generalizability and performance. Despite these advances, our understanding of how pretraining affects neural operators is still limited; studies generally propose tailored architectures and datasets that make it challenging to compare or examine different pretraining frameworks. To address this, we compare various pretraining methods without optimizing architecture choices to characterize pretraining dynamics on different models and datasets as well as to understand its scaling and generalization behavior. We find that pretraining is highly dependent on model and dataset choices, but in general transfer learning or physics-based pretraining strategies work best. In addition, pretraining performance can be further improved by using data augmentations. Lastly, pretraining is additionally beneficial when fine-tuning in scarce data regimes or when generalizing to downstream data similar to the pretraining distribution. Through providing insights into pretraining neural operators for physics prediction, we hope to motivate future work in developing and evaluating pretraining methods for PDEs.">
+        <tr id="Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a ``score function'' that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such ``discrete diffusion models'' (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the $d=1$ constrained Fredkin chain and the $d=2$ Ising model.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b775198af561b89e562f258af605c3daa577f748" target='_blank'>
-              Strategies for Pretraining Neural Operators
+          <td><a href="https://www.semanticscholar.org/paper/4033d59c9ab7aac9bd3ba446669a55ca00e0800c" target='_blank'>
+              Discrete generative diffusion models without stochastic differential equations: a tensor network approach
               </a>
             </td>
           <td>
-            Anthony Y. Zhou, Cooper Lorsung, AmirPouya Hemmasian, A. Farimani
+            Luke Causer, Grant M. Rotskoff, J. P. Garrahan
           </td>
-          <td>2024-06-12</td>
+          <td>2024-07-15</td>
           <td>ArXiv</td>
-          <td>1</td>
-          <td>33</td>
+          <td>0</td>
+          <td>54</td>
         </tr>
 
-        <tr id="We present an expansion of a many-body correlation function in a sum of pseudomodes - exponents with complex frequencies that encompass both decay and oscillations. We demonstrate that, typically, it is enough to take a few first terms of this infinite sum to obtain an excellent approximation to the correlation function at any time, with the large time behavior being determined solely by the first pseudomode. The pseudomode expansion emerges in the framework of the Heisenberg version of the recursion method. This method essentially solves Heisenberg equations in a Lanczos tridiagonal basis constructed in the Krylov space of a given observable. To obtain pseudomodes, we first add artificial dissipation satisfying the dissipative generalization of the universal operator growth hypothesis, and then take the limit of the vanishing dissipation strength. Fast convergence of the pseudomode expansion is facilitated by the localization in the Krylov space, which is generic in the presence of dissipation and can survive the limit of the vanishing dissipation strength. As an illustration, we apply the pseudomode expansion to calculate infinite-temperature autocorrelation functions in the quantum Ising and $XX$ spin-$1/2$ models on the square lattice.">
+        <tr id="In this study, we considered the problem of estimating epidemiological parameters based on physics-informed neural networks (PINNs). In practice, not all trajectory data corresponding to the population estimated by epidemic models can be obtained, and some observed trajectories are noisy. Learning PINNs to estimate unknown epidemiological parameters using such partial observations is challenging. Accordingly, we introduce the concept of algebraic observability into PINNs. The validity of the proposed PINN, named as an algebraically observable PINNs, in terms of estimation parameters and prediction of unobserved variables, is demonstrated through numerical experiments.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8c0e1c45eedb9a16b0066dded4a252c6974da710" target='_blank'>
-              Pseudomode expansion of many-body correlation functions
+          <td><a href="https://www.semanticscholar.org/paper/0f7cf742ff57aaaa10202e43c7d6149e073d6568" target='_blank'>
+              Estimate Epidemiological Parameters given Partial Observations based on Algebraically Observable PINNs
               </a>
             </td>
           <td>
-            Alexander Teretenkov, F. Uskov, Oleg Lychkovskiy
+            Mizuka Komatsu
           </td>
           <td>2024-07-17</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
-        </tr>
-
-        <tr id="The nonlinear filtering problem has enduringly been an active research topic in both academia and industry due to its ever-growing theoretical importance and practical significance. The main objective of nonlinear filtering is to infer the states of a nonlinear dynamical system of interest based on the available noisy measurements. In recent years, the advance of network communication technology has not only popularized the networked systems with apparent advantages in terms of installation, cost and maintenance, but also brought about a series of challenges to the design of nonlinear filtering algorithms, among which the communication constraint has been recognized as a dominating concern. In this context, a great number of investigations have been launched towards the networked nonlinear filtering problem with communication constraints, and many sample-based nonlinear filters have been developed to deal with the highly nonlinear and/or non-Gaussian scenarios. The aim of this paper is to provide a timely survey about the recent advances on the sample-based networked nonlinear filtering problem from the perspective of communication constraints. More specifically, we first review three important families of sample-based filtering methods known as the unscented Kalman filter, particle filter, and maximum correntropy filter. Then, the latest developments are surveyed with stress on the topics regarding incomplete/imperfect information, limited resources and cyber security. Finally, several challenges and open problems are highlighted to shed some lights on the possible trends of future research in this realm.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7b2ab547863c1e18aa730f1ca9040c34f915e81b" target='_blank'>
-              Nonlinear Filtering With Sample-Based Approximation Under Constrained Communication: Progress, Insights and Trends
-              </a>
-            </td>
-          <td>
-            Weihao Song, Zidong Wang, Zhongkui Li, Jianan Wang, Qing‐Long Han
-          </td>
-          <td>2024-07-01</td>
-          <td>IEEE/CAA Journal of Automatica Sinica</td>
           <td>0</td>
-          <td>27</td>
         </tr>
 
-        <tr id="Uncertainty-aware controllers that guarantee safety are critical for safety critical applications. Among such controllers, Control Barrier Functions (CBFs) based approaches are popular because they are fast, yet safe. However, most such works depend on Gaussian Processes (GPs) or MC-Dropout for learning and uncertainty estimation, and both approaches come with drawbacks: GPs are non-parametric methods that are slow, while MC-Dropout does not capture aleatoric uncertainty. On the other hand, modern Bayesian learning algorithms have shown promise in uncertainty quantification. The application of modern Bayesian learning methods to CBF-based controllers has not yet been studied. We aim to fill this gap by surveying uncertainty quantification algorithms and evaluating them on CBF-based safe controllers. We find that model variance-based algorithms (for example, Deep ensembles, MC-dropout, etc.) and direct estimation-based algorithms (such as DEUP) have complementary strengths. Algorithms in the former category can only estimate uncertainty accurately out-of-domain, while those in the latter category can only do so in-domain. We combine the two approaches to obtain more accurate uncertainty estimates both in- and out-of-domain. As measured by the failure rate of a simulated robot, this results in a safer CBF-based robot controller.">
+        <tr id="Identifying the causal relations between interested variables plays a pivotal role in representation learning as it provides deep insights into the dataset. Identifiability, as the central theme of this approach, normally hinges on leveraging data from multiple distributions (intervention, distribution shift, time series, etc.). Despite the exciting development in this field, a practical but often overlooked problem is: what if those distribution shifts happen sequentially? In contrast, any intelligence possesses the capacity to abstract and refine learned knowledge sequentially -- lifelong learning. In this paper, with a particular focus on the nonlinear independent component analysis (ICA) framework, we move one step forward toward the question of enabling models to learn meaningful (identifiable) representations in a sequential manner, termed continual causal representation learning. We theoretically demonstrate that model identifiability progresses from a subspace level to a component-wise level as the number of distributions increases. Empirically, we show that our method achieves performance comparable to nonlinear ICA methods trained jointly on multiple offline distributions and, surprisingly, the incoming new distribution does not necessarily benefit the identification of all latent variables.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9b8b25ad6df5d3bd294327053185a6ebb1b8f074" target='_blank'>
-              DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safety
+          <td><a href="https://www.semanticscholar.org/paper/d9dd025ff21a417d50c5564f864be35cbb2325c6" target='_blank'>
+              Continual Learning of Nonlinear Independent Representations
               </a>
             </td>
           <td>
-            Masoud Ataei, Vikas Dhiman
+            Boyang Sun, Ignavier Ng, Guan-Hong Chen, Yifan Shen, Qirong Ho, Kun Zhang
           </td>
-          <td>2024-06-30</td>
+          <td>2024-08-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>12</td>
         </tr>
 
-        <tr id="Validating safety-critical autonomous systems in high-dimensional domains such as robotics presents a significant challenge. Existing black-box approaches based on Markov chain Monte Carlo may require an enormous number of samples, while methods based on importance sampling often rely on simple parametric families that may struggle to represent the distribution over failures. We propose to sample the distribution over failures using a conditional denoising diffusion model, which has shown success in complex high-dimensional problems such as robotic task planning. We iteratively train a diffusion model to produce state trajectories closer to failure. We demonstrate the effectiveness of our approach on high-dimensional robotic validation tasks, improving sample efficiency and mode coverage compared to existing black-box techniques.">
+        <tr id="In this paper we introduce a Meshfree Variational Physics Informed Neural Network. It is a Variational Physics Informed Neural Network that does not require the generation of a triangulation of the entire domain and that can be trained with an adaptive set of test functions. In order to generate the test space we exploit an a posteriori error indicator and add test functions only where the error is higher. Four training strategies are proposed and compared. Numerical results show that the accuracy is higher than the one of a Variational Physics Informed Neural Network trained with the same number of test functions but defined on a quasi-uniform mesh.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/242ab76870b39bb8f1c8171690eb477f7170f167" target='_blank'>
-              Diffusion-Based Failure Sampling for Cyber-Physical Systems
+          <td><a href="https://www.semanticscholar.org/paper/8a9a2ceba8c6c319fce3b13aa5f1c315e14309ac" target='_blank'>
+              Meshfree Variational Physics Informed Neural Networks (MF-VPINN): an adaptive training strategy
               </a>
             </td>
           <td>
-            Harrison Delecki, Marc R. Schlichting, Mansur Arief, Anthony Corso, Marcell Vazquez-Chanlatte, Mykel J. Kochenderfer
+            S. Berrone, Moreno Pintore
           </td>
-          <td>2024-06-20</td>
+          <td>2024-06-28</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>16</td>
+          <td>23</td>
         </tr>
 
-        <tr id="Quantum mechanics is able to produce challenging behaviors even in the simplest situations. This is possible because of the important dynamical role that phase plays in the evolution of quantum systems, very similar, nonetheless, to effects observable in analogous optical systems. The present work focuses on how Bohmian mechanics proves to be a rather convenient theoretical framework to analyze phase-based phenomena, since the phase constitutes the central element in this hydrodynamical formulation of quantum mechanics. More specifically, it allows us to understand how spatial phase variations give rise to velocity fields that eventually rule the dynamical behavior of quantum systems, and that, when integrated in time locally (i.e., taking into account specific positions), they provide us with a neat local (point by point) description of the system evolution in the configuration space. Indeed, it will also be seen that this idea transcends the quantum realm and can be profitably used to describe the behavior of optical analogs with rather singular behaviors. With this purpose, two interesting phenomena that take place in free space are considered, namely, the self-acceleration and shape-invariance of Airy beams, and spontaneous self-focusing.">
+        <tr id="Over the course of four decades, model predictive control (MPC) has become one of the great success stories in systems and control. It has grown from its native habitat (chemical process control) into all domains of control applications—power and energy systems, mechatronics and robotics, as well as aerospace and aeronautics. Hence, in a modern systems and control curriculum, MPC triggers not so much the question of if it should be taught. In fact, industrial demand for and the continued research potential of MPC suggest that one should rather ask the Aristotelian 5W1H (what, when, where, why, who, and how?) about teaching MPC. This article presents insights into the 5Ws distilled from the results of a survey on teaching MPC conducted in the systems and control community. Moreover, the how is approached through blueprint suggestions for curricula for an undergraduate discrete-time linear-quadratic MPC course and for graduate courses covering the continuous-time nonlinear avenue and the learning-based route.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c0142e0cb3b8daeedf62b6b6c1e336cc21ef9694" target='_blank'>
-              Symmetries and singular behaviors with Bohmian trajectories
+          <td><a href="https://www.semanticscholar.org/paper/95cbb4bf5304c328ffa01fa4a5e73c270ccce7a8" target='_blank'>
+              Teaching Model Predictive Control: What, When, Where, Why, Who, and How? [Focus on Education]
               </a>
             </td>
           <td>
-            ´Angel S. Sanz
+            T. Faulwasser, Eric C. Kerrigan, Filip Logist, Sergio Lucia, M. Mönnigmann, Alessandra Parisio, M. S. Darup
           </td>
-          <td>2024-07-10</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>IEEE Control Systems</td>
           <td>0</td>
-          <td>1</td>
+          <td>29</td>
         </tr>
 
-        <tr id="Perceptual rivalry, where conflicting sensory information leads to alternating perceptions crucial for associated cognitive function, has attracted researcher's attention for long. Despite progresses being made, recent studies have revealed limitations and inconsistencies in our understanding across various rivalry contexts. We develop a unified physical framework, where perception undergoes a consecutive phase transition process encompassing different multi-state competitions. We reveal the underlying mechanisms of perceptual rivalry by identifying dominant switching paths among perceptual states and quantifying mean perceptual durations, switching frequencies, and proportions of different perceptions. We uncover the underlying nonequilibrium dynamics and thermodynamics by analyzing average nonequilibrium flux and entropy production rate, while associated time series irreversibility reflects the underlying nonequilibrium mechanism of perceptual rivalry and link thermodynamical results with neuro-electrophysiological experiments. Our framework provides a global and physical understanding of brain perception, which may go beyond cognitive science or psychology but embodies the connection with wider fields as decision-making.">
+        <tr id="Wild animals are commonly fitted with trackers that record their position through time, to learn about their behaviour. Broadly, statistical models for tracking data often fall into two categories: local models focus on describing small-scale movement decisions, and global models capture large-scale spatial distributions. Due to this dichotomy, it is challenging to describe mathematically how animals' distributions arise from their short-term movement patterns, and to combine data sets collected at different scales. We propose a multiscale model of animal movement and space use based on the underdamped Langevin process, widely used in statistical physics. The model is convenient to describe animal movement for three reasons: it is specified in continuous time (such that its parameters are not dependent on an arbitrary time scale), its speed and direction are autocorrelated (similarly to real animal trajectories), and it has a closed form stationary distribution that we can view as a model of long-term space use. We use the common form of a resource selection function for the stationary distribution, to model the environmental drivers behind the animal's movement decisions. We further increase flexibility by allowing movement parameters to be time-varying, e.g., to account for daily cycles in an animal's activity. We formulate the model as a state-space model and present a method of inference based on the Kalman filter. The approach requires discretising the continuous-time process, and we use simulations to investigate performance for various time resolutions of observation. The approach works well at fine resolutions, though the estimated stationary distribution tends to be too flat when time intervals between observations are very long.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fc441c92c5ed6177e25f25948db30fc79b328e33" target='_blank'>
-              Nonequilibrium dynamics and thermodynamics provide the underlying physical mechanism of the perceptual rivalry
+          <td><a href="https://www.semanticscholar.org/paper/9df6a9afdb8773bfa193d6bae41f91e4a44b70ca" target='_blank'>
+              Multiscale modelling of animal movement with persistent dynamics
               </a>
             </td>
           <td>
-            Yuxuan Wu, Liufang Xu, Jin Wang
+            T. Michelot
           </td>
-          <td>2024-06-29</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>6</td>
+          <td>14</td>
         </tr>
 
-        <tr id="In Clearing Up Mysteries -- The Original Goal (Maximum Entropy and Bayesian Methods: Cambridge, England, 1988 Springer, pp. 1-27) Jaynes derived Fick's Law for a dilute binary solution from Bayes' Theorem by considering, probabilistically, the motion of dilute solute molecules. Modifying Jaynes' prior, changing the frame of reference, and allowing for multicomponent systems, one can follow Jaynes' logic to arrive at several expressions for the diffusion coefficient that are widely used in application to solvent-polymer systems. These results, however, do not generally satisfy required conditions over the full concentration range. This limitation is resolved by considering the joint motion of all components in the solution with the inclusion of known physical constraints. Doing so, one arrives at a new set of constitutive equations for binary and multicomponent diffusion that include Darken's form as a limit and provide means to characterize inter-species correlations, removing the need for the ad hoc modifications of the thermodynamic term or substitution of bulk compositions with local compositions that have been proposed in the literature. In binary systems, the Bayesian expression for the mutual diffusion coefficient provides explicit limits on non-ideal mutual diffusion behavior, given component self-diffusion coefficients, that can be attributed to inter-species correlation versus stronger intra- and inter-species clustering. Applications of the model to published data for a set of binary systems are presented, along with pointers to further directions for research.">
+        <tr id="The ubiquity of multiscale interactions in complex systems is well-recognized, with development and heredity serving as a prime example of how processes at different temporal scales influence one another. This work introduces a novel multiscale state-space model to explore the dynamic interplay between systems interacting across different time scales, with feedback between each scale. We propose a Bayesian learning framework to estimate unknown states by learning the unknown process noise covariances within this multiscale model. We develop a Particle Gibbs with Ancestor Sampling (PGAS) algorithm for inference and demonstrate through simulations the efficacy of our approach.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/744d4dcaef77a8f1280b85645d110b5a7e2e1c43" target='_blank'>
-              Fickian Insights Using Probability Theory as Logic
+          <td><a href="https://www.semanticscholar.org/paper/6a4108fef8d82f9c5401baeb3eaafc732ca1c2a3" target='_blank'>
+              Bayesian Learning in a Nonlinear Multiscale State-Space Model
               </a>
             </td>
           <td>
-            Peter E. Price
+            Nayely V'elez-Cruz, Manfred D. Laubichler
           </td>
-          <td>2024-06-25</td>
+          <td>2024-08-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>1</td>
         </tr>
 
-        <tr id="In this article we study if a Deep Learning technique can be used to obtain an approximated value of the Lyapunov exponents of a dynamical system. Moreover, we want to know if Machine Learning techniques are able, once trained, to provide the complete Lyapunov exponents spectrum with just single-variable time series. We train a Convolutional Neural Network and we use the resulting network to approximate the complete spectrum using the time series of just one variable from the studied systems (Lorenz system and coupled Lorenz system). The results are quite stunning as all the values are well approximated with only partial data. This strategy permits to speed up the complete analysis of the systems and also to study the hyperchaotic dynamics in the coupled Lorenz system.">
+        <tr id="
+
+
+Ecosystems contain numerous species interacting with each other and the environment. However, data on all relevant state variables is rarely available, hampering inference and prediction. Empirical dynamic modelling (EDM) is a valuable tool for prediction, inference and control in such partially observed systems.
+
+However, EDM typically assumes that the available time series are observed without error. Failing to account for observation noise strongly biases estimates of Lyapunov exponents and reduces forecast accuracy. To address this limitation, we propose incorporating EDM into a hidden Markov framework and using an iterative scheme based on the expectation maximization (EM) algorithm to obtain filtered state and parameter estimates.
+
+We evaluate the performance of this approach on several simulated dynamical systems with a range of additive noise levels, as well as on insect population time series.
+
+Accounting for observation noise improved accuracy of population forecasts and estimates of Lyapunov exponents (LE) over a wide range of noise levels relevant to ecological time series.
+
+">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/09290aec6c4160820790c56611a3f3eca51095dc" target='_blank'>
-              Full Lyapunov Exponents spectrum with Deep Learning from single-variable time series
+          <td><a href="https://www.semanticscholar.org/paper/4e9c4d6519c0328c66d02635359f84c4d6cf2f4d" target='_blank'>
+              Accounting for observation noise in equation‐free forecasting: The hidden‐Markov S‐map
               </a>
             </td>
           <td>
-            C. Mayora-Cebollero, A. Mayora-Cebollero, 'Alvaro Lozano, Roberto Barrio
+            Dylan Esguerra, Stephan B. Munch
           </td>
-          <td>2024-06-23</td>
-          <td>ArXiv</td>
-          <td>1</td>
+          <td>2024-07-01</td>
+          <td>Methods in Ecology and Evolution</td>
+          <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="Trajectory inference seeks to recover the temporal dynamics of a population from snapshots of its (uncoupled) temporal marginals, i.e. where observed particles are not tracked over time. Lavenant et al. arXiv:2102.09204 addressed this challenging problem under a stochastic differential equation (SDE) model with a gradient-driven drift in the observed space, introducing a minimum entropy estimator relative to the Wiener measure. Chizat et al. arXiv:2205.07146 then provided a practical grid-free mean-field Langevin (MFL) algorithm using Schr\"odinger bridges. Motivated by the overwhelming success of observable state space models in the traditional paired trajectory inference problem (e.g. target tracking), we extend the above framework to a class of latent SDEs in the form of observable state space models. In this setting, we use partial observations to infer trajectories in the latent space under a specified dynamics model (e.g. the constant velocity/acceleration models from target tracking). We introduce PO-MFL to solve this latent trajectory inference problem and provide theoretical guarantees by extending the results of arXiv:2102.09204 to the partially observed setting. We leverage the MFL framework of arXiv:2205.07146, yielding an algorithm based on entropic OT between dynamics-adjusted adjacent time marginals. Experiments validate the robustness of our method and the exponential convergence of the MFL dynamics, and demonstrate significant outperformance over the latent-free method of arXiv:2205.07146 in key scenarios.">
+        <tr id="In this work, we introduce a novel learning-based controller tailored for autonomous control of a batch-type precipitation process involving calcium and magnesium carbonates. The process takes in fluid containing valuable materials such as Ca+2and Mg+2 ions, along with impurities and seed particles, to facilitate the sequential precipitation of these ions into their respective carbonates. The controller's goal is to attain a specified size of the precipitated particles under different process uncertainties. Here the residence time, i.e. the time allowed for the ions to remain in fluid phase, is used as the manipulation variable. The controller is designed as a solution to a stochastic optimal control problem and implemented using machine learning techniques. For the prediction model, we use convolutional neural networks (CNN) and for the control synthesis, we use a type of recurrent neural networks (RNNs). The designed control is learnable, adaptable to varying process dynamics and robust to random disturbances in the process, thus resulting in a learnable adaptive, and robust controller (LARC). The effectiveness of LARC is validated through different simulation-based tests.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/00a1683e0adbd5e56aa4f83d49091c5542d29179" target='_blank'>
-              Partially Observed Trajectory Inference using Optimal Transport and a Dynamics Prior
+          <td><a href="https://www.semanticscholar.org/paper/2ca52c12e0ce9a97c03f851037abfed99e3a3847" target='_blank'>
+              Learnable Adaptive and Robust Controller for a Two Particle Carbonate Precipitation Process
               </a>
             </td>
           <td>
-            Anming Gu, Edward Chien, K. Greenewald
+            Mikhail Kakanov, S. Hiremath, Andreas Voigt, Kai Sundmacher, N. Bajçinca
           </td>
-          <td>2024-06-11</td>
-          <td>ArXiv</td>
+          <td>2024-06-25</td>
+          <td>2024 European Control Conference (ECC)</td>
           <td>0</td>
-          <td>20</td>
+          <td>15</td>
         </tr>
 
-        <tr id="In this study, we employ analytical and numerical techniques to examine a phase transition model with moving boundaries. The model displays two relevant spatial scales pointing out to a macroscopic phase and a microscopic phase, interacting on disjoint inclusions. The shrinkage or the growth of the inclusions is governed by a modified Gibbs-Thomson law depending on the macroscopic temperature, but without accessing curvature information. We use the Hanzawa transformation to transform the problem onto a fixed reference domain. Then a fixed-point argument is employed to demonstrate the well-posedness of the system for a finite time interval. Due to the model's nonlinearities and the macroscopic parameters, which are given by differential equations that depend on the size of the inclusions, the problem is computationally expensive to solve numerically. We introduce a precomputing approach that solves multiple cell problems in an offline phase and uses an interpolation scheme afterward to determine the needed parameters. Additionally, we propose a semi-implicit time-stepping method to resolve the nonlinearity of the problem. We investigate the errors of both the precomputing and time-stepping procedures and verify the theoretical results via numerical simulations.">
+        <tr id="Compartment models with delay terms are widely used across a range of disciplines. The motivation to include delay terms varies across different contexts. In epidemiological and pharmacokinetic models, the delays are often used to represent an incubation period. In this work, we derive a compartment model with delay terms from an underlying non-Markov stochastic process. Delay terms arise when waiting times are drawn from a delay exponential distribution. This stochastic process approach allows us to preserve the physicality of the model, gaining understanding into the conditions under which delay terms can arise. By providing the conditions under which the delay exponential function is a probability distribution, we establish a critical value for the delay terms. An exact stochastic simulation method is introduced for the generalized model, enabling us to utilize the simulation in scenarios where intrinsic stochasticity is significant, such as when the population size is small. We illustrate the applications of the model and validate our simulation algorithm on examples drawn from epidemiology and pharmacokinetics.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d908e703e8f09b2c3874e3f73ac0a92003566cae" target='_blank'>
-              Precomputing approach for a two-scale phase transition model
+          <td><a href="https://www.semanticscholar.org/paper/15bad9e29f43321e2682f7822900b1143d36ab9c" target='_blank'>
+              Delay compartment models from a stochastic process
               </a>
             </td>
           <td>
-            Michael Eden, T. Freudenberg, Adrian Muntean
+            C. Angstmann, A. V. McGann, Zhuang Xu
           </td>
-          <td>2024-07-31</td>
+          <td>2024-06-25</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
+          <td>1</td>
+          <td>16</td>
         </tr>
 
-        <tr id="
- Reservoir computing is an efficient artificial neural network for model-free prediction and analysis of dynamical systems time series. As a data-based method, the capacity of reservoir computing is stongly affected by the time sampling interval of training data. In this paper, taking Lorenz system as an example, we explore the influence of this sampling interval on the performance of reservoir computing in predicting chaotic sequences. When the sampling interval increases, the prediction capacity of reservoir computing is first enhanced then weakened, presenting a bell-shaped curve. By slightly revising the calculation method of the output matrix, the prediction performance of reservoir computing with small sampling interval can be improved. Furthermore, reservoir computing can learn and reproduce the state of chaotic system with a large time interval, which is almost five times larger than that of the classic fourth-order Runge-Kutta method. Our results show the capacity of reservoir computing in the applications where the time sampling intervals are constrained and laid the foundation for building a fast algorithm with larger time iteration steps.">
+        <tr id="Modern climate projections often suffer from inadequate spatial and temporal resolution due to computational limitations, resulting in inaccurate representations of sub-grid processes. A promising technique to address this is the Multiscale Modeling Framework (MMF), which embeds a kilometer-resolution cloud-resolving model within each atmospheric column of a host climate model to replace traditional convection and cloud parameterizations. Machine learning (ML) offers a unique opportunity to make MMF more accessible by emulating the embedded cloud-resolving model and reducing its substantial computational cost. Although many studies have demonstrated proof-of-concept success of achieving stable hybrid simulations, it remains a challenge to achieve near operational-level success with real geography and comprehensive variable emulation that includes, for example, explicit cloud condensate coupling. In this study, we present a stable hybrid model capable of integrating for at least 5 years with near operational-level complexity, including real geography, seasonality, explicit cloud condensate predictions, and land coupling. Our model demonstrates skillful online performance in metrics such as 5-year zonal mean biases compared to previous MMF emulation studies. The monthly error against reference MMF simulations with the same initial condition approaches the fundamental predictability limit. Key factors contributing to our online performance include an expressive U-Net architecture, additional input features that include large-scale forcings and convection memory, and physical thermodynamic constraints for microphysics. With microphysical constraints mitigating unrealistic cloud formation, our work is the first to demonstrate realistic multi-year cloud condensate climatology under the MMF framework. Our work showcases ML parameterization's potential for operational-level climate simulations.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2299dd61e3d42dbb604ec45370f99d03bbd6e6f9" target='_blank'>
-              Large sampling intervals for learning and predicting chaotic systems with reservoir computing
+          <td><a href="https://www.semanticscholar.org/paper/71dfebd2303c30bf8e52df7f42375cda87b276cf" target='_blank'>
+              Stable Machine-Learning Parameterization of Subgrid Processes with Real Geography and Full-physics Emulation
               </a>
             </td>
           <td>
-            Qingyan Xie, Zixiang Yan, Hui Zhao, Jian Gao, Jinghua Xiao
+            Zeyuan Hu, Akshay Subramaniam, Zhiming Kuang, Jerry Lin, Sungduk Yu, Walter M. Hannah, Noah D. Brenowitz, Josh Romero, Michael S. Pritchard
           </td>
           <td>2024-06-28</td>
-          <td>Journal of Physics A: Mathematical and Theoretical</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Overparameterized stochastic differential equation (SDE) models have achieved remarkable success in various complex environments, such as PDE-constrained optimization, stochastic control and reinforcement learning, financial engineering, and neural SDEs. These models often feature system evolution coefficients that are parameterized by a high-dimensional vector $\theta \in \mathbb{R}^n$, aiming to optimize expectations of the SDE, such as a value function, through stochastic gradient ascent. Consequently, designing efficient gradient estimators for which the computational complexity scales well with $n$ is of significant interest. This paper introduces a novel unbiased stochastic gradient estimator--the generator gradient estimator--for which the computation time remains stable in $n$. In addition to establishing the validity of our methodology for general SDEs with jumps, we also perform numerical experiments that test our estimator in linear-quadratic control problems parameterized by high-dimensional neural networks. The results show a significant improvement in efficiency compared to the widely used pathwise differentiation method: Our estimator achieves near-constant computation times, increasingly outperforms its counterpart as $n$ increases, and does so without compromising estimation variance. These empirical findings highlight the potential of our proposed methodology for optimizing SDEs in contemporary applications.">
+        <tr id="This paper studies the stability and convergence properties of a class of multi-agent concurrent learning (CL) algorithms with momentum and restart. Such algorithms can be integrated as part of the estimation pipelines of data-enabled multi-agent control systems to enhance transient performance while maintaining stability guarantees. However, characterizing restarting policies that yield stable behaviors in decentralized CL systems, especially when the network topology of the communication graph is directed, has remained an open problem. In this paper, we provide an answer to this problem by synergistically leveraging tools from graph theory and hybrid dynamical systems theory. Specifically, we show that under a cooperative richness condition on the overall multi-agent system's data, and by employing coordinated periodic restart with a frequency that is tempered by the level of asymmetry of the communication graph, the resulting decentralized dynamics exhibit robust asymptotic stability properties, characterized in terms of input-to-state stability bounds, and also achieve a desirable transient performance. To demonstrate the practical implications of the theoretical findings, three applications are also presented: cooperative parameter estimation over networks with private data sets, cooperative model-reference adaptive control, and cooperative data-enabled feedback optimization of nonlinear plants.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6fc1545e20fb78c9271560d34a3512c20ad26286" target='_blank'>
-              An Efficient High-dimensional Gradient Estimator for Stochastic Differential Equations
+          <td><a href="https://www.semanticscholar.org/paper/567d4ebaa08c236655c7c5193532c8e7f8713fc7" target='_blank'>
+              Decentralized Concurrent Learning with Coordinated Momentum and Restart
               </a>
             </td>
           <td>
-            Shengbo Wang, Jose Blanchet, Peter Glynn
+            Daniel E. Ochoa, Muhammad U. Javed, Xudong Chen, Jorge I. Poveda
           </td>
-          <td>2024-07-14</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Stochastic systems are used to model a variety of phenomena in which noise plays an essential role. In these models, one potential goal is to determine if noise can induce transitions between states, and if so, to calculate the most probable escape path from an attractor. In the small noise limit, the Freidlin-Wentzell theory of large deviations provides a variational framework to calculate these paths. This work focuses on using large deviation theory to calculate such paths for stochastic gradient systems with non-gradient perturbations. While for gradient systems the most probable escape paths consist of time-reversed heteroclinic orbits, for general systems it can be a challenging calculation. By applying Melnikov theory to the resulting Euler-Lagrange equations recast in Hamiltonian form, we determine a condition for when the optimal escape path is the heteroclinic orbit for the perturbed system. We provide a numerical example to illustrate how the computed most probable escape path compares with the theoretical result.">
+        <tr id="This paper is concerned with the fundamental limits of nonlinear dynamical system learning from input-output traces. Specifically, we show that recurrent neural networks (RNNs) are capable of learning nonlinear systems that satisfy a Lipschitz property and forget past inputs fast enough in a metric-entropy optimal manner. As the sets of sequence-to-sequence maps realized by the dynamical systems we consider are significantly more massive than function classes generally considered in deep neural network approximation theory, a refined metric-entropy characterization is needed, namely in terms of order, type, and generalized dimension. We compute these quantities for the classes of exponentially-decaying and polynomially-decaying Lipschitz fading-memory systems and show that RNNs can achieve them.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/330a794bfa885f5551f29fba1960f92ebc6ccf55" target='_blank'>
-              Most probable escape paths in perturbed gradient systems
+          <td><a href="https://www.semanticscholar.org/paper/14056322161789dd48312016e9d0e76682856a25" target='_blank'>
+              Metric-Entropy Limits on Nonlinear Dynamical System Learning
               </a>
             </td>
           <td>
-            Katherine Slyman, Mackenzie Simper, John A Gemmer, Bjorn Sandstede
+            Yang Pan, Clemens Hutter, Helmut Bölcskei
           </td>
-          <td>2024-07-25</td>
+          <td>2024-07-01</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Many problems in Physics and Chemistry are formulated as the minimization of a functional. Therefore, methods for solving these problems typically require differentiating maps whose input and/or output are functions -- commonly referred to as variational differentiation. Such maps are not addressed at the mathematical level by the chain rule, which underlies modern symbolic and algorithmic differentiation (AD) systems. Although there are algorithmic solutions such as tracing and reverse accumulation, they do not provide human readability and introduce strict programming constraints that bottleneck performance, especially in high-performance computing (HPC) environments. In this manuscript, we propose a new computer theoretic model of differentiation by combining the pullback of the $\mathbf{B}$ and $\mathbf{C}$ combinators from the combinatory logic. Unlike frameworks based on the chain rule, this model differentiates a minimal complete basis for the space of computable functions. Consequently, the model is capable of analytic backpropagation and variational differentiation while supporting complex numbers. To demonstrate the generality of this approach we build a system named CombDiff, which can differentiate nontrivial variational problems such as Hartree-Fock (HF) theory and multilayer perceptrons.">
+        <tr id="Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For such liquid-metal dealloying (LMD) process, phase field models have been developed. However, the governing equations often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, stiffness in the PDEs requires an extremely small time steps (e.g. $10^{-12}$ or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose U-Shaped Adaptive Fourier Neural Operators (U-AFNO), a machine learning (ML) model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g. the deformation of the liquid-metal interface) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in-spite of the chaotic nature of LMD. Our model reproduces the key micro-structure statistics and QoIs with a level of accuracy on-par with the high-fidelity numerical solver. We also investigate the opportunity of using hybrid simulations, in which we alternate forward leap in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4c640b0ba0b06a2a81e8f349b2681297670ab04e" target='_blank'>
-              Automating Variational Differentiation
+          <td><a href="https://www.semanticscholar.org/paper/868bad8571187ae2f328db235d6feb8d496140d9" target='_blank'>
+              Accelerating Phase Field Simulations Through a Hybrid Adaptive Fourier Neural Operator with U-Net Backbone
               </a>
             </td>
           <td>
-            Kangbo Li, Anil Damle
+            Christophe Bonneville, N. Bieberdorf, Arun Hegde, Mark Asta, H. Najm, Laurent Capolungo, C. Safta
           </td>
-          <td>2024-06-23</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>44</td>
         </tr>
 
-        <tr id="Oscillatory behaviour underpins many essential biological functions and energy is required to sustain oscillation. In this paper, energy-based modelling of biochemical systems using the bond graph approach is combined with classical feedback control theory to give a novel approach to the analysis, and potentially synthesis, of biochemical oscillators. It is shown that oscillation is dependent on the interplay between active and passive feedback and this interplay is formalised using classical frequency-response analysis of feedback systems. In particular, the phase margin is suggested as a simple scalar indicator of the presence or absence of oscillations; it is shown how this indicator can be used to investigate the effect of both the structure and parameters of biochemical system on oscillation. It follows that the combination of classical feedback control theory and the bond graph approach to systems biology gives a novel analysis and design methodology for biochemical oscillators. The approach is illustrated using an introductory example similar to the Goodwin oscillator, the Sel’kov model of Glycolytic Oscillations and the Repressilator.">
+        <tr id="Data-driven deep learning models are on the verge of transforming global weather forecasting. It is an open question if this success can extend to climate modeling, where long inference rollouts and data complexity pose significant challenges. Here, we present the first conditional generative model able to produce global climate ensemble simulations that are accurate and physically consistent. Our model runs at 6-hourly time steps and is shown to be stable for 10-year-long simulations. Our approach beats relevant baselines and nearly reaches a gold standard for successful climate model emulation. We discuss the key design choices behind our dynamics-informed diffusion model-based approach which enables this significant step towards efficient, data-driven climate simulations that can help us better understand the Earth and adapt to a changing climate.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3a36b9fb2552ca9bf78bb6bf02aa0e381a3d8141" target='_blank'>
-              Energy-based Analysis of Biochemical Oscillators Using Bond Graphs and Linear Control Theory
+          <td><a href="https://www.semanticscholar.org/paper/d369ffa4e13e39e6b7c4b96ff3ad94b4aa9a3c23" target='_blank'>
+              Probabilistic Emulation of a Global Climate Model with Spherical DYffusion
               </a>
             </td>
           <td>
-            P. Gawthrop, Michael Pan
+            Salva Rühling Cachay, Brian Henn, Oliver Watt‐Meyer, Christopher S. Bretherton, Rose Yu
           </td>
-          <td>2024-06-09</td>
-          <td>bioRxiv</td>
+          <td>2024-06-21</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>43</td>
+          <td>11</td>
         </tr>
 
-        <tr id="Parameter identifiability is an important aspect of parameter estimation of dynamic system modelling. Several methods exist to determine identifiability of parameter sets using the model definition and analysis of experimental data. There is also the possibility of some parameters being independently unidentifiable but forming identifiable parameter combinations. These identifiable parameter combinations are useful in model reparameterisation to estimate parameters experimentally. Multiple numerical and algebraic methods exist to detect identifiable parameter combinations of dynamic system models represented as ordinary differential equations (ODE). Local identifiability analysis of hybrid system models are available in the literature. However, methods for structural identifiability analysis and identifiable combination detection for hybrid systems are not explored. Here, we have developed a parameter identifiable combination detection method for non-linear hybrid systems along with ODE systems using an SMT based parameter space exploration method. For higher dimensional systems and larger parameter space, SMT based approaches may easily become computationally intractable. This problem has been mitigated to a large extent by heuristically limiting the parameter space to be explored, using Gaussian process regression and gradient based approaches. The developed method has been demonstrated for some simple hybrid models, biochemical models of ODE systems and non-linear hybrid systems.">
+        <tr id="Analyzing complex experimental data with multiple parameters is challenging. We propose using Singular Value Decomposition (SVD) as an effective solution. This method, demonstrated through real experimental data analysis, surpasses conventional approaches in understanding complex physics data. Singular values and vectors distinguish and highlight various physical mechanisms and scales, revealing previously challenging elements. SVD emerges as a powerful tool for navigating complex experimental landscapes, showing promise for diverse experimental measurements.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0b71e8c79446f13006506dfdbfeaeb54816a6399" target='_blank'>
-              SMT based parameter identifiable combination detection for non-linear continuous and hybrid dynamics
+          <td><a href="https://www.semanticscholar.org/paper/24e7da06892289a90ca7ca4e5171ea48a7012501" target='_blank'>
+              Unraveling Complexity: Singular Value Decomposition in Complex Experimental Data Analysis
               </a>
             </td>
           <td>
-            Devleena Ghosh, C. Mandal
+            Judith F. Stein, Aviad Frydman, R. Berkovits
           </td>
-          <td>2024-06-07</td>
-          <td>Formal Aspects of Computing</td>
+          <td>2024-07-23</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>6</td>
+          <td>23</td>
         </tr>
 
-        <tr id="In this paper, we extend our previous work on a simplified model of the nervous system by solving the general optimization problem for the evolutionary cost of the nervous system. This optimization takes into account constraints on the scales of membrane potential kinetics and sensory response function to ensure finite, biologically plausible solutions. Our analysis reduces the variational problem to a system of two integro-differential equations, which we solve asymptotically using series expansions. This study confirms the emergence of sharp finite neuronal spikes and robust sensory and motor response functions as evolutionarily optimal solutions. We note that, in principle, alternative evolutionary solutions with different biophysical interpretations might exist for this optimization problem. This work provides a rigorous mathematical framework bridging evolutionary optimization with the fundamental properties of nervous systems.">
+        <tr id="The spin-vector Monte Carlo model is widely used as a benchmark for the classicality of quantum annealers but severely restricts the time evolution. The spin-vector Langevin (SVL) model has been proposed and tested as an alternative, closely reproducing the real-time dynamics of physical quantum annealers such as D-Wave machines in the dissipative regime. We investigate the SVL annealing dynamics of classical O(2) rotors on regular graphs, identifying universal features in the nonequilibrium dynamics when changing the range of interactions and the topology of the graph. Regular graphs with low connectance or edge density exhibit universal scaling dynamics consistent with the Kibble-Zurek mechanism, which leads to a power-law dependence of the density of defects and the residual energy as a function of the annealing time. As the interaction range is increased, the power-law scaling is suppressed, and an exponential scaling with the annealing time sets in. Our results establish a universal breakdown of the Kibble-Zurek mechanism in classical systems characterized by long-range interactions, in sharp contrast with previous findings in the quantum domain.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7efdfee978d2816c051990a2888f79b2d6828bae" target='_blank'>
-              Simplest Model of Nervous System. IV. General Solution
+          <td><a href="https://www.semanticscholar.org/paper/e358e334c41ef5944c2b2f71d0941cafc762ea6d" target='_blank'>
+              Annealing Dynamics of Regular Rotor Networks: Universality and Its Breakdown
               </a>
             </td>
           <td>
-            Anton V. Sinitskiy
+            Andr'as Grabarits, Gaetano Sammartino, Adolfo del Campo
           </td>
-          <td>2024-07-13</td>
-          <td>bioRxiv</td>
+          <td>2024-07-12</td>
+          <td>ArXiv</td>
           <td>0</td>
           <td>3</td>
         </tr>
 
-        <tr id="In this work, we explore the numerical solution of geometric shape optimization problems using neural network-based approaches. This involves minimizing a numerical criterion that includes solving a partial differential equation with respect to a domain, often under geometric constraints like constant volume. Our goal is to develop a proof of concept using a flexible and parallelizable methodology to tackle these problems. We focus on a prototypal problem: minimizing the so-called Dirichlet energy with respect to the domain under a volume constraint, involving a Poisson equation in $\mathbb R^2$. We use physics-informed neural networks (PINN) to approximate the Poisson equation's solution on a given domain and represent the shape through a neural network that approximates a volume-preserving transformation from an initial shape to an optimal one. These processes are combined in a single optimization algorithm that minimizes the Dirichlet energy. One of the significant advantages of this approach is its parallelizable nature, which makes it easy to handle the addition of parameters. Additionally, it does not rely on shape derivative or adjoint calculations. Our approach is tested on Dirichlet and Robin boundary conditions, parametric right-hand sides, and extended to Bernoulli-type free boundary problems. The source code for solving the shape optimization problem is open-source and freely available.">
+        <tr id="This work addresses the synthesis of optimal feedback control laws via machine learning. In particular, the Averaged Feedback Learning Scheme (AFLS) and a data driven method are considered. Hypotheses for each method ensuring the convergence of the evaluation of the objective function of the underlying control problem at the obtained feedback-laws towards the optimal value function are provided. These hypotheses are connected to the regularity of the value function and the stability of the dynamics. In the case of AFLS these hypotheses only require H\"older continuity of the value function, whereas for the data driven method the value function must be at least $C^2$. It is demonstrated that these methods are connected via their optimality conditions. Additionally, numerical experiments are provided by applying both methods to a family control problems, parameterized by a positive real number which controls the regularity of the value function. For small parameters the value function is smooth and in contrast for large parameters it is non-differentiable, but semi-concave. The results of the experiments indicate that both methods have a similar performance for the case that the value function is smooth. On the other hand, if the value function is not differentiable, AFLS has a better performance which is consistent with the obtained convergence results.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eb177a71238803ba9eff09921802eff318b55cec" target='_blank'>
-              Volume-preserving physics-informed geometric shape optimization of the Dirichlet energy
+          <td><a href="https://www.semanticscholar.org/paper/307b109ee8daf5810e48f9fba58490e24a131f80" target='_blank'>
+              Convergence of machine learning methods for feedback control laws: averaged feedback learning scheme and data driven method
               </a>
             </td>
           <td>
-            Amaury B'elieres--Frendo, Emmanuel Franck, Victor Michel-Dansac, Yannick Privat
+            Karl Kunisch, Donato V'asquez-Varas
           </td>
-          <td>2024-07-26</td>
+          <td>2024-07-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>6</td>
+          <td>2</td>
         </tr>
 
-        <tr id="The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.">
+        <tr id="Predicting the trajectories of systems with unknown dynamics (\textit{i.e.} the governing rules) is crucial in various research fields, including physics and biology. This challenge has gathered significant attention from diverse communities. Most existing works focus on learning fixed system dynamics within one single system. However, real-world applications often involve multiple systems with different types of dynamics or evolving systems with non-stationary dynamics (dynamics shifts). When data from those systems are continuously collected and sequentially fed to machine learning models for training, these models tend to be biased toward the most recently learned dynamics, leading to catastrophic forgetting of previously observed/learned system dynamics. To this end, we aim to learn system dynamics via continual learning. Specifically, we present a novel framework of Mode-switching Graph ODE (MS-GODE), which can continually learn varying dynamics and encode the system-specific dynamics into binary masks over the model parameters. During the inference stage, the model can select the most confident mask based on the observational data to identify the system and predict future trajectories accordingly. Empirically, we systematically investigate the task configurations and compare the proposed MS-GODE with state-of-the-art techniques. More importantly, we construct a novel benchmark of biological dynamic systems, featuring diverse systems with disparate dynamics and significantly enriching the research field of machine learning for dynamic systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/530b26ee44d4d565ee8661da86e03ef1f473385a" target='_blank'>
-              Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures
+          <td><a href="https://www.semanticscholar.org/paper/cb4045f3e6f4dfdaceedc6d8a70fc7a232722b3e" target='_blank'>
+              Learning System Dynamics without Forgetting
               </a>
             </td>
           <td>
-            S. Sanborn, Johan Mathe, Mathilde Papillon, Domas Buracas, Hansen Lillemark, Christian Shewmake, Abby Bertics, Xavier Pennec, Nina Miolane
+            Xikun Zhang, Dongjin Song, Yushan Jiang, Yixin Chen, Dacheng Tao
           </td>
-          <td>2024-07-12</td>
+          <td>2024-06-30</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>5</td>
         </tr>
 
-        <tr id="Among binary asteroids, (35107) 1991VH stands out as unique given the likely chaotic rotation within its secondary component. The source of this excited dynamical state is unknown. In this work we demonstrate that a past close encounter with Earth could have provided the necessary perturbation to allow the natural internal dynamics, characterized by spin-orbit coupling, to evolve the system into its current dynamical state. In this hypothesis, the secondary of 1991VH was previously in a classical 1:1 spin-orbit resonance with an orbit period likely between 28-35 hours before being perturbed by an Earth encounter within $\sim80,000$ km. We find if the energy dissipation within the secondary is relatively inefficient, this excited dynamical state could persist to today and produce the observed ground-based measurements. Coupled with the orbital history of 1991VH, we can then place a constraint on the tidal dissipation parameters of the secondary.">
+        <tr id="Detecting and quantifying causality is a focal topic in the fields of science, engineering, and interdisciplinary studies. However, causal studies on non-intervention systems attract much attention but remain extremely challenging. To address this challenge, we propose a framework named Interventional Dynamical Causality (IntDC) for such non-intervention systems, along with its computational criterion, Interventional Embedding Entropy (IEE), to quantify causality. The IEE criterion theoretically and numerically enables the deciphering of IntDC solely from observational (non-interventional) time-series data, without requiring any knowledge of dynamical models or real interventions in the considered system. Demonstrations of performance showed the accuracy and robustness of IEE on benchmark simulated systems as well as real-world systems, including the neural connectomes of C. elegans, COVID-19 transmission networks in Japan, and regulatory networks surrounding key circadian genes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2f694a003e2f1cc8bc9b14d47f6caa55abdf0e9c" target='_blank'>
-              An Earth Encounter As the Cause of Chaotic Dynamics in Binary Asteroid (35107) 1991VH
+          <td><a href="https://www.semanticscholar.org/paper/731fd0ad43f607161c56e7dddae19516d57b53d3" target='_blank'>
+              Deciphering interventional dynamical causality from non-intervention systems
               </a>
             </td>
           <td>
-            A. J. Meyer, Oscar Fuentes-Muñoz, I. Gkolias, K. Tsiganis, P. Pravec, S. Naidu, D. Scheeres
+            Jifan Shi, Yang Li, Juan Zhao, Siyang Leng, Kazuyuki Aihara, Luonan Chen, Wei Lin
           </td>
-          <td>2024-07-18</td>
+          <td>2024-06-29</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>47</td>
+          <td>11</td>
         </tr>
 
-        <tr id="Configuration-controllable phononic crystals (CCPCs) have broad application prospects in engineering because of their adjustable vibration-reduction properties. Owing to the complicated constitutive relationship and nonlinear geometric deformation, it is difficult to accurately predict the dynamic characteristics of CCPCs using the finite element method (FEM) or theoretical methods. In this study, we employed a nonlinear autoregressive with exogenous input (NARX) artificial neural network (ANN) to identify the dynamic model of the CCPC under an impact load, using data from over 100 experiments and numerous accumulated samples. The corresponding experimental data for the CCPC were used to train the ANN and determine the rational ANN model. The identification results indicate that appropriate number of neurons and time-delay orders can effectively reduce the identification errors. Compared with the response predicted by the FEM, the identification model can describe the nonlinear characteristics emerging from phononic crystal (PC) experiments more accurately. This study provides an efficient and accurate online identification approach for PC-modeling.">
+        <tr id="We propose a novel reduced-order methodology to describe complex multi-frequency fluid dynamics from time-resolved snapshot data. Starting point is the Cluster-based Network Model (CNM) thanks to its fully automatable development and human interpretability. Our key innovation is to model the transitions from cluster to cluster much more accurately by replacing snapshot states with short-term trajectories ("orbits") over multiple clusters, thus avoiding nonphysical intra-cluster diffusion in the dynamic reconstruction. The proposed orbital CNM (oCNM) employs functional clustering to coarse-grain the short-term trajectories. Specifically, different filtering techniques, resulting in different temporal basis expansions, demonstrate the versatility and capability of the oCNM to adapt to diverse flow phenomena. The oCNM is illustrated on the Stuart-Landau oscillator and its post-transient solution with time-varying parameters to test its ability to capture the amplitude selection mechanism and multi-frequency behaviours. Then, the oCNM is applied to the fluidic pinball across varying flow regimes at different Reynolds numbers, including the periodic, quasi-periodic, and chaotic dynamics. This orbital-focused perspective enhances the understanding of complex temporal behaviours by incorporating high-frequency behaviour into the kinematics of short-time trajectories while modelling the dynamics of the lower frequencies. In analogy to Spectral Proper Orthogonal Decomposition, which marked the transition from spatial-only modes to spatio-temporal ones, this work advances from analysing temporal local states to examining piecewise short-term trajectories, or orbits. By merging advanced analytical methods, such as the functional representation of short-time trajectories with CNM, this study paves the way for new approaches to dissect the complex dynamics characterising turbulent systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/63f3f0badfa56355242e4715c8727c81ea87125c" target='_blank'>
-              Dynamic modeling of configuration-controllable phononic crystal using NARX neural networks
+          <td><a href="https://www.semanticscholar.org/paper/413941f904c49031a4ce7ee2d45cc551a5cabb12" target='_blank'>
+              Orbital cluster-based network modelling
               </a>
             </td>
           <td>
-            Nan Li, Changqing Bai
+            A. Colanera, Nan Deng, M. Chiatto, Luigi De Luca, Bernd R. Noack
           </td>
-          <td>2024-06-14</td>
-          <td>Journal of Vibration and Control</td>
+          <td>2024-07-01</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>12</td>
         </tr>
 
-        <tr id="The modelling of linear quadratic Gaussian optimal control problems on large complex networks is intractable computationally. Graphon theory provides an approach to overcome these issues by defining limit objects for infinite sequences of graphs permitting one to approximate arbitrarily large networks by infinite dimensional operators. This is extended to stochastic systems by the use of Q-noise, a generalization of Wiener processes in finite dimensional spaces to processes in function spaces. The optimal control of linear quadratic problems on graphon systems with Q-noise disturbances are defined and shown to be the limit of the corresponding finite graph optimal control problem. The theory is extended to low rank systems, and a fully worked special case is presented. In addition, the worst-case long-range average and infinite horizon discounted optimal control performance with respect to Q-noise distribution are computed for a small set of standard graphon limits.">
+        <tr id="In this paper, we apply the Fourier neural operator (FNO) paradigm to ocean circulation and prediction problems. We aim to show that the complicated non-linear dynamics of an ocean circulation can be captured by a flexible, efficient, and expressive structure of the FNO networks. The machine learning model (FNO3D and the recurrent FNO2D networks) trained by simulated data as well as real data takes spatiotemporal input and predicts future ocean states (sea surface current and sea surface height). For this, the double gyre ocean circulation model driven by stochastic wind stress is considered to represent an ideal ocean circulation. In order to generate the training and test data that exhibits rich spatiotemporal variability, the initial states are perturbed by Gaussian random fields. Experimental results confirm that the trained models yield satisfactory prediction accuracy for both types of FNO models in this case. Second, as the training set, we used the HYCOM reanalysis data in a regional ocean. FNO2D experiments demonstrated that the 5-day input to 5-day prediction yields the averaged root mean square errors (RMSEs) of 5.0 cm/s, 6.7 cm/s, 7.9 cm/s, 8.9 cm/s, and 9.4 cm/s in surface current, calculated consecutively for each day, in a regional ocean circulation of the East/Japan Sea. Similarly, the RMSEs for sea surface height were 2.3 cm, 3.5 cm, 4.2 cm, 4.6 cm, and 4.9 cm, for each day. We also trained the model with 15-day input and 10-day prediction, resulting in comparable performance. Extensive numerical tests show that, once learned, the resolution-free FNO model instantly forecasts the ocean states and can be used as an alternative fast solver in various inference algorithms.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/79173733e4371062ced3a5a7d673a308b7ae7824" target='_blank'>
-              Quadratic Optimal Control of Graphon Q-noise Linear Systems
+          <td><a href="https://www.semanticscholar.org/paper/66940e0cf48566a2e9e8617081952275da1fa484" target='_blank'>
+              Applications of the Fourier neural operator in a regional ocean modeling and prediction
               </a>
             </td>
           <td>
-            Alex Dunyak, Peter E. Caines
+            Byoung-Ju Choi, H. Jin, Bataa Lkhagvasuren
           </td>
-          <td>2024-06-28</td>
-          <td>ArXiv</td>
+          <td>2024-07-02</td>
+          <td>Frontiers in Marine Science</td>
           <td>0</td>
-          <td>2</td>
+          <td>5</td>
         </tr>
 
-        <tr id="
-
-
-Ecosystems contain numerous species interacting with each other and the environment. However, data on all relevant state variables is rarely available, hampering inference and prediction. Empirical dynamic modelling (EDM) is a valuable tool for prediction, inference and control in such partially observed systems.
-
-However, EDM typically assumes that the available time series are observed without error. Failing to account for observation noise strongly biases estimates of Lyapunov exponents and reduces forecast accuracy. To address this limitation, we propose incorporating EDM into a hidden Markov framework and using an iterative scheme based on the expectation maximization (EM) algorithm to obtain filtered state and parameter estimates.
-
-We evaluate the performance of this approach on several simulated dynamical systems with a range of additive noise levels, as well as on insect population time series.
-
-Accounting for observation noise improved accuracy of population forecasts and estimates of Lyapunov exponents (LE) over a wide range of noise levels relevant to ecological time series.
-
-">
+        <tr id="In this paper, we design a transfer sparse identification algorithm under the Bayesian framework through introducing other system knowledge into the system to be identified. This method provides a new identification solution for a nonlinear autoregressive model with exogenous inputs (NARX). The estimates of the transferred parameters are calculated by adding the transfer correction term to the un‐transferred estimates. To achieve this, a joint prior distribution is devised for the parameters, ultimately enhancing the efficient utilization of existing data, reducing the reliance on new data, and achieving more accurate identification. The maximized marginal likelihood method is used to find the transfer gain and the transfer information matrix in the transfer correction term. Meanwhile, in order to make the algorithm automatically adapt to different data, we design an automatic structure detection method based on the transfer framework. The method automatically determines the sparsity threshold based on the maximum inter‐class variance. Two examples are provided to demonstrate the advantages of our algorithm.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4e9c4d6519c0328c66d02635359f84c4d6cf2f4d" target='_blank'>
-              Accounting for observation noise in equation‐free forecasting: The hidden‐Markov S‐map
+          <td><a href="https://www.semanticscholar.org/paper/275895802c6290128f34f9549d5e7ee7a46c6781" target='_blank'>
+              A Bayesian transfer sparse identification method for nonlinear ARX systems
               </a>
             </td>
           <td>
-            Dylan Esguerra, Stephan B. Munch
+            Kang Zhang, Xiaoli Luan, Feng Ding, Fei Liu
           </td>
-          <td>2024-07-01</td>
-          <td>Methods in Ecology and Evolution</td>
-          <td>0</td>
+          <td>2024-08-08</td>
+          <td>International Journal of Adaptive Control and Signal Processing</td>
           <td>0</td>
+          <td>3</td>
         </tr>
 
-        <tr id="None">
+        <tr id="Engineers often utilize data-driven surrogate models in optimization to partially replace the costly computational simulations of physics-based models. However, different aspects affect the accuracy and prediction capability of the surrogate models, e.g., the dimensionality of the data and nonlinearities in the mapping between input and output. Learning well-performing models by selecting appropriate techniques to fit the data benefits from the machine learning and data science expertise of the engineer which may vary depending on the application domain. Recently, large language models (LLMs) have shown promising capabilities to support humans through natural language-based interfaces in approaching technical problems, as well as to co-develop software and to democratize domain knowledge. In this paper, we utilize ChatGPT 4 to co-develop a framework to select and train surrogate models for engineering optimization tasks. More specifically, we interact with ChatGPT to outline a process and software to support the selection and application of regression techniques based on characteristics of the available data and target application. We evaluate the developed methodology on synthetic and realistic engineering optimization data and problems. In our experiments, we demonstrate that the models obtained through the methodology developed with ChatGPT achieve comparable performance in regression and optimization tasks than observed in existing works in the literature. Hence, despite some limitations, such as missing updates of available software libraries, LLMs can support less experienced engineers to solve surrogate-assisted optimization problems more efficiently by providing insights on the application data and software for deploying surrogate models.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0faa7b48df91690f3e92cf2ef0638118805ed816" target='_blank'>
-              Trajectory-based global sensitivity analysis in multiscale models
+          <td><a href="https://www.semanticscholar.org/paper/b199732a0ef844fff7389cc7d27737b52409f2df" target='_blank'>
+              Large Language Model-assisted Surrogate Modelling for Engineering Optimization
               </a>
             </td>
           <td>
-            Valentina Bazyleva, Victoria M. Garibay, Debraj Roy
+            Thiago Rios, Felix Lanfermann, Stefan Menzel
           </td>
-          <td>2024-06-17</td>
-          <td>Scientific Reports</td>
-          <td>0</td>
-          <td>0</td>
+          <td>2024-06-25</td>
+          <td>2024 IEEE Conference on Artificial Intelligence (CAI)</td>
+          <td>1</td>
+          <td>7</td>
         </tr>
 
-        <tr id="This work addresses the synthesis of optimal feedback control laws via machine learning. In particular, the Averaged Feedback Learning Scheme (AFLS) and a data driven method are considered. Hypotheses for each method ensuring the convergence of the evaluation of the objective function of the underlying control problem at the obtained feedback-laws towards the optimal value function are provided. These hypotheses are connected to the regularity of the value function and the stability of the dynamics. In the case of AFLS these hypotheses only require H\"older continuity of the value function, whereas for the data driven method the value function must be at least $C^2$. It is demonstrated that these methods are connected via their optimality conditions. Additionally, numerical experiments are provided by applying both methods to a family control problems, parameterized by a positive real number which controls the regularity of the value function. For small parameters the value function is smooth and in contrast for large parameters it is non-differentiable, but semi-concave. The results of the experiments indicate that both methods have a similar performance for the case that the value function is smooth. On the other hand, if the value function is not differentiable, AFLS has a better performance which is consistent with the obtained convergence results.">
+        <tr id="We study the dynamics of a continuous-time model of the Stochastic Gradient Descent (SGD) for the least-square problem. Indeed, pursuing the work of Li et al. (2019), we analyze Stochastic Differential Equations (SDEs) that model SGD either in the case of the training loss (finite samples) or the population one (online setting). A key qualitative feature of the dynamics is the existence of a perfect interpolator of the data, irrespective of the sample size. In both scenarios, we provide precise, non-asymptotic rates of convergence to the (possibly degenerate) stationary distribution. Additionally, we describe this asymptotic distribution, offering estimates of its mean, deviations from it, and a proof of the emergence of heavy-tails related to the step-size magnitude. Numerical simulations supporting our findings are also presented.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/307b109ee8daf5810e48f9fba58490e24a131f80" target='_blank'>
-              Convergence of machine learning methods for feedback control laws: averaged feedback learning scheme and data driven method
+          <td><a href="https://www.semanticscholar.org/paper/ecfeb578d6cbf8848e1912ad8e32e903a645ea7a" target='_blank'>
+              Stochastic Differential Equations models for Least-Squares Stochastic Gradient Descent
               </a>
             </td>
           <td>
-            Karl Kunisch, Donato V'asquez-Varas
+            Adrien Schertzer, Loucas Pillaud-Vivien
           </td>
-          <td>2024-07-25</td>
+          <td>2024-07-02</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>10</td>
         </tr>
 
-        <tr id="We investigate the accuracy of prediction in deterministic learning dynamics of zero-sum games with random initializations, specifically focusing on observer uncertainty and its relationship to the evolution of covariances. Zero-sum games are a prominent field of interest in machine learning due to their various applications. Concurrently, the accuracy of prediction in dynamical systems from mechanics has long been a classic subject of investigation since the discovery of the Heisenberg Uncertainty Principle. This principle employs covariance and standard deviation of particle states to measure prediction accuracy. In this study, we bring these two approaches together to analyze the Follow-the-Regularized-Leader (FTRL) algorithm in two-player zero-sum games. We provide growth rates of covariance information for continuous-time FTRL, as well as its two canonical discretization methods (Euler and Symplectic). A Heisenberg-type inequality is established for FTRL. Our analysis and experiments also show that employing Symplectic discretization enhances the accuracy of prediction in learning dynamics.">
+        <tr id="This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions, our approach leverages the relationship between MGFs and distribution moments to extend high-order uncertainty propagation techniques to non-Gaussian scenarios. This significantly broadens the applicability of these methods to a wider range of problems and uncertainty types. High-order moment computations are performed one-off and symbolically, reducing the computational burden of the technique to the calculation of Taylor series coefficients around a nominal trajectory, achieved by efficiently integrating the system's variational equations. Furthermore, the use of the proposed approach in combination with event transition tensors, allows for accurate propagation of uncertainties at specific events, such as the landing surface of a celestial body, the crossing of a predefined Poincar\'e section, or the trigger of an arbitrary event during the propagation. Via numerical simulations we demonstrate the effectiveness of our method in various astrodynamics applications, including the unperturbed and perturbed two-body problem, and the circular restricted three-body problem, showing that it accurately propagates non-Gaussian uncertainties both at future times and at event manifolds.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b71b055d5aeef1eef9b00c144b364421e6afd674" target='_blank'>
-              Prediction Accuracy of Learning in Games : Follow-the-Regularized-Leader meets Heisenberg
+          <td><a href="https://www.semanticscholar.org/paper/6afd2423f192d0672dfad436cf9f3cd283ac1177" target='_blank'>
+              Nonlinear Propagation of Non-Gaussian Uncertainties: Theory and Applications to Spacecraft Trajectory Design
               </a>
             </td>
           <td>
-            Yi Feng, G. Piliouras, Xiao Wang
+            Giacomo Acciarini, Nicola Baresi, David Lloyd, Dario Izzo
           </td>
-          <td>2024-06-15</td>
+          <td>2024-08-09</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>33</td>
+          <td>3</td>
         </tr>
 
     </tbody>
@@ -4795,7 +4811,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Symbolic regression</i>
 
   var trace1 = {
     x: ['2024'],
-    y: [25],
+    y: [32],
     name: 'Num of citations',
     yaxis: 'y1',
     type: 'scatter'
diff --git a/site/Time-series forecasting/index.html b/site/Time-series forecasting/index.html
index 922cf396..ef377bb0 100644
--- a/site/Time-series forecasting/index.html	
+++ b/site/Time-series forecasting/index.html	
@@ -453,7 +453,7 @@ <h1>Time-series forecasting</h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:01 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:19 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -517,9 +517,9 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Ming Jin, Huan Yee Koh, Qingsong Wen, Daniele Zambon, C. Alippi, G. I. Webb, Irwin King, Shirui Pan
           </td>
           <td>2023-07-07</td>
-          <td>ArXiv, arXiv.org</td>
-          <td>59</td>
-          <td>49</td>
+          <td>IEEE transactions on pattern analysis and machine intelligence</td>
+          <td>61</td>
+          <td>50</td>
 
             <td><a href='../recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -538,8 +538,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
           </td>
           <td>2021-10-11</td>
           <td>ArXiv, International Conference on Learning Representations</td>
-          <td>66</td>
-          <td>46</td>
+          <td>70</td>
+          <td>47</td>
 
             <td><a href='../recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -559,7 +559,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
           <td>2023-02-08</td>
           <td>Neural Information Processing Systems, ArXiv</td>
           <td>15</td>
-          <td>49</td>
+          <td>50</td>
 
             <td><a href='../recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -579,7 +579,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
           <td>2022-05-26</td>
           <td>J. Mach. Learn. Res., Journal of machine learning research</td>
           <td>11</td>
-          <td>49</td>
+          <td>50</td>
 
             <td><a href='../recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -597,9 +597,9 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Andrea Cini, Ivan Marisca, Daniele Zambon, C. Alippi
           </td>
           <td>2023-10-24</td>
-          <td>ArXiv, arXiv.org</td>
+          <td>arXiv.org, ArXiv</td>
           <td>4</td>
-          <td>49</td>
+          <td>50</td>
 
             <td><a href='../recommendations/ccea298edb788edf821aef58f0952c3e8debc25a' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -618,7 +618,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
           </td>
           <td>2023-10-11</td>
           <td>Neural Information Processing Systems, ArXiv</td>
-          <td>117</td>
+          <td>123</td>
           <td>14</td>
 
             <td><a href='../recommendations/123acfbccca0460171b6b06a4012dbb991cde55b' target='_blank'>
@@ -637,9 +637,9 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Chloe X. Wang, Oleksii Tsepa, Jun Ma, Bo Wang
           </td>
           <td>2024-02-01</td>
-          <td>ArXiv, arXiv.org</td>
-          <td>45</td>
-          <td>7</td>
+          <td>arXiv.org, ArXiv</td>
+          <td>47</td>
+          <td>5</td>
 
             <td><a href='../recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -657,8 +657,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Abhimanyu Das, Weihao Kong, Rajat Sen, Yichen Zhou
           </td>
           <td>2023-10-14</td>
-          <td>ArXiv, arXiv.org</td>
-          <td>44</td>
+          <td>arXiv.org, ArXiv</td>
+          <td>48</td>
           <td>14</td>
 
             <td><a href='../recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f' target='_blank'>
@@ -677,8 +677,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Gerald Woo, Chenghao Liu, Akshat Kumar, Caiming Xiong, Silvio Savarese, Doyen Sahoo
           </td>
           <td>2024-02-04</td>
-          <td>ArXiv, arXiv.org</td>
-          <td>26</td>
+          <td>arXiv.org, ArXiv</td>
+          <td>28</td>
           <td>22</td>
 
             <td><a href='../recommendations/4a111f7a3b56d0468f13104999844885157ef17d' target='_blank'>
@@ -697,8 +697,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y. Zhang, X. Shi, Pin-Yu Chen, Yuxuan Liang, Yuan-Fang Li, Shirui Pan, Qingsong Wen
           </td>
           <td>2023-10-03</td>
-          <td>ArXiv, arXiv.org</td>
-          <td>109</td>
+          <td>ArXiv, International Conference on Learning Representations</td>
+          <td>120</td>
           <td>9</td>
 
             <td><a href='../recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277' target='_blank'>
@@ -717,7 +717,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Vijay Ekambaram, Arindam Jati, Nam H. Nguyen, Pankaj Dayama, Chandra Reddy, Wesley M. Gifford, Jayant Kalagnanam
           </td>
           <td>2024-01-08</td>
-          <td>ArXiv, arXiv.org</td>
+          <td>arXiv.org, ArXiv</td>
           <td>2</td>
           <td>2</td>
 
@@ -738,8 +738,8 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
           </td>
           <td>2022-06-17</td>
           <td>Neural Information Processing Systems, ArXiv</td>
-          <td>155</td>
-          <td>46</td>
+          <td>162</td>
+          <td>47</td>
 
             <td><a href='../recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -757,9 +757,9 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Huan He, Owen Queen, Teddy Koker, Consuelo Cuevas, Theodoros Tsiligkaridis, M. Zitnik
           </td>
           <td>2023-02-06</td>
-          <td>DBLP, ArXiv</td>
+          <td>ArXiv, DBLP</td>
           <td>23</td>
-          <td>46</td>
+          <td>47</td>
 
             <td><a href='../recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -779,7 +779,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
           <td>None</td>
           <td>DBLP</td>
           <td>6</td>
-          <td>49</td>
+          <td>50</td>
 
             <td><a href='../recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -797,9 +797,9 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
             Daniele Zambon, Andrea Cini, L. Livi, C. Alippi
           </td>
           <td>2023-01-04</td>
-          <td>ArXiv, arXiv.org</td>
+          <td>arXiv.org, ArXiv</td>
           <td>3</td>
-          <td>49</td>
+          <td>50</td>
 
             <td><a href='../recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -819,7 +819,7 @@ <h3 id="manually_curated_articles">Manually curated articles on <i>Time-series f
           <td>2024-02-29</td>
           <td>ArXiv</td>
           <td>2</td>
-          <td>46</td>
+          <td>47</td>
 
             <td><a href='../recommendations/bcbcc2e1af8bcf6b07edf866be95116a8ed0bf91' target='_blank'>
               <i class="material-icons">open_in_new</i></a>
@@ -874,37 +874,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>2024-08-01</td>
           <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>2</td>
-        </tr>
-
-        <tr id="Time series forecasting (TSF) is crucial in fields like economic forecasting, weather prediction, traffic flow analysis, and public health surveillance. Real-world time series data often include noise, outliers, and missing values, making accurate forecasting challenging. Traditional methods model point-to-point relationships, which limits their ability to capture complex temporal patterns and increases their susceptibility to noise.To address these issues, we introduce the WindowMixer model, built on an all-MLP framework. WindowMixer leverages the continuous nature of time series by examining temporal variations from a window-based perspective. It decomposes time series into trend and seasonal components, handling them individually. For trends, a fully connected (FC) layer makes predictions. For seasonal components, time windows are projected to produce window tokens, processed by Intra-Window-Mixer and Inter-Window-Mixer modules. The Intra-Window-Mixer models relationships within each window, while the Inter-Window-Mixer models relationships between windows. This approach captures intricate patterns and long-range dependencies in the data.Experiments show WindowMixer consistently outperforms existing methods in both long-term and short-term forecasting tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0b5e7cfba3feae0a37aa3ce200bec06808907851" target='_blank'>
-              WindowMixer: Intra-Window and Inter-Window Modeling for Time Series Forecasting
-              </a>
-            </td>
-          <td>
-            Quangao Liu, Ruiqi Li, Maowei Jiang, Wei Yang, Chen Liang, Longlong Pang, Zhuozhang Zou
-          </td>
-          <td>2024-06-14</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-
-        <tr id="Time series, characterized by a sequence of data points arranged in a discrete-time order, are ubiquitous in real-world applications. Different from other modalities, time series present unique challenges due to their complex and dynamic nature, including the entanglement of nonlinear patterns and time-variant trends. Analyzing time series data is of great significance in real-world scenarios and has been widely studied over centuries. Recent years have witnessed remarkable breakthroughs in the time series community, with techniques shifting from traditional statistical methods to advanced deep learning models. In this paper, we delve into the design of deep time series models across various analysis tasks and review the existing literature from two perspectives: basic modules and model architectures. Further, we develop and release Time Series Library (TSLib) as a fair benchmark of deep time series models for diverse analysis tasks, which implements 24 mainstream models, covers 30 datasets from different domains, and supports five prevalent analysis tasks. Based on TSLib, we thoroughly evaluate 12 advanced deep time series models on different tasks. Empirical results indicate that models with specific structures are well-suited for distinct analytical tasks, which offers insights for research and adoption of deep time series models. Code is available at https://github.com/thuml/Time-Series-Library.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/425182f5c96c1d239da5cbe3a24371b2bab6319b" target='_blank'>
-              Deep Time Series Models: A Comprehensive Survey and Benchmark
-              </a>
-            </td>
-          <td>
-            Yuxuan Wang, Haixu Wu, Jiaxiang Dong, Yong Liu, Mingsheng Long, Jianmin Wang
-          </td>
-          <td>2024-07-18</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>65</td>
+          <td>3</td>
         </tr>
 
         <tr id="Long time series forecasting aims to utilize historical information to forecast future states over extended horizons. Traditional RNN-based series forecasting methods struggle to effectively address long-term dependencies and gradient issues in long time series problems. Recently, SegRNN has emerged as a leading RNN-based model tailored for long-term series forecasting, demonstrating state-of-the-art performance while maintaining a streamlined architecture through innovative segmentation and parallel decoding techniques. Nevertheless, SegRNN has several limitations: its fixed segmentation disrupts data continuity and fails to effectively leverage information across different segments, the segmentation strategy employed by SegRNN does not fundamentally address the issue of information loss within the recurrent structure. To address these issues, we propose the ISMRNN method with three key enhancements: we introduce an implicit segmentation structure to decompose the time series and map it to segmented hidden states, resulting in denser information exchange during the segmentation phase. Additionally, we incorporate residual structures in the encoding layer to mitigate information loss within the recurrent structure. To extract information more effectively, we further integrate the Mamba architecture to enhance time series information extraction. Experiments on several real-world long time series forecasting datasets demonstrate that our model surpasses the performance of current state-of-the-art models.">
@@ -922,49 +892,49 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>0</td>
         </tr>
 
-        <tr id="Multi-variate time series forecasting is an important problem with a wide range of applications. Recent works model the relations between time-series as graphs and have shown that propagating information over the relation graph can improve time series forecasting. However, in many cases, relational information is not available or is noisy and reliable. Moreover, most works ignore the underlying uncertainty of time-series both for structure learning and deriving the forecasts resulting in the structure not capturing the uncertainty resulting in forecast distributions with poor uncertainty estimates. We tackle this challenge and introduce STOIC, that leverages stochastic correlations between time-series to learn underlying structure between time-series and to provide well-calibrated and accurate forecasts. Over a wide-range of benchmark datasets STOIC provides around 16% more accurate and 14% better-calibrated forecasts. STOIC also shows better adaptation to noise in data during inference and captures important and useful relational information in various benchmarks.">
+        <tr id="Recent studies have raised questions about the suitability of the Transformer architecture for long sequence time-series forecasting. These forecasting models leverage Transformers to capture dependencies between multiple time steps in a time series, with embedding tokens composed of data from individual time steps. However, challenges arise when applying Transformers to predict long sequences with strong periodicity, leading to performance degradation and increased computational burden. Furthermore, embedding tokens formed one time step at a time may struggle to reveal meaningful information in long sequences, failing to capture correlations between different time steps. In this study, we propose Skip-Timeformer, a Transformer-based model that utilizes a skip-time interaction for long sequence time-series forecasting. Specifically, we decompose the time series into multiple subsequences based on different time intervals, embedding various time steps into variable tokens across multiple sequences. The skip-time interaction mechanism utilizes these variable tokens to capture dependencies in the skip-time dimension. Additionally, skip-time interaction is employed to learn dependencies between sequences missed by multiple skip time steps. The Skip-Timeformer model demonstrates state-of-the-art performance on various real-world datasets, further enhancing the long sequence forecasting capabilities of the Transformer variations and better adapting to arbitrary lookback windows.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7d4b412399f89c9cd66cffc4ab811b74172dcc63" target='_blank'>
-              Learning Graph Structures and Uncertainty for Accurate and Calibrated Time-series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/62917f180f12405293773a5f3689236727699caf" target='_blank'>
+              Skip-Timeformer: Skip-Time Interaction Transformer for Long Sequence Time-Series Forecasting
               </a>
             </td>
           <td>
-            Harshavardhan Kamarthi, Lingkai Kong, Alexander Rodríguez, Chao Zhang, B. A. Prakash
+            Wenchang Zhang, Hua Wang, Fan Zhang
           </td>
-          <td>2024-07-02</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>9</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Long-term time series forecasting in centralized environments poses unique challenges regarding data privacy, communication overhead, and scalability. To address these challenges, we propose FedTime, a federated large language model (LLM) tailored for long-range time series prediction. Specifically, we introduce a federated pre-trained LLM with fine-tuning and alignment strategies. Prior to the learning process, we employ K-means clustering to partition edge devices or clients into distinct clusters, thereby facilitating more focused model training. We also incorporate channel independence and patching to better preserve local semantic information, ensuring that important contextual details are retained while minimizing the risk of information loss. We demonstrate the effectiveness of our FedTime model through extensive experiments on various real-world forecasting benchmarks, showcasing substantial improvements over recent approaches. In addition, we demonstrate the efficiency of FedTime in streamlining resource usage, resulting in reduced communication overhead.">
+        <tr id="Time series, characterized by a sequence of data points arranged in a discrete-time order, are ubiquitous in real-world applications. Different from other modalities, time series present unique challenges due to their complex and dynamic nature, including the entanglement of nonlinear patterns and time-variant trends. Analyzing time series data is of great significance in real-world scenarios and has been widely studied over centuries. Recent years have witnessed remarkable breakthroughs in the time series community, with techniques shifting from traditional statistical methods to advanced deep learning models. In this paper, we delve into the design of deep time series models across various analysis tasks and review the existing literature from two perspectives: basic modules and model architectures. Further, we develop and release Time Series Library (TSLib) as a fair benchmark of deep time series models for diverse analysis tasks, which implements 24 mainstream models, covers 30 datasets from different domains, and supports five prevalent analysis tasks. Based on TSLib, we thoroughly evaluate 12 advanced deep time series models on different tasks. Empirical results indicate that models with specific structures are well-suited for distinct analytical tasks, which offers insights for research and adoption of deep time series models. Code is available at https://github.com/thuml/Time-Series-Library.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cfbf583c88970300ba4a74619b02be88524899df" target='_blank'>
-              A federated large language model for long-term time series forecasting
+          <td><a href="https://www.semanticscholar.org/paper/425182f5c96c1d239da5cbe3a24371b2bab6319b" target='_blank'>
+              Deep Time Series Models: A Comprehensive Survey and Benchmark
               </a>
             </td>
           <td>
-            Raed Abdel-Sater, A. B. Hamza
+            Yuxuan Wang, Haixu Wu, Jiaxiang Dong, Yong Liu, Mingsheng Long, Jianmin Wang
           </td>
-          <td>2024-07-30</td>
+          <td>2024-07-18</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>66</td>
         </tr>
 
-        <tr id="Transformer-based models have emerged as powerful tools for multivariate time series forecasting (MTSF). However, existing Transformer models often fall short of capturing both intricate dependencies across variate and temporal dimensions in MTS data. Some recent models are proposed to separately capture variate and temporal dependencies through either two sequential or parallel attention mechanisms. However, these methods cannot directly and explicitly learn the intricate inter-series and intra-series dependencies. In this work, we first demonstrate that these dependencies are very important as they usually exist in real-world data. To directly model these dependencies, we propose a transformer-based model UniTST containing a unified attention mechanism on the flattened patch tokens. Additionally, we add a dispatcher module which reduces the complexity and makes the model feasible for a potentially large number of variates. Although our proposed model employs a simple architecture, it offers compelling performance as shown in our extensive experiments on several datasets for time series forecasting.">
+        <tr id="Multi-variate time series forecasting is an important problem with a wide range of applications. Recent works model the relations between time-series as graphs and have shown that propagating information over the relation graph can improve time series forecasting. However, in many cases, relational information is not available or is noisy and reliable. Moreover, most works ignore the underlying uncertainty of time-series both for structure learning and deriving the forecasts resulting in the structure not capturing the uncertainty resulting in forecast distributions with poor uncertainty estimates. We tackle this challenge and introduce STOIC, that leverages stochastic correlations between time-series to learn underlying structure between time-series and to provide well-calibrated and accurate forecasts. Over a wide-range of benchmark datasets STOIC provides around 16% more accurate and 14% better-calibrated forecasts. STOIC also shows better adaptation to noise in data during inference and captures important and useful relational information in various benchmarks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9a1f121e4fc3b2ade9237ded9a4d91822e09714d" target='_blank'>
-              UniTST: Effectively Modeling Inter-Series and Intra-Series Dependencies for Multivariate Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/7d4b412399f89c9cd66cffc4ab811b74172dcc63" target='_blank'>
+              Learning Graph Structures and Uncertainty for Accurate and Calibrated Time-series Forecasting
               </a>
             </td>
           <td>
-            Juncheng Liu, Chenghao Liu, Gerald Woo, Yiwei Wang, Bryan Hooi, Caiming Xiong, Doyen Sahoo
+            Harshavardhan Kamarthi, Lingkai Kong, Alexander Rodríguez, Chao Zhang, B. A. Prakash
           </td>
-          <td>2024-06-07</td>
+          <td>2024-07-02</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>22</td>
+          <td>9</td>
         </tr>
 
         <tr id="To achieve more accurate prediction results in Time Series Forecasting (TSF), it is essential to distinguish between the valuable patterns (invariant patterns) of the spatial-temporal relationship and the patterns that are prone to generate distribution shift (variant patterns), then combine them for forecasting.The existing works, such as transformer-based models and GNN-based models, focus on capturing main forecasting dependencies whether it is stable or not, and they tend to overlook patterns that carry both useful information and distribution shift. In this paper, we propose a model for better forecasting time series: Decoupled Invariant Attention Network (DIAN), which contains two modules to learn spatial and temporal relationships respectively: 1) Spatial Decoupled Invariant-Variant Learning (SDIVL) to decouple the spatial invariant and variant attention scores, and then leverage convolutional networks to effectively integrate them for subsequent layers; 2) Temporal Augmented Invariant-Variant Learning (TAIVL) to decouple temporal invariant and variant patterns and combine them for further forecasting.In this module, we also design Temporal Intervention Mechanism to create multiple intervened samples by reassembling variant patterns across time stamps to eliminate the spurious impacts of variant patterns.In addition, we propose Joint Optimization to minimize the loss function considering all invariant patterns, variant patterns and intervened patterns so that our model can gain a more stable predictive ability.Extensive experiments on five datasets have demonstrated our superior performance with higher efficiency compared with state-of-the-art methods.">
@@ -979,19 +949,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>2024-08-01</td>
           <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>3</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Spatio-temporal graph (STG) forecasting is a critical task with extensive applications in the real world, including traffic and weather forecasting. Although several recent methods have been proposed to model complex dynamics in STGs, addressing long-range spatio-temporal dependencies remains a significant challenge, leading to limited performance gains. Inspired by a recently proposed state space model named Mamba, which has shown remarkable capability of capturing long-range dependency, we propose a new STG forecasting framework named SpoT-Mamba. SpoT-Mamba generates node embeddings by scanning various node-specific walk sequences. Based on the node embeddings, it conducts temporal scans to capture long-range spatio-temporal dependencies. Experimental results on the real-world traffic forecasting dataset demonstrate the effectiveness of SpoT-Mamba.">
+        <tr id="Long-term time series forecasting in centralized environments poses unique challenges regarding data privacy, communication overhead, and scalability. To address these challenges, we propose FedTime, a federated large language model (LLM) tailored for long-range time series prediction. Specifically, we introduce a federated pre-trained LLM with fine-tuning and alignment strategies. Prior to the learning process, we employ K-means clustering to partition edge devices or clients into distinct clusters, thereby facilitating more focused model training. We also incorporate channel independence and patching to better preserve local semantic information, ensuring that important contextual details are retained while minimizing the risk of information loss. We demonstrate the effectiveness of our FedTime model through extensive experiments on various real-world forecasting benchmarks, showcasing substantial improvements over recent approaches. In addition, we demonstrate the efficiency of FedTime in streamlining resource usage, resulting in reduced communication overhead.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/249b1ae3616ef24f7cea210b7e049f39f2586206" target='_blank'>
-              SpoT-Mamba: Learning Long-Range Dependency on Spatio-Temporal Graphs with Selective State Spaces
+          <td><a href="https://www.semanticscholar.org/paper/cfbf583c88970300ba4a74619b02be88524899df" target='_blank'>
+              A federated large language model for long-term time series forecasting
               </a>
             </td>
           <td>
-            Jinhyeok Choi, Heehyeon Kim, Minhyeong An, Joyce Jiyoung Whang
+            Raed Abdel-Sater, A. B. Hamza
           </td>
-          <td>2024-06-17</td>
+          <td>2024-07-30</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>1</td>
@@ -1027,49 +997,49 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>0</td>
         </tr>
 
-        <tr id="In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world da-tasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, po-tentially redefining the landscape of time series forecasting.">
+        <tr id="Deep models for Multivariate Time Series (MTS) forecasting have recently demonstrated significant success. Channel-dependent models capture complex dependencies that channel-independent models cannot capture. However, the number of channels in real-world applications outpaces the capabilities of existing channel-dependent models, and contrary to common expectations, some models underperform the channel-independent models in handling high-dimensional data, which raises questions about the performance of channel-dependent models. To address this, our study first investigates the reasons behind the suboptimal performance of these channel-dependent models on high-dimensional MTS data. Our analysis reveals that two primary issues lie in the introduced noise from unrelated series that increases the difficulty of capturing the crucial inter-channel dependencies, and challenges in training strategies due to high-dimensional data. To address these issues, we propose STHD, the Scalable Transformer for High-Dimensional Multivariate Time Series Forecasting. STHD has three components: a) Relation Matrix Sparsity that limits the noise introduced and alleviates the memory issue; b) ReIndex applied as a training strategy to enable a more flexible batch size setting and increase the diversity of training data; and c) Transformer that handles 2-D inputs and captures channel dependencies. These components jointly enable STHD to manage the high-dimensional MTS while maintaining computational feasibility. Furthermore, experimental results show STHD's considerable improvement on three high-dimensional datasets: Crime-Chicago, Wiki-People, and Traffic. The source code and dataset are publicly available https://github.com/xinzzzhou/ScalableTransformer4HighDimensionMTSF.git.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/286a643cebfa8149f02ead76b0be31caa7d8735f" target='_blank'>
-              xLSTMTime : Long-term Time Series Forecasting With xLSTM
+          <td><a href="https://www.semanticscholar.org/paper/c2e65d59302efd2605a7b44a9a92f5470b0660fb" target='_blank'>
+              Scalable Transformer for High Dimensional Multivariate Time Series Forecasting
               </a>
             </td>
           <td>
-            Musleh Alharthi, Ausif Mahmood
+            Xin Zhou, Weiqing Wang, W. Buntine, Shilin Qu, Abishek Sriramulu, Weicong Tan, Christoph Bergmeir
           </td>
-          <td>2024-07-14</td>
+          <td>2024-08-08</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>16</td>
         </tr>
 
-        <tr id="Pretraining plays a pivotal role in acquiring generalized knowledge from large-scale data, achieving remarkable successes as evidenced by large models in CV and NLP. However, progress in the graph domain remains limited due to fundamental challenges such as feature heterogeneity and structural heterogeneity. Recently, increasing efforts have been made to enhance node feature quality with Large Language Models (LLMs) on text-attributed graphs (TAGs), demonstrating superiority to traditional bag-of-words or word2vec techniques. These high-quality node features reduce the previously critical role of graph structure, resulting in a modest performance gap between Graph Neural Networks (GNNs) and structure-agnostic Multi-Layer Perceptrons (MLPs). Motivated by this, we introduce a feature-centric pretraining perspective by treating graph structure as a prior and leveraging the rich, unified feature space to learn refined interaction patterns that generalizes across graphs. Our framework, Graph Sequence Pretraining with Transformer (GSPT), samples node contexts through random walks and employs masked feature reconstruction to capture pairwise proximity in the LLM-unified feature space using a standard Transformer. By utilizing unified text representations rather than varying structures, our framework achieves significantly better transferability among graphs within the same domain. GSPT can be easily adapted to both node classification and link prediction, demonstrating promising empirical success on various datasets.">
+        <tr id="In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world da-tasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, po-tentially redefining the landscape of time series forecasting.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/98097c3d23e811717c4a9d958d144a5cb6dafe7c" target='_blank'>
-              A Pure Transformer Pretraining Framework on Text-attributed Graphs
+          <td><a href="https://www.semanticscholar.org/paper/286a643cebfa8149f02ead76b0be31caa7d8735f" target='_blank'>
+              xLSTMTime : Long-term Time Series Forecasting With xLSTM
               </a>
             </td>
           <td>
-            Yu Song, Haitao Mao, Jiachen Xiao, Jingzhe Liu, Zhikai Chen, Wei-dong Jin, Carl Yang, Jiliang Tang, Hui Liu
+            Musleh Alharthi, Ausif Mahmood
           </td>
-          <td>2024-06-19</td>
+          <td>2024-07-14</td>
           <td>ArXiv</td>
+          <td>0</td>
           <td>1</td>
-          <td>9</td>
         </tr>
 
-        <tr id="Graph Neural Networks (GNNs) have shown impressive performance in graph representation learning, but they face challenges in capturing long-range dependencies due to their limited expressive power. To address this, Graph Transformers (GTs) were introduced, utilizing self-attention mechanism to effectively model pairwise node relationships. Despite their advantages, GTs suffer from quadratic complexity w.r.t. the number of nodes in the graph, hindering their applicability to large graphs. In this work, we present Graph-Enhanced Contextual Operator (GECO), a scalable and effective alternative to GTs that leverages neighborhood propagation and global convolutions to effectively capture local and global dependencies in quasilinear time. Our study on synthetic datasets reveals that GECO reaches 169x speedup on a graph with 2M nodes w.r.t. optimized attention. Further evaluations on diverse range of benchmarks showcase that GECO scales to large graphs where traditional GTs often face memory and time limitations. Notably, GECO consistently achieves comparable or superior quality compared to baselines, improving the SOTA up to 4.5%, and offering a scalable and effective solution for large-scale graph learning.">
+        <tr id="In multivariate time-series forecasting (MTSF), extracting the temporal correlations of the input sequences is crucial. While popular Transformer-based predictive models can perform well, their quadratic computational complexity results in inefficiency and high overhead. The recently emerged Mamba, a selective state space model, has shown promising results in many fields due to its strong temporal feature extraction capabilities and linear computational complexity. However, due to the unilateral nature of Mamba, channel-independent predictive models based on Mamba cannot attend to the relationships among all variables in the manner of Transformer-based models. To address this issue, we combine fast-attention with Mamba to introduce a novel framework named FMamba for MTSF. Technically, we first extract the temporal features of the input variables through an embedding layer, then compute the dependencies among input variables via the fast-attention module. Subsequently, we use Mamba to selectively deal with the input features and further extract the temporal dependencies of the variables through the multi-layer perceptron block (MLP-block). Finally, FMamba obtains the predictive results through the projector, a linear layer. Experimental results on eight public datasets demonstrate that FMamba can achieve state-of-the-art performance while maintaining low computational overhead.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/48052c9ebe066b9fcd653897dabf18582ec7e7fb" target='_blank'>
-              A Scalable and Effective Alternative to Graph Transformers
+          <td><a href="https://www.semanticscholar.org/paper/3c5ced872aa5d16bf3aa59c40931ed85b54cb3e5" target='_blank'>
+              FMamba: Mamba based on Fast-attention for Multivariate Time-series Forecasting
               </a>
             </td>
           <td>
-            Kaan Sancak, Zhigang Hua, Jin Fang, Yan Xie, Andrey Malevich, Bo Long, M. F. Balin, Ümit V. Çatalyürek
+            Shusen Ma, Yu Kang, Peng Bai, Yunan Zhao
           </td>
-          <td>2024-06-17</td>
+          <td>2024-07-20</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>6</td>
+          <td>1</td>
         </tr>
 
         <tr id="None">
@@ -1087,51 +1057,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>18</td>
         </tr>
 
-        <tr id="In multivariate time-series forecasting (MTSF), extracting the temporal correlations of the input sequences is crucial. While popular Transformer-based predictive models can perform well, their quadratic computational complexity results in inefficiency and high overhead. The recently emerged Mamba, a selective state space model, has shown promising results in many fields due to its strong temporal feature extraction capabilities and linear computational complexity. However, due to the unilateral nature of Mamba, channel-independent predictive models based on Mamba cannot attend to the relationships among all variables in the manner of Transformer-based models. To address this issue, we combine fast-attention with Mamba to introduce a novel framework named FMamba for MTSF. Technically, we first extract the temporal features of the input variables through an embedding layer, then compute the dependencies among input variables via the fast-attention module. Subsequently, we use Mamba to selectively deal with the input features and further extract the temporal dependencies of the variables through the multi-layer perceptron block (MLP-block). Finally, FMamba obtains the predictive results through the projector, a linear layer. Experimental results on eight public datasets demonstrate that FMamba can achieve state-of-the-art performance while maintaining low computational overhead.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3c5ced872aa5d16bf3aa59c40931ed85b54cb3e5" target='_blank'>
-              FMamba: Mamba based on Fast-attention for Multivariate Time-series Forecasting
-              </a>
-            </td>
-          <td>
-            Shusen Ma, Yu Kang, Peng Bai, Yunan Zhao
-          </td>
-          <td>2024-07-20</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-
-        <tr id="In recent years, significant progress has been made in multivariate time series forecasting using Linear-based, Transformer-based, and Convolution-based models. However, these approaches face notable limitations: linear forecasters struggle with representation capacities, attention mechanisms suffer from quadratic complexity, and convolutional models have a restricted receptive field. These constraints impede their effectiveness in modeling complex time series, particularly those with numerous variables. Additionally, many models adopt the Channel-Independent (CI) strategy, treating multivariate time series as uncorrelated univariate series while ignoring their correlations. For models considering inter-channel relationships, whether through the self-attention mechanism, linear combination, or convolution, they all incur high computational costs and focus solely on weighted summation relationships, neglecting potential proportional relationships between channels. In this work, we address these issues by leveraging the newly introduced state space model and propose \textbf{C-Mamba}, a novel approach that captures cross-channel dependencies while maintaining linear complexity without losing the global receptive field. Our model consists of two key components: (i) channel mixup, where two channels are mixed to enhance the training sets; (ii) channel attention enhanced patch-wise Mamba encoder that leverages the ability of the state space models to capture cross-time dependencies and models correlations between channels by mining their weight relationships. Our model achieves state-of-the-art performance on seven real-world time series datasets. Moreover, the proposed mixup and attention strategy exhibits strong generalizability across other frameworks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b7ed7845bfa63b07899d44434a479f08f80ca268" target='_blank'>
-              C-Mamba: Channel Correlation Enhanced State Space Models for Multivariate Time Series Forecasting
-              </a>
-            </td>
-          <td>
-            Chaolv Zeng, Zhanyu Liu, Guanjie Zheng, Linghe Kong
-          </td>
-          <td>2024-06-08</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>5</td>
-        </tr>
-
-        <tr id="Traffic prediction is a challenging spatio-temporal forecasting problem that involves highly complex spatio-temporal correlations. This paper proposes a Multi-level Multi-view Augmented Spatio-temporal Transformer (LVSTformer) for traffic prediction. The model aims to capture spatial dependencies from three different levels: local geographic, global semantic, and pivotal nodes, along with long- and short-term temporal dependencies. Specifically, we design three spatial augmented views to delve into the spatial information from the perspectives of local, global, and pivotal nodes. By combining three spatial augmented views with three parallel spatial self-attention mechanisms, the model can comprehensively captures spatial dependencies at different levels. We design a gated temporal self-attention mechanism to effectively capture long- and short-term temporal dependencies. Furthermore, a spatio-temporal context broadcasting module is introduced between two spatio-temporal layers to ensure a well-distributed allocation of attention scores, alleviating overfitting and information loss, and enhancing the generalization ability and robustness of the model. A comprehensive set of experiments is conducted on six well-known traffic benchmarks, the experimental results demonstrate that LVSTformer achieves state-of-the-art performance compared to competing baselines, with the maximum improvement reaching up to 4.32%.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/22af70b0b268da0f71549bad07d5b3f24528fb16" target='_blank'>
-              Rethinking Spatio-Temporal Transformer for Traffic Prediction:Multi-level Multi-view Augmented Learning Framework
-              </a>
-            </td>
-          <td>
-            Jiaqi Lin, Qianqian Ren
-          </td>
-          <td>2024-06-17</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>0</td>
-        </tr>
-
         <tr id="This technical report describes the Time Series Optimized Transformer for Observability (Toto), a new state of the art foundation model for time series forecasting developed by Datadog. In addition to advancing the state of the art on generalized time series benchmarks in domains such as electricity and weather, this model is the first general-purpose time series forecasting foundation model to be specifically tuned for observability metrics. Toto was trained on a dataset of one trillion time series data points, the largest among all currently published time series foundation models. Alongside publicly available time series datasets, 75% of the data used to train Toto consists of fully anonymous numerical metric data points from the Datadog platform. In our experiments, Toto outperforms existing time series foundation models on observability data. It does this while also excelling at general-purpose forecasting tasks, achieving state-of-the-art zero-shot performance on multiple open benchmark datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/325e7ce8ff734f133cfa379bd8ac1021604c68aa" target='_blank'>
@@ -1147,21 +1072,6 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>4</td>
         </tr>
 
-        <tr id="Inspired by Large Language Models (LLMs), Time Series Forecasting (TSF), a long-standing task in time series analysis, is undergoing a transition towards Large Time Series Models (LTSMs), aiming to train universal transformer-based models for TSF. However, training LTSMs on heterogeneous time series data poses unique challenges, including diverse frequencies, dimensions, and patterns across datasets. Recent endeavors have studied and evaluated various design choices aimed at enhancing LTSM training and generalization capabilities, spanning pre-processing techniques, model configurations, and dataset configurations. In this work, we comprehensively analyze these design choices and aim to identify the best practices for training LTSM. Moreover, we propose \emph{time series prompt}, a novel statistical prompting strategy tailored to time series data. Furthermore, based on the observations in our analysis, we introduce \texttt{LTSM-bundle}, which bundles the best design choices we have identified. Empirical results demonstrate that \texttt{LTSM-bundle} achieves superior zero-shot and few-shot performances compared to state-of-the-art LSTMs and traditional TSF methods on benchmark datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/631c05be8806b43fac7aaf4d041de59562ac17f9" target='_blank'>
-              Understanding Different Design Choices in Training Large Time Series Models
-              </a>
-            </td>
-          <td>
-            Yu-Neng Chuang, Songchen Li, Jiayi Yuan, Guanchu Wang, Kwei-Herng Lai, Leisheng Yu, Sirui Ding, Chia-yuan Chang, Qiaoyu Tan, D. Zha, Xia Hu
-          </td>
-          <td>2024-06-20</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>22</td>
-        </tr>
-
         <tr id="It is challenging to scale time series forecasting models such that they forecast accurately for multiple distinct domains and datasets, all with potentially different underlying collection procedures (e.g., sample resolution), patterns (e.g., periodicity), and prediction requirements (e.g., reconstruction vs. forecasting). We call this general task universal forecasting. Existing methods usually assume that input data is regularly sampled, and they forecast to pre-determined horizons, resulting in failure to generalise outside of the scope of their training. We propose the DAM - a neural model that takes randomly sampled histories and outputs an adjustable basis composition as a continuous function of time for forecasting to non-fixed horizons. It involves three key components: (1) a flexible approach for using randomly sampled histories from a long-tail distribution, that enables an efficient global perspective of the underlying temporal dynamics while retaining focus on the recent history; (2) a transformer backbone that is trained on these actively sampled histories to produce, as representational output, (3) the basis coefficients of a continuous function of time. We show that a single univariate DAM, trained on 25 time series datasets, either outperformed or closely matched existing SoTA models at multivariate long-term forecasting across 18 datasets, including 8 held-out for zero-shot transfer, even though these models were trained to specialise for each dataset-horizon combination. This single DAM excels at zero-shot transfer and very-long-term forecasting, performs well at imputation, is interpretable via basis function composition and attention, can be tuned for different inference-cost requirements, is robust to missing and irregularly sampled data {by design}.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/e177ce13d5e3ca4673b2fff9481408cd98bba0d3" target='_blank'>
@@ -1177,64 +1087,64 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>43</td>
         </tr>
 
-        <tr id="In multivariate time series (MTS) forecasting, existing state-of-the-art deep learning approaches tend to focus on autoregressive formulations and overlook the information within exogenous indicators. To address this limitation, we present DeformTime, a neural network architecture that attempts to capture correlated temporal patterns from the input space, and hence, improve forecasting accuracy. It deploys two core operations performed by deformable attention blocks (DABs): learning dependencies across variables from different time steps (variable DAB), and preserving temporal dependencies in data from previous time steps (temporal DAB). Input data transformation is explicitly designed to enhance learning from the deformed series of information while passing through a DAB. We conduct extensive experiments on 6 MTS data sets, using previously established benchmarks as well as challenging infectious disease modelling tasks with more exogenous variables. The results demonstrate that DeformTime improves accuracy against previous competitive methods across the vast majority of MTS forecasting tasks, reducing the mean absolute error by 10% on average. Notably, performance gains remain consistent across longer forecasting horizons.">
+        <tr id="Long-term time series forecasting (LTSF) has been widely applied in finance, traffic prediction, and other domains. Recently, patch-based transformers have emerged as a promising approach, segmenting data into sub-level patches that serve as input tokens. However, existing methods mostly rely on predetermined patch lengths, necessitating expert knowledge and posing challenges in capturing diverse characteristics across various scales. Moreover, time series data exhibit diverse variations and fluctuations across different temporal scales, which traditional approaches struggle to model effectively. In this paper, we propose a dynamic tokenizer with a dynamic sparse learning algorithm to capture diverse receptive fields and sparse patterns of time series data. In order to build hierarchical receptive fields, we develop a multi-scale Transformer model, coupled with multi-scale sequence extraction, capable of capturing multi-resolution features. Additionally, we introduce a group-aware rotary position encoding technique to enhance intra- and inter-group position awareness among representations across different temporal scales. Our proposed model, named DRFormer, is evaluated on various real-world datasets, and experimental results demonstrate its superiority compared to existing methods. Our code is available at: https://github.com/ruixindingECNU/DRFormer.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6c5ad359f1ca77ebaca62cae8263c48864b786d4" target='_blank'>
-              DeformTime: Capturing Variable Dependencies with Deformable Attention for Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/93c28e3a8cfde1fbb13658d2f625053edc878a02" target='_blank'>
+              DRFormer: Multi-Scale Transformer Utilizing Diverse Receptive Fields for Long Time-Series Forecasting
               </a>
             </td>
           <td>
-            Yuxuan Shu, Vasileios Lampos
+            Ruixin Ding, Yuqi Chen, Yu-Ting Lan, Wei Zhang
           </td>
-          <td>2024-06-11</td>
+          <td>2024-08-05</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>24</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Machine learning on graphs has recently found extensive applications across domains. However, the commonly used Message Passing Neural Networks (MPNNs) suffer from limited expressive power and struggle to capture long-range dependencies. Graph transformers offer a strong alternative due to their global attention mechanism, but they come with great computational overheads, especially for large graphs. In recent years, State Space Models (SSMs) have emerged as a compelling approach to replace full attention in transformers to model sequential data. It blends the strengths of RNNs and CNNs, offering a) efficient computation, b) the ability to capture long-range dependencies, and c) good generalization across sequences of various lengths. However, extending SSMs to graph-structured data presents unique challenges due to the lack of canonical node ordering in graphs. In this work, we propose Graph State Space Convolution (GSSC) as a principled extension of SSMs to graph-structured data. By leveraging global permutation-equivariant set aggregation and factorizable graph kernels that rely on relative node distances as the convolution kernels, GSSC preserves all three advantages of SSMs. We demonstrate the provably stronger expressiveness of GSSC than MPNNs in counting graph substructures and show its effectiveness across 10 real-world, widely used benchmark datasets, where GSSC achieves best results on 7 out of 10 datasets with all significant improvements compared to the state-of-the-art baselines and second-best results on the other 3 datasets. Our findings highlight the potential of GSSC as a powerful and scalable model for graph machine learning. Our code is available at https://github.com/Graph-COM/GSSC.">
+        <tr id="Spatial-temporal forecasting and imputation are important for real-world dynamic systems such as intelligent transportation, urban planning, and public health. Most existing methods are tailored for individual forecasting or imputation tasks but are not designed for both. Additionally, they are less effective for zero-shot and few-shot learning. While large language models (LLMs) have exhibited strong pattern recognition and reasoning abilities across various tasks, including few-shot and zero-shot learning, their development in understanding spatial-temporal data has been constrained by insufficient modeling of complex correlations such as the temporal correlations, spatial connectivity, non-pairwise and high-order spatial-temporal correlations within data. In this paper, we propose STD-LLM for understanding both spatial and temporal properties of \underline{S}patial-\underline{T}emporal \underline{D}ata with \underline{LLM}s, which is capable of implementing both spatial-temporal forecasting and imputation tasks. STD-LLM understands spatial-temporal correlations via explicitly designed spatial and temporal tokenizers as well as virtual nodes. Topology-aware node embeddings are designed for LLMs to comprehend and exploit the topology structure of data. Additionally, to capture the non-pairwise and higher-order correlations, we design a hypergraph learning module for LLMs, which can enhance the overall performance and improve efficiency. Extensive experiments demonstrate that STD-LLM exhibits strong performance and generalization capabilities across the forecasting and imputation tasks on various datasets. Moreover, STD-LLM achieves promising results on both few-shot and zero-shot learning tasks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/93a9b7940e902f989e27f94061d3b699a2fc4d13" target='_blank'>
-              What Can We Learn from State Space Models for Machine Learning on Graphs?
+          <td><a href="https://www.semanticscholar.org/paper/87ddff7927e4489327dc17239e87f040bb86c0ab" target='_blank'>
+              STD-LLM: Understanding Both Spatial and Temporal Properties of Spatial-Temporal Data with LLMs
               </a>
             </td>
           <td>
-            Yinan Huang, Siqi Miao, Pan Li
+            Yiheng Huang, Xiaowei Mao, S. Guo, Yubin Chen, Youfang Lin, Huaiyu Wan
           </td>
-          <td>2024-06-09</td>
+          <td>2024-07-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>18</td>
         </tr>
 
-        <tr id="Recent advancements in language modeling have shown promising results when applied to time series data. In particular, fine-tuning pre-trained large language models (LLMs) for time series classification tasks has achieved state-of-the-art (SOTA) performance on standard benchmarks. However, these LLM-based models have a significant drawback due to the large model size, with the number of trainable parameters in the millions. In this paper, we propose an alternative approach to leveraging the success of language modeling in the time series domain. Instead of fine-tuning LLMs, we utilize a language embedding model to embed time series and then pair the embeddings with a simple classification head composed of convolutional neural networks (CNN) and multilayer perceptron (MLP). We conducted extensive experiments on well-established time series classification benchmark datasets. We demonstrated LETS-C not only outperforms the current SOTA in classification accuracy but also offers a lightweight solution, using only 14.5% of the trainable parameters on average compared to the SOTA model. Our findings suggest that leveraging language encoders to embed time series data, combined with a simple yet effective classification head, offers a promising direction for achieving high-performance time series classification while maintaining a lightweight model architecture.">
+        <tr id="We propose a transformer architecture for time series forecasting with a focus on time series tokenisation and apply it to a real-world prediction problem from the pricing domain. Our architecture aims to learn effective representations at many scales across all available data simultaneously. The model contains a number of novel modules: a differentiated form of time series patching which employs multiple resolutions, a multiple-resolution module for time-varying known variables, a mixer-based module for capturing cross-series information, and a novel output head with favourable scaling to account for the increased number of tokens. We present an application of this model to a real world prediction problem faced by the markdown team at a very large retailer. On the experiments conducted our model outperforms in-house models and the selected existing deep learning architectures.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d55b63343538e0ba5e954542707b90b860dd2e48" target='_blank'>
-              LETS-C: Leveraging Language Embedding for Time Series Classification
+          <td><a href="https://www.semanticscholar.org/paper/d7954d6328e25d15549188da2570cc67407bbd56" target='_blank'>
+              Multiple-Resolution Tokenization for Time Series Forecasting with an Application to Pricing
               </a>
             </td>
           <td>
-            Rachneet Kaur, Zhen Zeng, T. Balch, Manuela Veloso
+            Egon Persak, Miguel F. Anjos, Sebastian Lautz, Aleksandar Kolev
           </td>
-          <td>2024-07-09</td>
+          <td>2024-07-03</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>12</td>
+          <td>1</td>
         </tr>
 
-        <tr id="We propose a transformer architecture for time series forecasting with a focus on time series tokenisation and apply it to a real-world prediction problem from the pricing domain. Our architecture aims to learn effective representations at many scales across all available data simultaneously. The model contains a number of novel modules: a differentiated form of time series patching which employs multiple resolutions, a multiple-resolution module for time-varying known variables, a mixer-based module for capturing cross-series information, and a novel output head with favourable scaling to account for the increased number of tokens. We present an application of this model to a real world prediction problem faced by the markdown team at a very large retailer. On the experiments conducted our model outperforms in-house models and the selected existing deep learning architectures.">
+        <tr id="Recent advancements in language modeling have shown promising results when applied to time series data. In particular, fine-tuning pre-trained large language models (LLMs) for time series classification tasks has achieved state-of-the-art (SOTA) performance on standard benchmarks. However, these LLM-based models have a significant drawback due to the large model size, with the number of trainable parameters in the millions. In this paper, we propose an alternative approach to leveraging the success of language modeling in the time series domain. Instead of fine-tuning LLMs, we utilize a language embedding model to embed time series and then pair the embeddings with a simple classification head composed of convolutional neural networks (CNN) and multilayer perceptron (MLP). We conducted extensive experiments on well-established time series classification benchmark datasets. We demonstrated LETS-C not only outperforms the current SOTA in classification accuracy but also offers a lightweight solution, using only 14.5% of the trainable parameters on average compared to the SOTA model. Our findings suggest that leveraging language encoders to embed time series data, combined with a simple yet effective classification head, offers a promising direction for achieving high-performance time series classification while maintaining a lightweight model architecture.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d7954d6328e25d15549188da2570cc67407bbd56" target='_blank'>
-              Multiple-Resolution Tokenization for Time Series Forecasting with an Application to Pricing
+          <td><a href="https://www.semanticscholar.org/paper/d55b63343538e0ba5e954542707b90b860dd2e48" target='_blank'>
+              LETS-C: Leveraging Language Embedding for Time Series Classification
               </a>
             </td>
           <td>
-            Egon Pervsak, Miguel F. Anjos, Sebastian Lautz, Aleksandar Kolev
+            Rachneet Kaur, Zhen Zeng, T. Balch, Manuela Veloso
           </td>
-          <td>2024-07-03</td>
+          <td>2024-07-09</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>12</td>
         </tr>
 
         <tr id="Discrete-Time Dynamic Graphs (DTDGs), which are prevalent in real-world implementations and notable for their ease of data acquisition, have garnered considerable attention from both academic researchers and industry practitioners. The representation learning of DTDGs has been extensively applied to model the dynamics of temporally changing entities and their evolving connections. Currently, DTDG representation learning predominantly relies on GNN+RNN architectures, which manifest the inherent limitations of both Graph Neural Networks (GNNs) and Recurrent Neural Networks (RNNs). GNNs suffer from the over-smoothing issue as the models architecture goes deeper, while RNNs struggle to capture long-term dependencies effectively. GNN+RNN architectures also grapple with scaling to large graph sizes and long sequences. Additionally, these methods often compute node representations separately and focus solely on individual node characteristics, thereby overlooking the behavior intersections between the two nodes whose link is being predicted, such as instances where the two nodes appear together in the same context or share common neighbors. This paper introduces a novel representation learning method DTFormer for DTDGs, pivoting from the traditional GNN+RNN framework to a Transformer-based architecture. Our approach exploits the attention mechanism to concurrently process topological information within the graph at each timestamp and temporal dynamics of graphs along the timestamps, circumventing the aforementioned fundamental weakness of both GNNs and RNNs. Moreover, we enhance the model's expressive capability by incorporating the intersection relationships among nodes and integrating a multi-patching module. Extensive experiments conducted on six public dynamic graph benchmark datasets confirm our model's efficacy, achieving the SOTA performance.">
@@ -1252,19 +1162,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>4</td>
         </tr>
 
-        <tr id="The rapid development of time series forecasting research has brought many deep learning-based modules in this field. However, despite the increasing amount of new forecasting architectures, it is still unclear if we have leveraged the full potential of these existing modules within a properly designed architecture. In this work, we propose a novel hierarchical neural architecture search approach for time series forecasting tasks. With the design of a hierarchical search space, we incorporate many architecture types designed for forecasting tasks and allow for the efficient combination of different forecasting architecture modules. Results on long-term-time-series-forecasting tasks show that our approach can search for lightweight high-performing forecasting architectures across different forecasting tasks.">
+        <tr id="Transformer has gained widespread adoption in modeling time series due to the exceptional ability of its self-attention mechanism in capturing long-range dependencies. However, when processing time series data with numerous variates, the vanilla self-attention mechanism tends to distribute attention weights evenly and smoothly, causing row-homogenization in attention maps and further hampering time series forecasting. To tackle this issue, we propose an advanced Transformer architecture entitled SDformer, which designs two novel modules, Spectral-Filter-Transform (SFT) and Dynamic-Directional-Attention (DDA), and integrates them into the encoder of Transformer to achieve more intensive attention allocation. Specifically, the SFT module utilizes the Fast Fourier Transform to select the most prominent frequencies, along with a Hamming Window to smooth and denoise the filtered series data; The DDA module applies a specialized kernel function to the query and key vectors projected from the denoised data, concentrating this innovative attention mechanism more effectively on the most informative variates to obtain a sharper attention distribution. These two modules jointly enable attention weights to be more salient among numerous variates, which in turn enhances the attention's ability to capture multivariate correlations, improving the performance in forecasting. Extensive experiments on public datasets demonstrate its superior performance over other state-of-the-art models. Code is available at https://github.com/zhouziyu02/SDformer.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/31947145652dd384fbc8b2abef02779bb95c7a72" target='_blank'>
-              Optimizing Time Series Forecasting Architectures: A Hierarchical Neural Architecture Search Approach
+          <td><a href="https://www.semanticscholar.org/paper/2059f2f21fb401de3268af0691764082ba5fdfbd" target='_blank'>
+              SDformer: Transformer with Spectral Filter and Dynamic Attention for Multivariate Time Series Long-term Forecasting
               </a>
             </td>
           <td>
-            Difan Deng, Marius Lindauer
+            Ziyu Zhou, Gengyu Lyu, Yiming Huang, Zihao Wang, Ziyu Jia, Zhen Yang
           </td>
-          <td>2024-06-07</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>6</td>
+          <td>11</td>
         </tr>
 
         <tr id="Exploiting self-supervised learning (SSL) to extract the universal representations of time series could not only capture the natural properties of time series but also offer huge help to the downstream tasks. Nevertheless, existing time series representation learning (TSRL) methods face challenges in attaining universality. Indeed, existing methods relying solely on one SSL strategy (either contrastive learning (CL) or generative) often fall short in capturing rich semantic information for various downstream tasks. Moreover, time series exhibit diverse distributions and inherent characteristics, particularly with the common occurrence of missing values, posing a notable challenge for existing backbones in effectively handling such diverse time series data. To bridge these gaps, we propose CTRL, a framework for universal TSRL. For the first time, we employ Neural Controlled Differential Equation (NCDE) as the backbone for TSRL, which captures the continuous processes and exhibits robustness to missing data. Additionally, a dual-task SSL strategy, integrating both reconstruction and contrasting tasks, is proposed to enrich the semantic information of the learned representations. Furthermore, novel hard negative construction and false negative elimination mechanisms are proposed to improve sampling efficiency and reduce sampling bias in CL. Finally, extensive experiments demonstrate the superiority of CTRL in forecasting, classification, and imputation tasks, particularly its outstanding robustness to missing data.">
@@ -1282,19 +1192,19 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>25</td>
         </tr>
 
-        <tr id="Transformer has gained widespread adoption in modeling time series due to the exceptional ability of its self-attention mechanism in capturing long-range dependencies. However, when processing time series data with numerous variates, the vanilla self-attention mechanism tends to distribute attention weights evenly and smoothly, causing row-homogenization in attention maps and further hampering time series forecasting. To tackle this issue, we propose an advanced Transformer architecture entitled SDformer, which designs two novel modules, Spectral-Filter-Transform (SFT) and Dynamic-Directional-Attention (DDA), and integrates them into the encoder of Transformer to achieve more intensive attention allocation. Specifically, the SFT module utilizes the Fast Fourier Transform to select the most prominent frequencies, along with a Hamming Window to smooth and denoise the filtered series data; The DDA module applies a specialized kernel function to the query and key vectors projected from the denoised data, concentrating this innovative attention mechanism more effectively on the most informative variates to obtain a sharper attention distribution. These two modules jointly enable attention weights to be more salient among numerous variates, which in turn enhances the attention's ability to capture multivariate correlations, improving the performance in forecasting. Extensive experiments on public datasets demonstrate its superior performance over other state-of-the-art models. Code is available at https://github.com/zhouziyu02/SDformer.">
+        <tr id="Accurate workload forecasting is critical for efficient resource management in cloud computing systems, enabling effective scheduling and autoscaling. Despite recent advances with transformer-based forecasting models, challenges remain due to the non-stationary, nonlinear characteristics of workload time series and the long-term dependencies. In particular, inconsistent performance between long-term history and near-term forecasts hinders long-range predictions. This paper proposes a novel framework leveraging self-supervised multiscale representation learning to capture both long-term and near-term workload patterns. The long-term history is encoded through multiscale representations while the near-term observations are modeled via temporal flow fusion. These representations of different scales are fused using an attention mechanism and characterized with normalizing flows to handle non-Gaussian/non-linear distributions of time series. Extensive experiments on 9 benchmarks demonstrate superiority over existing methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2059f2f21fb401de3268af0691764082ba5fdfbd" target='_blank'>
-              SDformer: Transformer with Spectral Filter and Dynamic Attention for Multivariate Time Series Long-term Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/690e772c64d7f67b330d55aa96ffa09ecc7d2ae2" target='_blank'>
+              Multiscale Representation Enhanced Temporal Flow Fusion Model for Long-Term Workload Forecasting
               </a>
             </td>
           <td>
-            Ziyu Zhou, Gengyu Lyu, Yiming Huang, Zihao Wang, Ziyu Jia, Zhen Yang
+            Shiyu Wang, Zhixuan Chu, Yinbo Sun, Yu Liu, Yuliang Guo, Yang Chen, Huiyang Jian, Lintao Ma, Xingyu Lu, Jun Zhou
           </td>
-          <td>2024-08-01</td>
-          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
+          <td>2024-07-29</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>11</td>
+          <td>4</td>
         </tr>
 
         <tr id="Spatio-temporal forecasting of traffic flow data represents a typical problem in the field of machine learning, impacting urban traffic management systems. Traditional statistical and machine learning methods cannot adequately handle both the temporal and spatial dependencies in these complex traffic flow datasets. A prevalent approach in the field is to combine graph convolutional networks and multi-head attention mechanisms for spatio-temporal processing. This paper proposes a wavelet-based temporal attention model, namely a wavelet-based dynamic spatio-temporal aware graph neural network (W-DSTAGNN), for tackling the traffic forecasting problem. Benchmark experiments using several statistical metrics confirm that our proposal efficiently captures spatio-temporal correlations and outperforms ten state-of-the-art models on three different real-world traffic datasets. Our proposed ensemble data-driven method can handle dynamic temporal and spatial dependencies and make long-term forecasts in an efficient manner.">
@@ -1309,52 +1219,37 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>2024-07-05</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
-        </tr>
-
-        <tr id="Graph neural networks are typically trained on individual datasets, often requiring highly specialized models and extensive hyperparameter tuning. This dataset-specific approach arises because each graph dataset often has unique node features and diverse connectivity structures, making it difficult to build a generalist model. To address these challenges, we introduce a scalable multi-graph multi-task pretraining approach specifically tailored for node classification tasks across diverse graph datasets from different domains. Our method, Graph Foundation Model (GraphFM), leverages a Perceiver-based encoder that employs learned latent tokens to compress domain-specific features into a common latent space. This approach enhances the model's ability to generalize across different graphs and allows for scaling across diverse data. We demonstrate the efficacy of our approach by training a model on 152 different graph datasets comprising over 7.4 million nodes and 189 million edges, establishing the first set of scaling laws for multi-graph pretraining on datasets spanning many domains (e.g., molecules, citation and product graphs). Our results show that pretraining on a diverse array of real and synthetic graphs improves the model's adaptability and stability, while performing competitively with state-of-the-art specialist models. This work illustrates that multi-graph pretraining can significantly reduce the burden imposed by the current graph training paradigm, unlocking new capabilities for the field of graph neural networks by creating a single generalist model that performs competitively across a wide range of datasets and tasks.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d1aa656a9c5e57166b70806519a12c48e828a4cc" target='_blank'>
-              GraphFM: A Scalable Framework for Multi-Graph Pretraining
-              </a>
-            </td>
-          <td>
-            Divyansha Lachi, Mehdi Azabou, Vinam Arora, Eva L. Dyer
-          </td>
-          <td>2024-07-16</td>
-          <td>ArXiv</td>
-          <td>0</td>
-          <td>8</td>
+          <td>11</td>
         </tr>
 
-        <tr id="Frequency domain representation of time series feature offers a concise representation for handling real-world time series data with inherent complexity and dynamic nature. However, current frequency-based methods with complex operations still fall short of state-of-the-art time domain methods for general time series analysis. In this work, we present Omni-Dimensional Frequency Learner (ODFL) model based on a in depth analysis among all the three aspects of the spectrum feature: channel redundancy property among the frequency dimension, the sparse and un-salient frequency energy distribution among the frequency dimension, and the semantic diversity among the variable dimension. Technically, our method is composed of a semantic-adaptive global filter with attention to the un-salient frequency bands and partial operation among the channel dimension. Empirical results show that ODFL achieves consistent state-of-the-art in five mainstream time series analysis tasks, including short- and long-term forecasting, imputation, classification, and anomaly detection, offering a promising foundation for time series analysis.">
+        <tr id="This research examines the use of Large Language Models (LLMs) in predicting time series, with a specific focus on the LLMTIME model. Despite the established effectiveness of LLMs in tasks such as text generation, language translation, and sentiment analysis, this study highlights the key challenges that large language models encounter in the context of time series prediction. We assess the performance of LLMTIME across multiple datasets and introduce classical almost periodic functions as time series to gauge its effectiveness. The empirical results indicate that while large language models can perform well in zero-shot forecasting for certain datasets, their predictive accuracy diminishes notably when confronted with diverse time series data and traditional signals. The primary finding of this study is that the predictive capacity of LLMTIME, similar to other LLMs, significantly deteriorates when dealing with time series data that contain both periodic and trend components, as well as when the signal comprises complex frequency components.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/de75ddcb9fb13372a31ee08af8dd80b5913d70f3" target='_blank'>
-              Omni-Dimensional Frequency Learner for General Time Series Analysis
+          <td><a href="https://www.semanticscholar.org/paper/11e794835a1f7d46560666d90c8eab3c24d84c05" target='_blank'>
+              An Evaluation of Standard Statistical Models and LLMs on Time Series Forecasting
               </a>
             </td>
           <td>
-            Xianing Chen.Hanting Chen, Hanting Chen, Hailin Hu
+            Rui Cao, Qiaohua Wang
           </td>
-          <td>2024-07-15</td>
+          <td>2024-08-09</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Graph pre-training has been concentrated on graph-level on small graphs (e.g., molecular graphs) or learning node representations on a fixed graph. Extending graph pre-trained models to web-scale graphs with billions of nodes in industrial scenarios, while avoiding negative transfer across graphs or tasks, remains a challenge. We aim to develop a general graph pre-trained model with inductive ability that can make predictions for unseen new nodes and even new graphs. In this work, we introduce a scalable transformer-based graph pre-training framework called PGT (Pre-trained Graph Transformer). Specifically, we design a flexible and scalable graph transformer as the backbone network. Meanwhile, based on the masked autoencoder architecture, we design two pre-training tasks: one for reconstructing node features and the other one for reconstructing local structures. Unlike the original autoencoder architecture where the pre-trained decoder is discarded, we propose a novel strategy that utilizes the decoder for feature augmentation. We have deployed our framework on Tencent's online game data. Extensive experiments have demonstrated that our framework can perform pre-training on real-world web-scale graphs with over 540 million nodes and 12 billion edges and generalizes effectively to unseen new graphs with different downstream tasks. We further conduct experiments on the publicly available ogbn-papers100M dataset, which consists of 111 million nodes and 1.6 billion edges. Our framework achieves state-of-the-art performance on both industrial datasets and public datasets, while also enjoying scalability and efficiency.">
+        <tr id="The complexity and heterogeneity of data in many real-world applications pose significant challenges for traditional machine learning and signal processing techniques. For instance, in medicine, effective analysis of diverse physiological signals is crucial for patient monitoring and clinical decision-making and yet highly challenging. We introduce MedTsLLM, a general multimodal large language model (LLM) framework that effectively integrates time series data and rich contextual information in the form of text to analyze physiological signals, performing three tasks with clinical relevance: semantic segmentation, boundary detection, and anomaly detection in time series. These critical tasks enable deeper analysis of physiological signals and can provide actionable insights for clinicians. We utilize a reprogramming layer to align embeddings of time series patches with a pretrained LLM's embedding space and make effective use of raw time series, in conjunction with textual context. Given the multivariate nature of medical datasets, we develop methods to handle multiple covariates. We additionally tailor the text prompt to include patient-specific information. Our model outperforms state-of-the-art baselines, including deep learning models, other LLMs, and clinical methods across multiple medical domains, specifically electrocardiograms and respiratory waveforms. MedTsLLM presents a promising step towards harnessing the power of LLMs for medical time series analysis that can elevate data-driven tools for clinicians and improve patient outcomes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a2dd8b031dfd71e27fb062685589208744197902" target='_blank'>
-              Generalizing Graph Transformers Across Diverse Graphs and Tasks via Pre-Training on Industrial-Scale Data
+          <td><a href="https://www.semanticscholar.org/paper/6ac9e9c8bdd4eebe3cf6adf7187b9ffb16ff5b64" target='_blank'>
+              MedTsLLM: Leveraging LLMs for Multimodal Medical Time Series Analysis
               </a>
             </td>
           <td>
-            Yufei He, Zhenyu Hou, Yukuo Cen, Feng He, Xu Cheng, Bryan Hooi
+            Nimeesha Chan, Felix Parker, William Bennett, Tianyi Wu, Mung Yao Jia, James Fackler, Kimia Ghobadi
           </td>
-          <td>2024-07-04</td>
+          <td>2024-08-14</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>12</td>
+          <td>1</td>
         </tr>
 
         <tr id="Current Transformer methods for Multivariate Time-Series Forecasting (MTSF) are all based on the conventional attention mechanism. They involve sequence embedding and performing a linear projection of Q, K, and V, and then computing attention within this latent space. We have never delved into the attention mechanism to explore whether such a mapping space is optimal for MTSF. To investigate this issue, this study first proposes Frequency Spectrum attention (FSatten), a novel attention mechanism based on the frequency domain space. It employs the Fourier transform for embedding and introduces Multi-head Spectrum Scaling (MSS) to replace the conventional linear mapping of Q and K. FSatten can accurately capture the periodic dependencies between sequences and outperform the conventional attention without changing mainstream architectures. We further design a more general method dubbed Scaled Orthogonal attention (SOatten). We propose an orthogonal embedding and a Head-Coupling Convolution (HCC) based on the neighboring similarity bias to guide the model in learning comprehensive dependency patterns. Experiments show that FSatten and SOatten surpass the SOTA which uses conventional attention, making it a good alternative as a basic attention mechanism for MTSF. The codes and log files will be released at: https://github.com/Joeland4/FSatten-SOatten.">
@@ -1372,34 +1267,34 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>0</td>
         </tr>
 
-        <tr id="Short fixed-length inputs are the main bottleneck of deep learning methods in long time-series forecasting tasks. Prolonging input length causes overfitting, rapidly deteriorating accuracy. Our research indicates that the overfitting is a combination reaction of the multi-scale pattern coupling in time series and the fixed focusing scale of current models. First, we find that the patterns exhibited by a time series across various scales are reflective of its multi-periodic nature, where each scale corresponds to specific period length. Second, We find that the token size predominantly dictates model behavior, as it determines the scale at which the model focuses and the context size it can accommodate. Our idea is to decouple the multi-scale temporal patterns of time series and to model each pattern with its corresponding period length as token size. We introduced a novel series-decomposition module(MPSD), and a Multi-Token Pattern Recognition neural network(MTPR), enabling the model to handle \textit{inputs up to $10\times$ longer}. Sufficient context enhances performance(\textit{38% maximum precision improvement}), and the decoupling approach offers \textit{Low complexity($0.22\times$ cost)} and \textit{high interpretability}.">
+        <tr id="Tabular data is ubiquitous in many real-life systems. In particular, time-dependent tabular data, where rows are chronologically related, is typically used for recording historical events, e.g., financial transactions, healthcare records, or stock history. Recently, hierarchical variants of the attention mechanism of transformer architectures have been used to model tabular time-series data. At first, rows (or columns) are encoded separately by computing attention between their fields. Subsequently, encoded rows (or columns) are attended to one another to model the entire tabular time-series. While efficient, this approach constrains the attention granularity and limits its ability to learn patterns at the field-level across separate rows, or columns. We take a first step to address this gap by proposing Fieldy, a fine-grained hierarchical model that contextualizes fields at both the row and column levels. We compare our proposal against state of the art models on regression and classification tasks using public tabular time-series datasets. Our results show that combining row-wise and column-wise attention improves performance without increasing model size. Code and data are available at https://github.com/raphaaal/fieldy.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/380b86c3909fe3e098a4ec9618f09d59bb9ef626" target='_blank'>
-              Long Input Sequence Network for Long Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/a9e5c4649872cb3a4b417acdce4fae0ea8d72ebf" target='_blank'>
+              Fine-grained Attention in Hierarchical Transformers for Tabular Time-series
               </a>
             </td>
           <td>
-            Chao Ma, Yikai Hou, Xiang Li, Yinggang Sun, Haining Yu
+            Raphaël Azorin, Zied Ben-Houidi, Massimo Gallo, A. Finamore, Pietro Michiardi
           </td>
-          <td>2024-07-18</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>24</td>
         </tr>
 
-        <tr id="Graph Neural Networks (GNNs) have attracted immense attention in the past decade due to their numerous real-world applications built around graph-structured data. On the other hand, Large Language Models (LLMs) with extensive pretrained knowledge and powerful semantic comprehension abilities have recently shown a remarkable ability to benefit applications using vision and text data. In this paper, we investigate how LLMs can be leveraged in a computationally efficient fashion to benefit rich graph-structured data, a modality relatively unexplored in LLM literature. Prior works in this area exploit LLMs to augment every node features in an ad-hoc fashion (not scalable for large graphs), use natural language to describe the complex structural information of graphs, or perform computationally expensive finetuning of LLMs in conjunction with GNNs. We propose E-LLaGNN (Efficient LLMs augmented GNNs), a framework with an on-demand LLM service that enriches message passing procedure of graph learning by enhancing a limited fraction of nodes from the graph. More specifically, E-LLaGNN relies on sampling high-quality neighborhoods using LLMs, followed by on-demand neighborhood feature enhancement using diverse prompts from our prompt catalog, and finally information aggregation using message passing from conventional GNN architectures. We explore several heuristics-based active node selection strategies to limit the computational and memory footprint of LLMs when handling millions of nodes. Through extensive experiments&ablation on popular graph benchmarks of varying scales (Cora, PubMed, ArXiv,&Products), we illustrate the effectiveness of our E-LLaGNN framework and reveal many interesting capabilities such as improved gradient flow in deep GNNs, LLM-free inference ability etc.">
+        <tr id="Short fixed-length inputs are the main bottleneck of deep learning methods in long time-series forecasting tasks. Prolonging input length causes overfitting, rapidly deteriorating accuracy. Our research indicates that the overfitting is a combination reaction of the multi-scale pattern coupling in time series and the fixed focusing scale of current models. First, we find that the patterns exhibited by a time series across various scales are reflective of its multi-periodic nature, where each scale corresponds to specific period length. Second, We find that the token size predominantly dictates model behavior, as it determines the scale at which the model focuses and the context size it can accommodate. Our idea is to decouple the multi-scale temporal patterns of time series and to model each pattern with its corresponding period length as token size. We introduced a novel series-decomposition module(MPSD), and a Multi-Token Pattern Recognition neural network(MTPR), enabling the model to handle \textit{inputs up to $10\times$ longer}. Sufficient context enhances performance(\textit{38% maximum precision improvement}), and the decoupling approach offers \textit{Low complexity($0.22\times$ cost)} and \textit{high interpretability}.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0a2cdb13a15d95a5ab05aa5ec921518aa3655e93" target='_blank'>
-              All Against Some: Efficient Integration of Large Language Models for Message Passing in Graph Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/380b86c3909fe3e098a4ec9618f09d59bb9ef626" target='_blank'>
+              Long Input Sequence Network for Long Time Series Forecasting
               </a>
             </td>
           <td>
-            Ajay Jaiswal, Nurendra Choudhary, Ravinarayana Adkathimar, M. P. Alagappan, G. Hiranandani, Ying Ding, Zhangyang Wang, E-Wen Huang, Karthik Subbian
+            Chao Ma, Yikai Hou, Xiang Li, Yinggang Sun, Haining Yu
           </td>
-          <td>2024-07-20</td>
+          <td>2024-07-18</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>21</td>
+          <td>0</td>
         </tr>
 
         <tr id="The non-stationary nature of real-world Multivariate Time Series (MTS) data presents forecasting models with a formidable challenge of the time-variant distribution of time series, referred to as distribution shift. Existing studies on the distribution shift mostly adhere to adaptive normalization techniques for alleviating temporal mean and covariance shifts or time-variant modeling for capturing temporal shifts. Despite improving model generalization, these normalization-based methods often assume a time-invariant transition between outputs and inputs but disregard specific intra-/inter-series correlations, while time-variant models overlook the intrinsic causes of the distribution shift. This limits model expressiveness and interpretability of tackling the distribution shift for MTS forecasting. To mitigate such a dilemma, we present a unified Probabilistic Graphical Model to Jointly capturing intra-/inter-series correlations and modeling the time-variant transitional distribution, and instantiate a neural framework called JointPGM for non-stationary MTS forecasting. Specifically, JointPGM first employs multiple Fourier basis functions to learn dynamic time factors and designs two distinct learners: intra-series and inter-series learners. The intra-series learner effectively captures temporal dynamics by utilizing temporal gates, while the inter-series learner explicitly models spatial dynamics through multi-hop propagation, incorporating Gumbel-softmax sampling. These two types of series dynamics are subsequently fused into a latent variable, which is inversely employed to infer time factors, generate final prediction, and perform reconstruction. We validate the effectiveness and efficiency of JointPGM through extensive experiments on six highly non-stationary MTS datasets, achieving state-of-the-art forecasting performance of MTS forecasting.">
@@ -1414,52 +1309,52 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>2024-07-18</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>5</td>
         </tr>
 
-        <tr id="Tabular data is ubiquitous in many real-life systems. In particular, time-dependent tabular data, where rows are chronologically related, is typically used for recording historical events, e.g., financial transactions, healthcare records, or stock history. Recently, hierarchical variants of the attention mechanism of transformer architectures have been used to model tabular time-series data. At first, rows (or columns) are encoded separately by computing attention between their fields. Subsequently, encoded rows (or columns) are attended to one another to model the entire tabular time-series. While efficient, this approach constrains the attention granularity and limits its ability to learn patterns at the field-level across separate rows, or columns. We take a first step to address this gap by proposing Fieldy, a fine-grained hierarchical model that contextualizes fields at both the row and column levels. We compare our proposal against state of the art models on regression and classification tasks using public tabular time-series datasets. Our results show that combining row-wise and column-wise attention improves performance without increasing model size. Code and data are available at https://github.com/raphaaal/fieldy.">
+        <tr id="Learning useful representations for continuous-time dynamic graphs (CTDGs) is challenging, due to the concurrent need to span long node interaction histories and grasp nuanced temporal details. In particular, two problems emerge: (1) Encoding longer histories requires more computational resources, making it crucial for CTDG models to maintain low computational complexity to ensure efficiency; (2) Meanwhile, more powerful models are needed to identify and select the most critical temporal information within the extended context provided by longer histories. To address these problems, we propose a CTDG representation learning model named DyGMamba, originating from the popular Mamba state space model (SSM). DyGMamba first leverages a node-level SSM to encode the sequence of historical node interactions. Another time-level SSM is then employed to exploit the temporal patterns hidden in the historical graph, where its output is used to dynamically select the critical information from the interaction history. We validate DyGMamba experimentally on the dynamic link prediction task. The results show that our model achieves state-of-the-art in most cases. DyGMamba also maintains high efficiency in terms of computational resources, making it possible to capture long temporal dependencies with a limited computation budget.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a9e5c4649872cb3a4b417acdce4fae0ea8d72ebf" target='_blank'>
-              Fine-grained Attention in Hierarchical Transformers for Tabular Time-series
+          <td><a href="https://www.semanticscholar.org/paper/aeb6fbef9a2f455a71773488e09f1c4f6686ac55" target='_blank'>
+              DyGMamba: Efficiently Modeling Long-Term Temporal Dependency on Continuous-Time Dynamic Graphs with State Space Models
               </a>
             </td>
           <td>
-            Raphaël Azorin, Z. B. Houidi, Massimo Gallo, A. Finamore, Pietro Michiardi
+            Zifeng Ding, Yifeng Li, Yuan He, Antonio Norelli, Jingcheng Wu, Volker Tresp, Yunpu Ma, Michael Bronstein
           </td>
-          <td>2024-06-21</td>
+          <td>2024-08-08</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>24</td>
+          <td>22</td>
         </tr>
 
-        <tr id="The COVID-19 pandemic and influenza outbreaks have underscored the critical need for predictive models that can effectively integrate spatial and temporal dynamics to enable accurate epidemic forecasting. Traditional time-series analysis approaches have fallen short in capturing the intricate interplay between these factors. Recent advancements have witnessed the incorporation of graph neural networks and machine learning techniques to bridge this gap, enhancing predictive accuracy and providing novel insights into disease spread mechanisms. Notable endeavors include leveraging human mobility data, employing transfer learning, and integrating advanced models such as Transformers and Graph Convolutional Networks (GCNs) to improve forecasting performance across diverse geographies for both influenza and COVID-19. However, these models often face challenges related to data quality, model transferability, and potential overfitting, highlighting the necessity for more adaptable and robust approaches. This paper introduces the Graph Attention-based Spatial Temporal (GAST) model, which employs graph attention networks (GATs) to overcome these limitations by providing a nuanced understanding of epidemic dynamics through a sophisticated spatio-temporal analysis framework. Our contributions include the development and validation of the GAST model, demonstrating its superior forecasting capabilities for influenza and COVID-19 spread, with a particular focus on short-term, daily predictions. The model’s application to both influenza and COVID-19 datasets showcases its versatility and potential to inform public health interventions across a range of infectious diseases.">
+        <tr id="Intelligent transportation systems based on sensor signals are crucial in addressing contemporary transportation issues, accomplishing dynamic traffic management, and facilitating route planning. However, the highly dynamic and intricate nature of traffic sensor signals presents difficulties for traffic prediction, with current models for traffic prediction inadequate in meeting the requirements of both long-term and short-term prediction tasks. In this paper, we propose a novel deep-learning framework called dynamic spatial-temporal correlation learning network (DSTLNet) that jointly leverages dynamical spatial and temporal features of traffic sensor signals to further improve the accuracy of long-and short-term traffic modeling and route planning. Specifically, we leverage the temporal convolutional network to capture long-term correlations. In addition, a spatial graph convolutional network is developed to dynamically model spatial features, and long-and short-term fusion layers are used to fuse the extracted long-and short-term temporal features, respectively. Experimental results on real-world datasets show that DSTLNet is competitive with the state-of-the-art, especially for long-term traffic prediction.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/628bd28abb35127fc3d4e794dfc8e0860b738427" target='_blank'>
-              Modeling epidemic dynamics using Graph Attention based Spatial Temporal networks
+          <td><a href="https://www.semanticscholar.org/paper/c2ed14c7ddd2366e53463d2401366cc0c6036604" target='_blank'>
+              DSTLNet: Dynamic Spatial-Temporal Correlation Learning Network for Traffic Sensor Signal Prediction
               </a>
             </td>
           <td>
-            Xiaofeng Zhu, Yi Zhang, Haoru Ying, Huanning Chi, Guanqun Sun, Lingxia Zeng
+            Yuxiang Shan, Hailiang Lu, Weidong Lou
           </td>
-          <td>2024-07-15</td>
-          <td>PLOS ONE</td>
-          <td>0</td>
+          <td>2024-08-08</td>
+          <td>Sensors and Materials</td>
           <td>0</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Time series models, typically trained on numerical data, are designed to forecast future values. These models often rely on weighted averaging techniques over time intervals. However, real-world time series data is seldom isolated and is frequently influenced by non-numeric factors. For instance, stock price fluctuations are impacted by daily random events in the broader world, with each event exerting a unique influence on price signals. Previously, forecasts in financial markets have been approached in two main ways: either as time-series problems over price sequence or sentiment analysis tasks. The sentiment analysis tasks aim to determine whether news events will have a positive or negative impact on stock prices, often categorizing them into discrete labels. Recognizing the need for a more comprehensive approach to accurately model time series prediction, we propose a collaborative modeling framework that incorporates textual information about relevant events for predictions. Specifically, we leverage the intuition of large language models about future changes to update real number time series predictions. We evaluated the effectiveness of our approach on financial market data.">
+        <tr id="Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex dynamic patterns in continuous-time stream data. Neural Differential Equations (NDEs) are among the state-of-the-art methods for learning continuous-time traffic dynamics. However, the traditional NDE models face issues in long-term traffic forecasting due to failures in capturing delayed traffic patterns, dynamic edge (location-to-location correlation) patterns, and abrupt trend patterns. To fill this gap, we propose a new NDE architecture called Multi-View Neural Differential Equations. Our model captures current states, delayed states, and trends in different state variables (views) by learning latent multiple representations within Neural Differential Equations. Extensive experiments conducted on several real-world traffic datasets demonstrate that our proposed method outperforms the state-of-the-art and achieves superior prediction accuracy for long-term forecasting and robustness with noisy or missing inputs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7c2fd193f7d8f4fb40c5f865884bd2b528a475a4" target='_blank'>
-              Text2TimeSeries: Enhancing Financial Forecasting through Time Series Prediction Updates with Event-Driven Insights from Large Language Models
+          <td><a href="https://www.semanticscholar.org/paper/713b5e17e000120673eebab412e9b9ae591db136" target='_blank'>
+              Multi-View Neural Differential Equations for Continuous-Time Stream Data in Long-Term Traffic Forecasting
               </a>
             </td>
           <td>
-            Litton J. Kurisinkel, Pruthwik Mishra, Yue Zhang
+            Zibo Liu, Zhe Jiang, Shigang Chen
           </td>
-          <td>2024-07-04</td>
+          <td>2024-08-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>5</td>
+          <td>2</td>
         </tr>
 
         <tr id="Continuous-time dynamic graphs (CTDGs) are essential for modeling interconnected, evolving systems. Traditional methods for extracting knowledge from these graphs often depend on feature engineering or deep learning. Feature engineering is limited by the manual and time-intensive nature of crafting features, while deep learning approaches suffer from high inference latency, making them impractical for real-time applications. This paper introduces Deep-Graph-Sprints (DGS), a novel deep learning architecture designed for efficient representation learning on CTDGs with low-latency inference requirements. We benchmark DGS against state-of-the-art feature engineering and graph neural network methods using five diverse datasets. The results indicate that DGS achieves competitive performance while improving inference speed up to 12x compared to other deep learning approaches on our tested benchmarks. Our method effectively bridges the gap between deep representation learning and low-latency application requirements for CTDGs.">
@@ -1474,289 +1369,274 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
           <td>2024-07-10</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>17</td>
+          <td>18</td>
         </tr>
 
-        <tr id="Temporal graphs are ubiquitous in real-world scenarios, such as social network, trade and transportation. Predicting dynamic links between nodes in a temporal graph is of vital importance. Traditional methods usually leverage the temporal neighborhood of interaction history to generate node embeddings first and then aggregate the source and target node embeddings to predict the link. However, such methods focus on learning individual node representations, but overlook the pairwise representation learning nature of link prediction and fail to capture the important pairwise features of links such as common neighbors (CN). Motivated by the success of Neural Common Neighbor (NCN) for static graph link prediction, we propose TNCN, a temporal version of NCN for link prediction in temporal graphs. TNCN dynamically updates a temporal neighbor dictionary for each node, and utilizes multi-hop common neighbors between the source and target node to learn a more effective pairwise representation. We validate our model on five large-scale real-world datasets from the Temporal Graph Benchmark (TGB), and find that it achieves new state-of-the-art performance on three of them. Additionally, TNCN demonstrates excellent scalability on large datasets, outperforming popular GNN baselines by up to 6.4 times in speed. Our code is available at https: //github.com/GraphPKU/TNCN.">
+        <tr id="Time series models, typically trained on numerical data, are designed to forecast future values. These models often rely on weighted averaging techniques over time intervals. However, real-world time series data is seldom isolated and is frequently influenced by non-numeric factors. For instance, stock price fluctuations are impacted by daily random events in the broader world, with each event exerting a unique influence on price signals. Previously, forecasts in financial markets have been approached in two main ways: either as time-series problems over price sequence or sentiment analysis tasks. The sentiment analysis tasks aim to determine whether news events will have a positive or negative impact on stock prices, often categorizing them into discrete labels. Recognizing the need for a more comprehensive approach to accurately model time series prediction, we propose a collaborative modeling framework that incorporates textual information about relevant events for predictions. Specifically, we leverage the intuition of large language models about future changes to update real number time series predictions. We evaluated the effectiveness of our approach on financial market data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2f1fa6e1da084b408c8acc026269aed9d98ed400" target='_blank'>
-              Efficient Neural Common Neighbor for Temporal Graph Link Prediction
+          <td><a href="https://www.semanticscholar.org/paper/7c2fd193f7d8f4fb40c5f865884bd2b528a475a4" target='_blank'>
+              Text2TimeSeries: Enhancing Financial Forecasting through Time Series Prediction Updates with Event-Driven Insights from Large Language Models
               </a>
             </td>
           <td>
-            Xiaohui Zhang, Yanbo Wang, Xiyuan Wang, Muhan Zhang
+            Litton J. Kurisinkel, Pruthwik Mishra, Yue Zhang
           </td>
-          <td>2024-06-12</td>
+          <td>2024-07-04</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>6</td>
+          <td>5</td>
         </tr>
 
-        <tr id="Representing temporal-structured samples is essential for effective time series analysis tasks. So far, recurrent networks, convolution networks and transformer-style models have been successively applied in temporal data representation, yielding notable results. However, most existing methods primarily focus on modeling and representing the variation patterns within time series in the time domain. As a highly abstracted information entity, 1D time series couples various patterns such as trends, seasonality, and dramatic changes (instantaneous high dynamic), it is difficult to exploit these highly coupled properties merely by analysis tools on purely time domain. To this end, we present Spectrogram Analysis and Representation Network (SpecAR-Net). SpecAR-Net aims at learning more comprehensive representations by modeling raw time series in both time and frequency domain, where an efficient joint extraction of time-frequency features is achieved through a group of learnable 2D multi-scale parallel complex convolution blocks. Experimental results show that the SpecAR-Net achieves excellent performance on 5 major downstream tasks i.e., classification, anomaly detection, imputation, long- and short-term forecasting. Code and appendix are available at https://github.com/Dongyi2go/SpecAR_Net.">
+        <tr id="The COVID-19 pandemic and influenza outbreaks have underscored the critical need for predictive models that can effectively integrate spatial and temporal dynamics to enable accurate epidemic forecasting. Traditional time-series analysis approaches have fallen short in capturing the intricate interplay between these factors. Recent advancements have witnessed the incorporation of graph neural networks and machine learning techniques to bridge this gap, enhancing predictive accuracy and providing novel insights into disease spread mechanisms. Notable endeavors include leveraging human mobility data, employing transfer learning, and integrating advanced models such as Transformers and Graph Convolutional Networks (GCNs) to improve forecasting performance across diverse geographies for both influenza and COVID-19. However, these models often face challenges related to data quality, model transferability, and potential overfitting, highlighting the necessity for more adaptable and robust approaches. This paper introduces the Graph Attention-based Spatial Temporal (GAST) model, which employs graph attention networks (GATs) to overcome these limitations by providing a nuanced understanding of epidemic dynamics through a sophisticated spatio-temporal analysis framework. Our contributions include the development and validation of the GAST model, demonstrating its superior forecasting capabilities for influenza and COVID-19 spread, with a particular focus on short-term, daily predictions. The model’s application to both influenza and COVID-19 datasets showcases its versatility and potential to inform public health interventions across a range of infectious diseases.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1dfaff572dd20e45c52824bd90981982d242c6dc" target='_blank'>
-              SpecAR-Net: Spectrogram Analysis and Representation Network for Time Series
+          <td><a href="https://www.semanticscholar.org/paper/628bd28abb35127fc3d4e794dfc8e0860b738427" target='_blank'>
+              Modeling epidemic dynamics using Graph Attention based Spatial Temporal networks
               </a>
             </td>
           <td>
-            Yi Dong, Liwen Zhang, Youcheng Zhang, Shi Peng, Wen Chen, Zhe Ma
+            Xiaofeng Zhu, Yi Zhang, Haoru Ying, Huanning Chi, Guanqun Sun, Lingxia Zeng
           </td>
-          <td>2024-08-01</td>
-          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
+          <td>2024-07-15</td>
+          <td>PLOS ONE</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="The field of temporal graph learning aims to learn from evolving network data to forecast future interactions. Given a collection of observed temporal graphs, is it possible to predict the evolution of an unseen network from the same domain? To answer this question, we first present the Temporal Graph Scaling (TGS) dataset, a large collection of temporal graphs consisting of eighty-four ERC20 token transaction networks collected from 2017 to 2023. Next, we evaluate the transferability of Temporal Graph Neural Networks (TGNNs) for the temporal graph property prediction task by pre-training on a collection of up to sixty-four token transaction networks and then evaluating the downstream performance on twenty unseen token networks. We find that the neural scaling law observed in NLP and Computer Vision also applies in temporal graph learning, where pre-training on greater number of networks leads to improved downstream performance. To the best of our knowledge, this is the first empirical demonstration of the transferability of temporal graphs learning. On downstream token networks, the largest pre-trained model outperforms single model TGNNs on thirteen unseen test networks. Therefore, we believe that this is a promising first step towards building foundation models for temporal graphs.">
+        <tr id="Urban traffic speed prediction aims to estimate the future traffic speed for improving urban transportation services. Enormous efforts have been made to exploit Graph Neural Networks (GNNs) for modeling spatial correlations and temporal dependencies of traffic speed evolving patterns, regularized by graph topology. While achieving promising results, current traffic speed prediction methods still suffer from ignoring topology-free patterns, which cannot be captured by GNNs. To tackle this challenge, we propose a generic model for enabling the current GNN-based methods to preserve topology-free patterns. Specifically, we first develop a Dual Cross-Scale Transformer (DCST) architecture, including a Spatial Transformer and a Temporal Transformer, to preserve the cross-scale topology-free patterns and associated dynamics, respectively. Then, to further integrate both topology-regularized/-free patterns, we propose a distillation-style learning framework, in which the existing GNN-based methods are considered as the teacher model, and the proposed DCST architecture is considered as the student model. The teacher model would inject the learned topology-regularized patterns into the student model for integrating topology-free patterns. The extensive experimental results demonstrated the effectiveness of our methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7296550cef5154a13eafc3eb00a54296113d8a8a" target='_blank'>
-              Towards Neural Scaling Laws for Foundation Models on Temporal Graphs
+          <td><a href="https://www.semanticscholar.org/paper/3911024df853ccf11138d35835572ce863df51bf" target='_blank'>
+              Make Graph Neural Networks Great Again: A Generic Integration Paradigm of Topology-Free Patterns for Traffic Speed Prediction
               </a>
             </td>
           <td>
-            Razieh Shirzadkhani, Tran Gia Bao Ngo, Kiarash Shamsi, Shenyang Huang, Farimah Poursafaei, Poupak Azad, Reihaneh Rabbany, Baris Coskunuzer, Guillaume Rabusseau, C. Akcora
+            Yicheng Zhou, P. Wang, Hao Dong, Denghui Zhang, Dingqi Yang, Yanjie Fu, Pengyang Wang
           </td>
-          <td>2024-06-14</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>19</td>
+          <td>17</td>
         </tr>
 
-        <tr id="Recent studies have raised questions about the suitability of the Transformer architecture for long sequence time-series forecasting. These forecasting models leverage Transformers to capture dependencies between multiple time steps in a time series, with embedding tokens composed of data from individual time steps. However, challenges arise when applying Transformers to predict long sequences with strong periodicity, leading to performance degradation and increased computational burden. Furthermore, embedding tokens formed one time step at a time may struggle to reveal meaningful information in long sequences, failing to capture correlations between different time steps. In this study, we propose Skip-Timeformer, a Transformer-based model that utilizes a skip-time interaction for long sequence time-series forecasting. Specifically, we decompose the time series into multiple subsequences based on different time intervals, embedding various time steps into variable tokens across multiple sequences. The skip-time interaction mechanism utilizes these variable tokens to capture dependencies in the skip-time dimension. Additionally, skip-time interaction is employed to learn dependencies between sequences missed by multiple skip time steps. The Skip-Timeformer model demonstrates state-of-the-art performance on various real-world datasets, further enhancing the long sequence forecasting capabilities of the Transformer variations and better adapting to arbitrary lookback windows.">
+        <tr id="Representing temporal-structured samples is essential for effective time series analysis tasks. So far, recurrent networks, convolution networks and transformer-style models have been successively applied in temporal data representation, yielding notable results. However, most existing methods primarily focus on modeling and representing the variation patterns within time series in the time domain. As a highly abstracted information entity, 1D time series couples various patterns such as trends, seasonality, and dramatic changes (instantaneous high dynamic), it is difficult to exploit these highly coupled properties merely by analysis tools on purely time domain. To this end, we present Spectrogram Analysis and Representation Network (SpecAR-Net). SpecAR-Net aims at learning more comprehensive representations by modeling raw time series in both time and frequency domain, where an efficient joint extraction of time-frequency features is achieved through a group of learnable 2D multi-scale parallel complex convolution blocks. Experimental results show that the SpecAR-Net achieves excellent performance on 5 major downstream tasks i.e., classification, anomaly detection, imputation, long- and short-term forecasting. Code and appendix are available at https://github.com/Dongyi2go/SpecAR_Net.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/62917f180f12405293773a5f3689236727699caf" target='_blank'>
-              Skip-Timeformer: Skip-Time Interaction Transformer for Long Sequence Time-Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/1dfaff572dd20e45c52824bd90981982d242c6dc" target='_blank'>
+              SpecAR-Net: Spectrogram Analysis and Representation Network for Time Series
               </a>
             </td>
           <td>
-            Wenchang Zhang, Hua Wang, Fan Zhang
+            Yi Dong, Liwen Zhang, Youcheng Zhang, Shi Peng, Wen Chen, Zhe Ma
           </td>
           <td>2024-08-01</td>
           <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>4</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Graph neural networks (GNNs) are widely applied in graph data modeling. However, existing GNNs are often trained in a task-driven manner that fails to fully capture the intrinsic nature of the graph structure, resulting in sub-optimal node and graph representations. To address this limitation, we propose a novel Graph structure Prompt Learning method (GPL) to enhance the training of GNNs, which is inspired by prompt mechanisms in natural language processing. GPL employs task-independent graph structure losses to encourage GNNs to learn intrinsic graph characteristics while simultaneously solving downstream tasks, producing higher-quality node and graph representations. In extensive experiments on eleven real-world datasets, after being trained by GPL, GNNs significantly outperform their original performance on node classification, graph classification, and edge prediction tasks (up to 10.28%, 16.5%, and 24.15%, respectively). By allowing GNNs to capture the inherent structural prompts of graphs in GPL, they can alleviate the issue of over-smooth and achieve new state-of-the-art performances, which introduces a novel and effective direction for GNN research with potential applications in various domains.">
+        <tr id="The scaling of large language models (LLMs) has revolutionized their capabilities in various tasks, yet this growth must be matched with efficient computational strategies. The Mixture-of-Experts (MoE) architecture stands out for its ability to scale model size without significantly increasing training costs. Despite their advantages, current MoE models often display parameter inefficiency. For instance, a pre-trained MoE-based LLM with 52 billion parameters might perform comparably to a standard model with 6.7 billion parameters. Being a crucial part of MoE, current routers in different layers independently assign tokens without leveraging historical routing information, potentially leading to suboptimal token-expert combinations and the parameter inefficiency problem. To alleviate this issue, we introduce the Layerwise Recurrent Router for Mixture-of-Experts (RMoE). RMoE leverages a Gated Recurrent Unit (GRU) to establish dependencies between routing decisions across consecutive layers. Such layerwise recurrence can be efficiently parallelly computed for input tokens and introduces negotiable costs. Our extensive empirical evaluations demonstrate that RMoE-based language models consistently outperform a spectrum of baseline models. Furthermore, RMoE integrates a novel computation stage orthogonal to existing methods, allowing seamless compatibility with other MoE architectures. Our analyses attribute RMoE's gains to its effective cross-layer information sharing, which also improves expert selection and diversity. Our code is at https://github.com/qiuzh20/RMoE">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c7879caf6538fc087678244d45d2ba15cd1a2482" target='_blank'>
-              Graph Structure Prompt Learning: A Novel Methodology to Improve Performance of Graph Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/541773c4cbb30bcdcbc82b8d02eba15af811f739" target='_blank'>
+              Layerwise Recurrent Router for Mixture-of-Experts
               </a>
             </td>
           <td>
-            Zhenhua Huang, Kunhao Li, Shaojie Wang, Zhaohong Jia, Wentao Zhu, Sharad Mehrotra
+            Zihan Qiu, Zeyu Huang, Shuang Cheng, Yizhi Zhou, Zili Wang, Ivan Titov, Jie Fu
           </td>
-          <td>2024-07-16</td>
+          <td>2024-08-13</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Learning temporal dependencies among targets (TDT) benefits better time series forecasting, where targets refer to the predicted sequence. Although autoregressive methods model TDT recursively, they suffer from inefficient inference and error accumulation. We argue that integrating TDT learning into non-autoregressive methods is essential for pursuing effective and efficient time series forecasting. In this study, we introduce the differencing approach to represent TDT and propose a parameter-free and plug-and-play solution through an optimization objective, namely TDT Loss. It leverages the proportion of inconsistent signs between predicted and ground truth TDT as an adaptive weight, dynamically balancing target prediction and fine-grained TDT fitting. Importantly, TDT Loss incurs negligible additional cost, with only $\mathcal{O}(n)$ increased computation and $\mathcal{O}(1)$ memory requirements, while significantly enhancing the predictive performance of non-autoregressive models. To assess the effectiveness of TDT loss, we conduct extensive experiments on 7 widely used datasets. The experimental results of plugging TDT loss into 6 state-of-the-art methods show that out of the 168 experiments, 75.00\% and 94.05\% exhibit improvements in terms of MSE and MAE with the maximum 24.56\% and 16.31\%, respectively.">
+        <tr id="Battery life estimation is critical for optimizing battery performance and guaranteeing minimal degradation for better efficiency and reliability of battery-powered systems. The existing methods to predict the Remaining Useful Life(RUL) of Lithium-ion Batteries (LiBs) neglect the relational dependencies of the battery parameters to model the nonlinear degradation trajectories. We present the Battery GraphNets framework that jointly learns to incorporate a discrete dependency graph structure between battery parameters to capture the complex interactions and the graph-learning algorithm to model the intrinsic battery degradation for RUL prognosis. The proposed method outperforms several popular methods by a significant margin on publicly available battery datasets and achieves SOTA performance. We report the ablation studies to support the efficacy of our approach.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3c5c365a674479cb9c45cf75b5a8928764322cad" target='_blank'>
-              TDT Loss Takes It All: Integrating Temporal Dependencies among Targets into Non-Autoregressive Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/cb566703033116a6d7a3066560ba85a02a8f83cf" target='_blank'>
+              Battery GraphNets : Relational Learning for Lithium-ion Batteries(LiBs) Life Estimation
               </a>
             </td>
           <td>
-            Qi Xiong, Kai Tang, Minbo Ma, Jie Xu, Tianrui Li
+            Sakhinana Sagar Srinivas, Rajat Kumar Sarkar, Venkataramana Runkana
           </td>
-          <td>2024-06-07</td>
+          <td>2024-08-14</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Significant efforts have been directed toward integrating powerful Large Language Models (LLMs) with diverse modalities, particularly focusing on the fusion of vision, language, and audio data. However, the graph-structured data, inherently rich in structural and domain-specific knowledge, have not yet been gracefully adapted to LLMs. Existing methods either describe the graph with raw text, suffering the loss of graph structural information, or feed Graph Neural Network (GNN) embeddings directly into LLM at the cost of losing semantic representation. To bridge this gap, we introduce an innovative, end-to-end modality-aligning framework, equipped with a pretrained Dual-Residual Vector Quantized-Variational AutoEncoder (Dr.E). This framework is specifically designed to facilitate token-level alignment with LLMs, enabling an effective translation of the intrinsic `language' of graphs into comprehensible natural language. Our experimental evaluations on standard GNN node classification tasks demonstrate competitive performance against other state-of-the-art approaches. Additionally, our framework ensures interpretability, efficiency, and robustness, with its effectiveness further validated under both fine-tuning and few-shot settings. This study marks the first successful endeavor to achieve token-level alignment between GNNs and LLMs.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/791d076f62ad65b719dfe07a87ecd954c27051d5" target='_blank'>
-              Dr.E Bridges Graphs with Large Language Models through Words
+          <td><a href="https://www.semanticscholar.org/paper/6fbaa841f1f012a9be06d56da6a1921f5d50f305" target='_blank'>
+              MGLEP: Multimodal Graph Learning for Modeling Emerging Pandemics with Big Data
               </a>
             </td>
           <td>
-            Zipeng Liu, Likang Wu, Ming He, Zhong Guan, Hongke Zhao, Nan Feng
+            Khanh-Tung Tran, T. Hy, Lili Jiang, Xuan-Son Vu
           </td>
-          <td>2024-06-19</td>
-          <td>ArXiv</td>
+          <td>2023-10-23</td>
+          <td>Scientific Reports</td>
           <td>0</td>
-          <td>10</td>
+          <td>7</td>
         </tr>
 
-        <tr id="In the realm of cloud computing, long sequence prediction of workloads plays a pivotal role, crucial for optimizing resource allocation and enhancing system performance. However, current research of long-sequence workload forecasting faces a series of challenges, mainly due to the high randomness and instability characteristics of long workload sequences, making it difficult for traditional machine learning methods to provide accurate results. Therefore, we designed a novel approach for long sequence forecasting, thoroughly considering the latent characteristics of cloud workload sequences. Initially, we employ convolution kernels of varying sizes to perform multiscale sequence decomposition, better capturing contextual information and periodic features in long sequence. Furthermore, through fast Fourier transformation, we convert one-dimensional sequences into two-dimensional space, leveraging dilated convolutions to extract effective features within the intra-period and inter-period variations. Ultimately, we introduce an attention mechanism, effectively integrating the intra-period and inter-period variation features into the proposed model. Our method has undergone comprehensive evaluation on publicly available datasets from Google, Alibaba, and Microsoft. Experimental results demonstrate superior accuracy and robustness of our model across various workload types, showcasing its excellent adaptability to dynamic and complex workload scenarios.">
+        <tr id="Traffic flow forecasting is considered a critical task in the field of intelligent transportation systems. In this paper, to address the issue of low accuracy in long-term forecasting of spatial-temporal big data on traffic flow, we propose an innovative model called Spatial-Temporal Retentive Network (ST-RetNet). We extend the Retentive Network to address the task of traffic flow forecasting. At the spatial scale, we integrate a topological graph structure into Spatial Retentive Network(S-RetNet), utilizing an adaptive adjacency matrix to extract dynamic spatial features of the road network. We also employ Graph Convolutional Networks to extract static spatial features of the road network. These two components are then fused to capture dynamic and static spatial correlations. At the temporal scale, we propose the Temporal Retentive Network(T-RetNet), which has been demonstrated to excel in capturing long-term dependencies in traffic flow patterns compared to other time series models, including Recurrent Neural Networks based and transformer models. We achieve the spatial-temporal traffic flow forecasting task by integrating S-RetNet and T-RetNet to form ST-RetNet. Through experimental comparisons conducted on four real-world datasets, we demonstrate that ST-RetNet outperforms the state-of-the-art approaches in traffic flow forecasting.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/af61cab4d7fb915b58034e3fad0f5db0170a6c3f" target='_blank'>
-              Exploiting sequence characteristics for long-term workload prediction in cloud data centers
+          <td><a href="https://www.semanticscholar.org/paper/2ff0fb7e804a47b3a7fc6957f58fb65aa01ba12a" target='_blank'>
+              ST-RetNet: A Long-term Spatial-Temporal Traffic Flow Prediction Method
               </a>
             </td>
           <td>
-            Zongxiao Chen, Weijian Zheng, Yusong Zhou, Huile Wang, Weiping Zheng
+            Baichao Long, Wang Zhu, Jianli Xiao
           </td>
-          <td>2024-06-08</td>
-          <td>None</td>
+          <td>2024-07-13</td>
+          <td>ArXiv</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Key elements of human events are extracted as quadruples that consist of subject, relation, object, and timestamp. This representation can be extended to a quintuple by adding a fifth element: a textual summary that briefly describes the event. These quadruples or quintuples, when organized within a specific domain, form a temporal knowledge graph (TKG). Current learning frameworks focus on a few TKG-related tasks, such as predicting an object given a subject and a relation or forecasting the occurrences of multiple types of events (i.e., relation) in the next time window. They typically rely on complex structural and sequential models like graph neural networks (GNNs) and recurrent neural networks (RNNs) to update intermediate embeddings. However, these methods often neglect the contextual information inherent in each quintuple, which can be effectively captured through concise textual descriptions. In this paper, we investigate how large language models (LLMs) can streamline the design of TKG learning frameworks while maintaining competitive accuracy in prediction and forecasting tasks. We develop multiple prompt templates to frame the object prediction (OP) task as a standard question-answering (QA) task, suitable for instruction fine-tuning with an encoder-decoder generative LLM. For multi-event forecasting (MEF), we design simple yet effective prompt templates for each TKG quintuple. This novel approach removes the need for GNNs and RNNs, instead utilizing an encoder-only LLM to generate fixed intermediate embeddings, which are subsequently processed by a prediction head with a self-attention mechanism to forecast potential future relations. Extensive experiments on multiple real-world datasets using various evaluation metrics validate the effectiveness and robustness of our approach.">
+        <tr id="In the AIOps (Artificial Intelligence for IT Operations) era, accurately forecasting system states is crucial. In microservices systems, this task encounters the challenge of dynamic and complex spatio-temporal relationships among microservice instances, primarily due to dynamic deployments, diverse call paths, and cascading effects among instances. Current time-series forecasting methods, which focus mainly on intrinsic patterns, are insufficient in environments where spatial relationships are critical. Similarly, spatio-temporal graph approaches often neglect the nature of temporal trend, concentrating mostly on message passing between nodes. Moreover, current research in microservices domain frequently underestimates the importance of network metrics and topological structures in capturing the evolving dynamics of systems. This paper introduces STMformer, a model tailored for forecasting system states in microservices environments, capable of handling multi-node and multivariate time series. Our method leverages dynamic network connection data and topological information to assist in modeling the intricate spatio-temporal relationships within the system. Additionally, we integrate the PatchCrossAttention module to compute the impact of cascading effects globally. We have developed a dataset based on a microservices system and conducted comprehensive experiments with STMformer against leading methods. In both short-term and long-term forecasting tasks, our model consistently achieved a 8.6% reduction in MAE(Mean Absolute Error) and a 2.2% reduction in MSE (Mean Squared Error). The source code is available at https://github.com/xuyifeiiie/STMformer.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/173bd3b71792bf891ab5af4a6454e6ba07576bcd" target='_blank'>
-              Large Language Models as Event Forecasters
+          <td><a href="https://www.semanticscholar.org/paper/d0bdfae99d444ac389fd3590ebcd41ac91a7b2f4" target='_blank'>
+              System States Forecasting of Microservices with Dynamic Spatio-Temporal Data
               </a>
             </td>
           <td>
-            Libo Zhang, Yue Ning
+            Yifei Xu, Jingguo Ge, Haina Tang, Shuai Ding, Tong Li, Hui Li
           </td>
-          <td>2024-06-15</td>
+          <td>2024-08-15</td>
           <td>ArXiv</td>
-          <td>1</td>
           <td>0</td>
+          <td>1</td>
         </tr>
 
-        <tr id="The emergence of large language models (LLMs) has revolutionized the way we interact with graphs, leading to a new paradigm called GraphLLM. Despite the rapid development of GraphLLM methods in recent years, the progress and understanding of this field remain unclear due to the lack of a benchmark with consistent experimental protocols. To bridge this gap, we introduce GLBench, the first comprehensive benchmark for evaluating GraphLLM methods in both supervised and zero-shot scenarios. GLBench provides a fair and thorough evaluation of different categories of GraphLLM methods, along with traditional baselines such as graph neural networks. Through extensive experiments on a collection of real-world datasets with consistent data processing and splitting strategies, we have uncovered several key findings. Firstly, GraphLLM methods outperform traditional baselines in supervised settings, with LLM-as-enhancers showing the most robust performance. However, using LLMs as predictors is less effective and often leads to uncontrollable output issues. We also notice that no clear scaling laws exist for current GraphLLM methods. In addition, both structures and semantics are crucial for effective zero-shot transfer, and our proposed simple baseline can even outperform several models tailored for zero-shot scenarios. The data and code of the benchmark can be found at https://github.com/NineAbyss/GLBench.">
+        <tr id="Temporal graphs have gained increasing importance due to their ability to model dynamically evolving relationships. These graphs can be represented through either a stream of edge events or a sequence of graph snapshots. Until now, the development of machine learning methods for both types has occurred largely in isolation, resulting in limited experimental comparison and theoretical crosspollination between the two. In this paper, we introduce Unified Temporal Graph (UTG), a framework that unifies snapshot-based and event-based machine learning models under a single umbrella, enabling models developed for one representation to be applied effectively to datasets of the other. We also propose a novel UTG training procedure to boost the performance of snapshot-based models in the streaming setting. We comprehensively evaluate both snapshot and event-based models across both types of temporal graphs on the temporal link prediction task. Our main findings are threefold: first, when combined with UTG training, snapshotbased models can perform competitively with event-based models such as TGN and GraphMixer even on event datasets. Second, snapshot-based models are at least an order of magnitude faster than most event-based models during inference. Third, while event-based methods such as NAT and DyGFormer outperforms snapshotbased methods on both types of temporal graphs, this is because they leverage joint neighborhood structural features thus emphasizing the potential to incorporate these features into snapshot-based models as well. These findings highlight the importance of comparing model architectures independent of the data format and suggest the potential of combining the efficiency of snapshot-based models with the performance of event-based models in the future.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/918a6de8979fe0550cb7e986410419030928efd7" target='_blank'>
-              GLBench: A Comprehensive Benchmark for Graph with Large Language Models
+          <td><a href="https://www.semanticscholar.org/paper/7fff2ad251ff12c30edda0c89831123380698940" target='_blank'>
+              UTG: Towards a Unified View of Snapshot and Event Based Models for Temporal Graphs
               </a>
             </td>
           <td>
-            Yuhan Li, Peisong Wang, Xiao Zhu, Aochuan Chen, Haiyun Jiang, Deng Cai, Victor Wai Kin Chan, Jia Li
+            Shenyang Huang, Farimah Poursafaei, Reihaneh Rabbany, Guillaume Rabusseau, Emanuele Rossi
           </td>
-          <td>2024-07-10</td>
+          <td>2024-07-17</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>5</td>
         </tr>
 
-        <tr id="The recent rapid development of language models (LMs) has attracted attention in the field of time series, including multimodal time series modeling. However, we note that current time series multimodal methods are biased, often assigning a primary role to one modality while the other assumes a secondary role. They overlook the mutual benefits and complementary of different modalities. For example, in seizure diagnosis, relying solely on textual clinical reports makes it difficult to pinpoint the area and type of the disease, while electroencephalograms (EEGs) alone cannot provide an accurate diagnosis without considering the symptoms. In this study, based on the complementary information mining of time series multimodal data, we propose DualTime, a Dual-adapter multimodal language model for Time series representation implementing temporal-primary and textual-primary modeling simultaneously. By injecting lightweight adaption tokens, the LM pipeline shared by dual adapters encourages embedding alignment and achieves efficient fine-tuning. Empirically, our method outperforms state-of-the-art models in both supervised and unsupervised settings, highlighting the complementary benefits of different modalities. In addition, we conduct few-shot label transfer experiments, which further verifies the transferability and expressiveness of our proposed DualTime.">
+        <tr id="Demand prediction is a crucial task for e-commerce and physical retail businesses, especially during high-stake sales events. However, the limited availability of historical data from these peak periods poses a significant challenge for traditional forecasting methods. In this paper, we propose a novel approach that leverages strategically chosen proxy data reflective of potential sales patterns from similar entities during non-peak periods, enriched by features learned from a graph neural networks (GNNs)-based forecasting model, to predict demand during peak events. We formulate the demand prediction as a meta-learning problem and develop the Feature-based First-Order Model-Agnostic Meta-Learning (F-FOMAML) algorithm that leverages proxy data from non-peak periods and GNN-generated relational metadata to learn feature-specific layer parameters, thereby adapting to demand forecasts for peak events. Theoretically, we show that by considering domain similarities through task-specific metadata, our model achieves improved generalization, where the excess risk decreases as the number of training tasks increases. Empirical evaluations on large-scale industrial datasets demonstrate the superiority of our approach. Compared to existing state-of-the-art models, our method demonstrates a notable improvement in demand prediction accuracy, reducing the Mean Absolute Error by 26.24% on an internal vending machine dataset and by 1.04% on the publicly accessible JD.com dataset.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3b2b86f956f070934e0947d25e2c9c6fff5b157e" target='_blank'>
-              DualTime: A Dual-Adapter Multimodal Language Model for Time Series Representation
+          <td><a href="https://www.semanticscholar.org/paper/fb0749b9bc04914e294f57c89199572e3cb5183c" target='_blank'>
+              F-FOMAML: GNN-Enhanced Meta-Learning for Peak Period Demand Forecasting with Proxy Data
               </a>
             </td>
           <td>
-            Weiqi Zhang, Jiexia Ye, Ziyue Li, Jia Li, F. Tsung
+            Zexing Xu, Linjun Zhang, Sitan Yang, Rasoul Etesami, Hanghang Tong, Huan Zhang, Jiawei Han
           </td>
-          <td>2024-06-07</td>
+          <td>2024-06-23</td>
           <td>ArXiv</td>
-          <td>3</td>
-          <td>47</td>
+          <td>1</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Time series forecasting is one of the crucial tasks in many industrial fields and bears financial, resource, and control benefits. The leading solutions in this domain are often associated with machine learning approaches. The drawback in many approaches is the missing interpretability of the lookback and the predicted time series. Therefore, we propose a novel method named Bag-of-Future, to introduce interpretability in a backcast as well as forecast of the given series. Our approach aims to select and predict multiple patterns for the input series, based on continuous functions in a preselected bag of functions. Furthermore, stacking multiple encodings results in a continuous parameterization of the given dataset. The predicted bags are used to give precise forecasts and can unveil black box systems. Among synthetic as well as multiple industrial energy datasets we present competitive results in terms of performance, interpretability and pattern detection of the forecast as well as the given time series. Lastly, we present ablations on the main parameters of our approach, evaluated on multiple criterions to provide parameter recommendations.">
+        <tr id="In the field of machine learning and artificial intelligence, time series forecasting plays a pivotal role across various domains such as finance, healthcare, and weather. However, the task of selecting the most suitable forecasting method for a given dataset is a complex task due to the diversity of data patterns and characteristics. This research aims to address this challenge by proposing a comprehensive benchmark for evaluating and ranking time series forecasting methods across a wide range of datasets. This study investigates the comparative performance of many methods from two prominent time series forecasting frameworks, AutoGluon-Timeseries, and sktime to shed light on their applicability in different real-world scenarios. This research contributes to the field of time series forecasting by providing a robust benchmarking methodology and facilitating informed decision-making when choosing forecasting methods for achieving optimal prediction.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/354ecda4d141b4bec61e3c359ef1cf109f3f29c3" target='_blank'>
-              Bag-of-Future: Time Series Forecasting by Continuous Function Candidates
+          <td><a href="https://www.semanticscholar.org/paper/52869870f9e404f4e69a10b76ca410b00d19088d" target='_blank'>
+              Can time series forecasting be automated? A benchmark and analysis
               </a>
             </td>
           <td>
-            Hendrik Klopries, Vignesh Chandramouli, Andreas Schwung
+            Anvitha Thirthapura Sreedhara, Joaquin Vanschoren
           </td>
-          <td>2024-06-18</td>
-          <td>2024 IEEE 33rd International Symposium on Industrial Electronics (ISIE)</td>
+          <td>2024-07-23</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>13</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Traffic prediction plays a key role in various smart city applications, which can help traffic managers make traffic plans in advance, assist online ride-hailing companies in deploying vehicles reasonably, and provide early warning of congestion for safety authorities. While increasingly complex models achieve impressive prediction performance, there are concerns about the effectiveness of these models in handling large-scale road networks. Especially for researchers who don't have access to powerful GPU devices, the expensive memory burden limits the usefulness of these models. In this paper, we take the first step of learning on the large-scale spatio-temporal graph and propose a divide-and-conquer training strategy for Large Spatio-Temporal Graph Learning, namely LarSTL. The core idea behind this strategy is to divide the large graph into multiple subgraphs, which are treated as task streams to sequentially train the model to conquer each subgraph one by one. We introduce a novel perspective based on the continuous learning paradigm to achieve this goal. In order to overcome forgetting the knowledge learned from previous subgraphs, an experience-replay strategy consolidates the learned knowledge by replaying nodes sampled from previous subgraphs. Moreover, we configure specific feature adaptors for each subgraph to extract personalized features, and it is also beneficial to consolidate the learned knowledge from the perspective of parameters. We conduct experiments using multiple large-scale traffic network datasets on a V100 GPU with only 16GB memory, and the results demonstrate that our LarSTL can achieve competitive performance and high efficiency.">
+        <tr id="The Variable Subset Forecasting (VSF) problem, where the majority of variables are unavailable in the inference stage of multivariate forecasting, has been an important but under-explored task with broad impacts in many real-world applications. Missing values, absent inter-correlation, and the impracticality of retraining largely hinder the ability of multivariate forecasting models to capture inherent relationships among variables, impacting their performance. However, existing approaches towards these issues either heavily rely on local temporal correlation or face limitations in fully recovering missing information from the unavailable subset, accompanied by notable computational expenses. To address these problems, we propose a novel density estimation solution to recover the information of missing variables via flows-based generative framework. In particular, a novel generative network for time series, namely Time-series Reconstruction Flows (TRF), is proposed to estimate and reconstruct the missing variable subset. In addition, a novel meta-training framework, Variable-Agnostic Meta Learning, has been developed to enhance the generalization ability of TRF, enabling it to adapt to diverse missing variables situations. Finally, extensive experiments are conducted to demonstrate the superiority of our proposed method compared with baseline methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/646751856e85cda770f12efc51c740e239c78444" target='_blank'>
-              Make Bricks with a Little Straw: Large-Scale Spatio-Temporal Graph Learning with Restricted GPU-Memory Capacity
+          <td><a href="https://www.semanticscholar.org/paper/5dcee67fc3a8091cc9cc24057f5c0b9c933f4044" target='_blank'>
+              Reconstructing Missing Variables for Multivariate Time Series Forecasting via Conditional Generative Flows
               </a>
             </td>
           <td>
-            Binwu Wang, Pengkun Wang, Zhen-Qiang Zhou, Zhe Zhao, Wei Xu, Yang Wang
+            Xuanming Hu, Wei Fan, Haifeng Chen, Pengyang Wang, Yanjie Fu
           </td>
           <td>2024-08-01</td>
           <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>6</td>
+          <td>3</td>
         </tr>
 
-        <tr id="In recent years, graph prompt learning/tuning has garnered increasing attention in adapting pre-trained models for graph representation learning. As a kind of universal graph prompt learning method, Graph Prompt Feature (GPF) has achieved remarkable success in adapting pre-trained models for Graph Neural Networks (GNNs). By fixing the parameters of a pre-trained GNN model, the aim of GPF is to modify the input graph data by adding some (learnable) prompt vectors into graph node features to better align with the downstream tasks on the smaller dataset. However, existing GPFs generally suffer from two main limitations. First, GPFs generally focus on node prompt learning which ignore the prompting for graph edges. Second, existing GPFs generally conduct the prompt learning on all nodes equally which fails to capture the importances of different nodes and may perform sensitively w.r.t noisy nodes in aligning with the downstream tasks. To address these issues, in this paper, we propose a new unified Graph Selective Prompt Feature learning (GSPF) for GNN fine-tuning. The proposed GSPF integrates the prompt learning on both graph node and edge together, which thus provides a unified prompt model for the graph data. Moreover, it conducts prompt learning selectively on nodes and edges by concentrating on the important nodes and edges for prompting which thus make our model be more reliable and compact. Experimental results on many benchmark datasets demonstrate the effectiveness and advantages of the proposed GSPF method.">
+        <tr id="Transformer, a deep neural network architecture, has long dominated the field of natural language processing and beyond. Nevertheless, the recent introduction of Mamba challenges its supremacy, sparks considerable interest among researchers, and gives rise to a series of Mamba-based models that have exhibited notable potential. This survey paper orchestrates a comprehensive discussion, diving into essential research dimensions, covering: (i) the functioning of the Mamba mechanism and its foundation on the principles of structured state space models; (ii) the proposed improvements and the integration of Mamba with various networks, exploring its potential as a substitute for Transformers; (iii) the combination of Transformers and Mamba to compensate for each other's shortcomings. We have also made efforts to interpret Mamba and Transformer in the framework of kernel functions, allowing for a comparison of their mathematical nature within a unified context. Our paper encompasses the vast majority of improvements related to Mamba to date.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3b3369db0e5602cdc0f3038540cc8d50f51ae58a" target='_blank'>
-              A Unified Graph Selective Prompt Learning for Graph Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/7343105953d6b67d9b94dc891649fb7197a33776" target='_blank'>
+              Venturing into Uncharted Waters: The Navigation Compass from Transformer to Mamba
               </a>
             </td>
           <td>
-            Bo Jiang, Hao Wu, Ziyan Zhang, Beibei Wang, Jinhui Tang
+            Yuchen Zou, Yineng Chen, Z. Li, Lefei Zhang, Hai Zhao
           </td>
-          <td>2024-06-15</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>20</td>
         </tr>
 
-        <tr id="None">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6fbaa841f1f012a9be06d56da6a1921f5d50f305" target='_blank'>
-              MGLEP: Multimodal Graph Learning for Modeling Emerging Pandemics with Big Data
-              </a>
-            </td>
-          <td>
-            Khanh-Tung Tran, T. Hy, Lili Jiang, Xuan-Son Vu
-          </td>
-          <td>2023-10-23</td>
-          <td>Scientific Reports</td>
-          <td>0</td>
-          <td>7</td>
-        </tr>
-
-        <tr id="Traffic flow forecasting is considered a critical task in the field of intelligent transportation systems. In this paper, to address the issue of low accuracy in long-term forecasting of spatial-temporal big data on traffic flow, we propose an innovative model called Spatial-Temporal Retentive Network (ST-RetNet). We extend the Retentive Network to address the task of traffic flow forecasting. At the spatial scale, we integrate a topological graph structure into Spatial Retentive Network(S-RetNet), utilizing an adaptive adjacency matrix to extract dynamic spatial features of the road network. We also employ Graph Convolutional Networks to extract static spatial features of the road network. These two components are then fused to capture dynamic and static spatial correlations. At the temporal scale, we propose the Temporal Retentive Network(T-RetNet), which has been demonstrated to excel in capturing long-term dependencies in traffic flow patterns compared to other time series models, including Recurrent Neural Networks based and transformer models. We achieve the spatial-temporal traffic flow forecasting task by integrating S-RetNet and T-RetNet to form ST-RetNet. Through experimental comparisons conducted on four real-world datasets, we demonstrate that ST-RetNet outperforms the state-of-the-art approaches in traffic flow forecasting.">
+        <tr id="Irregular and asynchronous event sequences are prevalent in many domains, such as social media, finance, and healthcare. Traditional temporal point processes (TPPs), like Hawkes processes, often struggle to model mutual inhibition and nonlinearity effectively. While recent neural network models, including RNNs and Transformers, address some of these issues, they still face challenges with long-term dependencies and computational efficiency. In this paper, we introduce the Mamba Hawkes Process (MHP), which leverages the Mamba state space architecture to capture long-range dependencies and dynamic event interactions. Our results show that MHP outperforms existing models across various datasets. Additionally, we propose the Mamba Hawkes Process Extension (MHP-E), which combines Mamba and Transformer models to enhance predictive capabilities. We present the novel application of the Mamba architecture to Hawkes processes, a flexible and extensible model structure, and a theoretical analysis of the synergy between state space models and Hawkes processes. Experimental results demonstrate the superior performance of both MHP and MHP-E, advancing the field of temporal point process modeling.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2ff0fb7e804a47b3a7fc6957f58fb65aa01ba12a" target='_blank'>
-              ST-RetNet: A Long-term Spatial-Temporal Traffic Flow Prediction Method
+          <td><a href="https://www.semanticscholar.org/paper/01159bef23c8f357e01445fe63b05caff1959dc5" target='_blank'>
+              Mamba Hawkes Process
               </a>
             </td>
           <td>
-            Baichao Long, Wang Zhu, Jianli Xiao
+            Anningzhe Gao, Shan Dai, Yan Hu
           </td>
-          <td>2024-07-13</td>
+          <td>2024-07-07</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Temporal graphs have gained increasing importance due to their ability to model dynamically evolving relationships. These graphs can be represented through either a stream of edge events or a sequence of graph snapshots. Until now, the development of machine learning methods for both types has occurred largely in isolation, resulting in limited experimental comparison and theoretical crosspollination between the two. In this paper, we introduce Unified Temporal Graph (UTG), a framework that unifies snapshot-based and event-based machine learning models under a single umbrella, enabling models developed for one representation to be applied effectively to datasets of the other. We also propose a novel UTG training procedure to boost the performance of snapshot-based models in the streaming setting. We comprehensively evaluate both snapshot and event-based models across both types of temporal graphs on the temporal link prediction task. Our main findings are threefold: first, when combined with UTG training, snapshotbased models can perform competitively with event-based models such as TGN and GraphMixer even on event datasets. Second, snapshot-based models are at least an order of magnitude faster than most event-based models during inference. Third, while event-based methods such as NAT and DyGFormer outperforms snapshotbased methods on both types of temporal graphs, this is because they leverage joint neighborhood structural features thus emphasizing the potential to incorporate these features into snapshot-based models as well. These findings highlight the importance of comparing model architectures independent of the data format and suggest the potential of combining the efficiency of snapshot-based models with the performance of event-based models in the future.">
+        <tr id="Hierarchical time-series forecasting (HTSF) is an important problem for many real-world business applications where the goal is to simultaneously forecast multiple time-series that are related to each other via a hierarchical relation. Recent works, however, do not address two important challenges that are typically observed in many demand forecasting applications at large companies. First, many time-series at lower levels of the hierarchy have high sparsity i.e., they have a significant number of zeros. Most HTSF methods do not address this varying sparsity across the hierarchy. Further, they do not scale well to the large size of the real-world hierarchy typically unseen in benchmarks used in literature. We resolve both these challenges by proposing HAILS, a novel probabilistic hierarchical model that enables accurate and calibrated probabilistic forecasts across the hierarchy by adaptively modeling sparse and dense time-series with different distributional assumptions and reconciling them to adhere to hierarchical constraints. We show the scalability and effectiveness of our methods by evaluating them against real-world demand forecasting datasets. We deploy HAILS at a large chemical manufacturing company for a product demand forecasting application with over ten thousand products and observe a significant 8.5\% improvement in forecast accuracy and 23% better improvement for sparse time-series. The enhanced accuracy and scalability make HAILS a valuable tool for improved business planning and customer experience.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7fff2ad251ff12c30edda0c89831123380698940" target='_blank'>
-              UTG: Towards a Unified View of Snapshot and Event Based Models for Temporal Graphs
+          <td><a href="https://www.semanticscholar.org/paper/e7c76a66b9e8e91e00f152d5a723fd37775613e4" target='_blank'>
+              Large Scale Hierarchical Industrial Demand Time-Series Forecasting incorporating Sparsity
               </a>
             </td>
           <td>
-            Shenyang Huang, Farimah Poursafaei, Reihaneh Rabbany, Guillaume Rabusseau, Emanuele Rossi
+            Harshavardhan Kamarthi, Aditya B. Sasanur, Xinjie Tong, Xingyu Zhou, James Peters, Joe Czyzyk, B. A. Prakash
           </td>
-          <td>2024-07-17</td>
+          <td>2024-07-02</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>5</td>
+          <td>7</td>
         </tr>
 
-        <tr id="Transformers have revolutionized machine learning with their simple yet effective architecture. Pre-training Transformers on massive text datasets from the Internet has led to unmatched generalization for natural language understanding (NLU) tasks. However, such language models remain fragile when tasked with algorithmic forms of reasoning, where computations must be precise and robust. To address this limitation, we propose a novel approach that combines the Transformer's language understanding with the robustness of graph neural network (GNN)-based neural algorithmic reasoners (NARs). Such NARs proved effective as generic solvers for algorithmic tasks, when specified in graph form. To make their embeddings accessible to a Transformer, we propose a hybrid architecture with a two-phase training procedure, allowing the tokens in the language model to cross-attend to the node embeddings from the NAR. We evaluate our resulting TransNAR model on CLRS-Text, the text-based version of the CLRS-30 benchmark, and demonstrate significant gains over Transformer-only models for algorithmic reasoning, both in and out of distribution.">
+        <tr id="Human mobility is intricately influenced by urban contexts spatially and temporally, constituting essential domain knowledge in understanding traffic systems. While existing traffic forecasting models primarily rely on raw traffic data and advanced deep learning techniques, incorporating contextual information remains underexplored due to the lack of effective integration frameworks and the complexity of urban contexts. This study proposes a novel context-aware knowledge graph (CKG) framework to enhance traffic speed forecasting by effectively modeling spatial and temporal contexts. Employing a relation-dependent integration strategy, the framework generates context-aware representations from the spatial and temporal units of CKG to capture spatio-temporal dependencies of urban contexts. A CKG-GNN model, combining the CKG, dual-view multi-head self-attention (MHSA), and graph neural network (GNN), is then designed to predict traffic speed using these context-aware representations. Our experiments demonstrate that CKG's configuration significantly influences embedding performance, with ComplEx and KG2E emerging as optimal for embedding spatial and temporal units, respectively. The CKG-GNN model surpasses benchmark models, achieving an average MAE of $3.46\pm0.01$ and a MAPE of $14.76\pm0.09\%$ for traffic speed predictions from 10 to 120 minutes. The dual-view MHSA analysis reveals the crucial role of relation-dependent features from the context-based view and the model's ability to prioritize recent time slots in prediction from the sequence-based view. The CKG framework's model-agnostic nature suggests its potential applicability in various applications of intelligent transportation systems. Overall, this study underscores the importance of incorporating domain-specific contexts into traffic forecasting and merging context-aware knowledge graphs with neural networks to enhance accuracy.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3fc132fff0fcda6d9f33d22e43499ca8478235f6" target='_blank'>
-              Transformers meet Neural Algorithmic Reasoners
+          <td><a href="https://www.semanticscholar.org/paper/0865c15082b62b4f18ab6dbdb8fae8daa0b14da6" target='_blank'>
+              Context-aware knowledge graph framework for traffic speed forecasting using graph neural network
               </a>
             </td>
           <td>
-            Wilfried Bounsi, Borja Ibarz, Andrew Dudzik, Jessica B. Hamrick, Larisa Markeeva, Alex Vitvitskyi, Razvan Pascanu, Petar Velivckovi'c
+            Yatao Zhang, Yi Wang, Song Gao, Martin Raubal
           </td>
-          <td>2024-06-13</td>
+          <td>2024-07-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>67</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Demand prediction is a crucial task for e-commerce and physical retail businesses, especially during high-stake sales events. However, the limited availability of historical data from these peak periods poses a significant challenge for traditional forecasting methods. In this paper, we propose a novel approach that leverages strategically chosen proxy data reflective of potential sales patterns from similar entities during non-peak periods, enriched by features learned from a graph neural networks (GNNs)-based forecasting model, to predict demand during peak events. We formulate the demand prediction as a meta-learning problem and develop the Feature-based First-Order Model-Agnostic Meta-Learning (F-FOMAML) algorithm that leverages proxy data from non-peak periods and GNN-generated relational metadata to learn feature-specific layer parameters, thereby adapting to demand forecasts for peak events. Theoretically, we show that by considering domain similarities through task-specific metadata, our model achieves improved generalization, where the excess risk decreases as the number of training tasks increases. Empirical evaluations on large-scale industrial datasets demonstrate the superiority of our approach. Compared to existing state-of-the-art models, our method demonstrates a notable improvement in demand prediction accuracy, reducing the Mean Absolute Error by 26.24% on an internal vending machine dataset and by 1.04% on the publicly accessible JD.com dataset.">
+        <tr id="Recently, the emerging graph Transformers have made significant advancements for node classification on graphs. In most graph Transformers, a crucial step involves transforming the input graph into token sequences as the model input, enabling Transformer to effectively learn the node representations. However, we observe that existing methods only express partial graph information of nodes through single-type token generation. Consequently, they require tailored strategies to encode additional graph-specific features into the Transformer to ensure the quality of node representation learning, limiting the model flexibility to handle diverse graphs. To this end, we propose a new graph Transformer called NTFormer to address this issue. NTFormer introduces a novel token generator called Node2Par, which constructs various token sequences using different token elements for each node. This flexibility allows Node2Par to generate valuable token sequences from different perspectives, ensuring comprehensive expression of rich graph features. Benefiting from the merits of Node2Par, NTFormer only leverages a Transformer-based backbone without graph-specific modifications to learn node representations, eliminating the need for graph-specific modifications. Extensive experiments conducted on various benchmark datasets containing homophily and heterophily graphs with different scales demonstrate the superiority of NTFormer over representative graph Transformers and graph neural networks for node classification.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fb0749b9bc04914e294f57c89199572e3cb5183c" target='_blank'>
-              F-FOMAML: GNN-Enhanced Meta-Learning for Peak Period Demand Forecasting with Proxy Data
+          <td><a href="https://www.semanticscholar.org/paper/012b888fe3db6a2cd56d30404db3dd58e423b8bd" target='_blank'>
+              NTFormer: A Composite Node Tokenized Graph Transformer for Node Classification
               </a>
             </td>
           <td>
-            Zexing Xu, Linjun Zhang, Sitan Yang, Rasoul Etesami, Hanghang Tong, Huan Zhang, Jiawei Han
+            Jinsong Chen, Siyu Jiang, Kun He
           </td>
-          <td>2024-06-23</td>
+          <td>2024-06-27</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>1</td>
@@ -1772,3108 +1652,3055 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
             Wei Fan, Kun Yi, Hangting Ye, Zhiyuan Ning, Qi Zhang, Ning An
           </td>
           <td>2024-06-29</td>
-          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
+          <td>ArXiv</td>
           <td>1</td>
-          <td>3</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Time-series forecasting (TSF) finds broad applications in real-world scenarios. Due to the dynamic nature of time-series data, it is crucial to equip TSF models with out-of-distribution (OOD) generalization abilities, as historical training data and future test data can have different distributions. In this paper, we aim to alleviate the inherent OOD problem in TSF via invariant learning. We identify fundamental challenges of invariant learning for TSF. First, the target variables in TSF may not be sufficiently determined by the input due to unobserved core variables in TSF, breaking the conventional assumption of invariant learning. Second, time-series datasets lack adequate environment labels, while existing environmental inference methods are not suitable for TSF. To address these challenges, we propose FOIL, a model-agnostic framework that enables timeseries Forecasting for Out-of-distribution generalization via Invariant Learning. FOIL employs a novel surrogate loss to mitigate the impact of unobserved variables. Further, FOIL implements a joint optimization by alternately inferring environments effectively with a multi-head network while preserving the temporal adjacency structure, and learning invariant representations across inferred environments for OOD generalized TSF. We demonstrate that the proposed FOIL significantly improves the performance of various TSF models, achieving gains of up to 85%.">
+        <tr id="Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the oversmoothing of learned embeddings and long-range dependency being more pronounced in dynamic graphs, as features are aggregated both across neighborhood and time, no prior work has proposed an implicit graph neural model in a dynamic setting. In this paper, we present Implicit Dynamic Graph Neural Network (IDGNN) a novel implicit neural network for dynamic graphs which is the first of its kind. A key characteristic of IDGNN is that it demonstrably is well-posed, i.e., it is theoretically guaranteed to have a fixed-point representation. We then demonstrate that the standard iterative algorithm often used to train implicit models is computationally expensive in our dynamic setting as it involves computing gradients, which themselves have to be estimated in an iterative manner. To overcome this, we pose an equivalent bilevel optimization problem and propose an efficient single-loop training algorithm that avoids iterative computation by maintaining moving averages of key components of the gradients. We conduct extensive experiments on real-world datasets on both classification and regression tasks to demonstrate the superiority of our approach over the state-of-the-art baselines. We also demonstrate that our bi-level optimization framework maintains the performance of the expensive iterative algorithm while obtaining up to \textbf{1600x} speed-up.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4abd3e56a26bd8301e7ac2f4cd4eccb543744471" target='_blank'>
-              Time-Series Forecasting for Out-of-Distribution Generalization Using Invariant Learning
+          <td><a href="https://www.semanticscholar.org/paper/3093322772df05295e0448968c691f9fa9b30d06" target='_blank'>
+              Efficient and Effective Implicit Dynamic Graph Neural Network
               </a>
             </td>
           <td>
-            Haoxin Liu, Harshavardhan Kamarthi, Lingkai Kong, Zhiyuan Zhao, Chao Zhang, B. A. Prakash
+            Yongjian Zhong, Hieu Vu, Tianbao Yang, Bijaya Adhikari
           </td>
-          <td>2024-06-13</td>
+          <td>2024-06-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>9</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Mini-batch Graph Transformer (MGT), as an emerging graph learning model, has demonstrated significant advantages in semi-supervised node prediction tasks with improved computational efficiency and enhanced model robustness. However, existing methods for processing local information either rely on sampling or simple aggregation, which respectively result in the loss and squashing of critical neighbor information.Moreover, the limited number of nodes in each mini-batch restricts the model's capacity to capture the global characteristic of the graph. In this paper, we propose LGMformer, a novel MGT model that employs a two-stage augmented interaction strategy, transitioning from local to global perspectives, to address the aforementioned bottlenecks.The local interaction augmentation (LIA) presents a neighbor-target interaction Transformer (NTIformer) to acquire an insightful understanding of the co-interaction patterns between neighbors and the target node, resulting in a locally effective token list that serves as input for the MGT. In contrast, global interaction augmentation (GIA) adopts a cross-attention mechanism to incorporate entire graph prototypes into the target node epresentation, thereby compensating for the global graph information to ensure a more comprehensive perception. To this end, LGMformer achieves the enhancement of node representations under the MGT paradigm.Experimental results related to node classification on the ten benchmark datasets demonstrate the effectiveness of the proposed method. Our code is available at https://github.com/l-wd/LGMformer.">
+        <tr id="Accurate evaluation of forecasting models is essential for ensuring reliable predictions. Current practices for evaluating and comparing forecasting models focus on summarising performance into a single score, using metrics such as SMAPE. We hypothesize that averaging performance over all samples dilutes relevant information about the relative performance of models. Particularly, conditions in which this relative performance is different than the overall accuracy. We address this limitation by proposing a novel framework for evaluating univariate time series forecasting models from multiple perspectives, such as one-step ahead forecasting versus multi-step ahead forecasting. We show the advantages of this framework by comparing a state-of-the-art deep learning approach with classical forecasting techniques. While classical methods (e.g. ARIMA) are long-standing approaches to forecasting, deep neural networks (e.g. NHITS) have recently shown state-of-the-art forecasting performance in benchmark datasets. We conducted extensive experiments that show NHITS generally performs best, but its superiority varies with forecasting conditions. For instance, concerning the forecasting horizon, NHITS only outperforms classical approaches for multi-step ahead forecasting. Another relevant insight is that, when dealing with anomalies, NHITS is outperformed by methods such as Theta. These findings highlight the importance of aspect-based model evaluation.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4d553084ed1ea6035a3c904a657ef55bdbc1a1bd" target='_blank'>
-              Learning a Mini-batch Graph Transformer via Two-stage Interaction Augmentation
+          <td><a href="https://www.semanticscholar.org/paper/11c0631ee5b9502a277f7561c809f6a420e0df60" target='_blank'>
+              Forecasting with Deep Learning: Beyond Average of Average of Average Performance
               </a>
             </td>
           <td>
-            Wenda Li, Kaixuan Chen, Shunyu Liu, Tongya Zheng, Wenjie Huang, Mingli Song
+            Vítor Cerqueira, Luis Roque, Carlos Soares
           </td>
-          <td>2024-07-13</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>14</td>
         </tr>
 
-        <tr id="Time series forecasting has become an increasingly popular research area due to its critical applications in various real-world domains such as traffic management, weather prediction, and financial analysis. Despite significant advancements, existing models face notable challenges, including the necessity of manual hyperparameter tuning for different datasets, and difficulty in effectively distinguishing signal from redundant features in data characterized by strong seasonality. These issues hinder the generalization and practical application of time series forecasting models. To solve this issues, we propose an innovative time series forecasting model TimeSieve designed to address these challenges. Our approach employs wavelet transforms to preprocess time series data, effectively capturing multi-scale features without the need for additional parameters or manual hyperparameter tuning. Additionally, we introduce the information bottleneck theory that filters out redundant features from both detail and approximation coefficients, retaining only the most predictive information. This combination reduces significantly improves the model's accuracy. Extensive experiments demonstrate that our model outperforms existing state-of-the-art methods on 70\% of the datasets, achieving higher predictive accuracy and better generalization across diverse datasets. Our results validate the effectiveness of our approach in addressing the key challenges in time series forecasting, paving the way for more reliable and efficient predictive models in practical applications. The code for our model is available at https://github.com/xll0328/TimeSieve.">
+        <tr id="While tokenized graph Transformers have demonstrated strong performance in node classification tasks, their reliance on a limited subset of nodes with high similarity scores for constructing token sequences overlooks valuable information from other nodes, hindering their ability to fully harness graph information for learning optimal node representations. To address this limitation, we propose a novel graph Transformer called GCFormer. Unlike previous approaches, GCFormer develops a hybrid token generator to create two types of token sequences, positive and negative, to capture diverse graph information. And a tailored Transformer-based backbone is adopted to learn meaningful node representations from these generated token sequences. Additionally, GCFormer introduces contrastive learning to extract valuable information from both positive and negative token sequences, enhancing the quality of learned node representations. Extensive experimental results across various datasets, including homophily and heterophily graphs, demonstrate the superiority of GCFormer in node classification, when compared to representative graph neural networks (GNNs) and graph Transformers.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/30abc65ed6831f90758b733c7c5335f5ca52a6bc" target='_blank'>
-              TimeSieve: Extracting Temporal Dynamics through Information Bottlenecks
+          <td><a href="https://www.semanticscholar.org/paper/e5e10bd5b694099c88e649d9502adecd0acd52f7" target='_blank'>
+              Leveraging Contrastive Learning for Enhanced Node Representations in Tokenized Graph Transformers
               </a>
             </td>
           <td>
-            Ninghui Feng, Songning Lai, Fobao Zhou, Zhenxiao Yin, Hang Zhao
+            Jinsong Chen, Hanpeng Liu, J. Hopcroft, Kun He
           </td>
-          <td>2024-06-07</td>
+          <td>2024-06-27</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>75</td>
         </tr>
 
-        <tr id="Analyzing sequential data is crucial in many domains, particularly due to the abundance of data collected from the Internet of Things paradigm. Time series classification, the task of categorizing sequential data, has gained prominence, with machine learning approaches demonstrating remarkable performance on public benchmark datasets. However, progress has primarily been in designing architectures for learning representations from raw data at fixed (or ideal) time scales, which can fail to generalize to longer sequences. This work introduces a \textit{compositional representation learning} approach trained on statistically coherent components extracted from sequential data. Based on a multi-scale change space, an unsupervised approach is proposed to segment the sequential data into chunks with similar statistical properties. A sequence-based encoder model is trained in a multi-task setting to learn compositional representations from these temporal components for time series classification. We demonstrate its effectiveness through extensive experiments on publicly available time series classification benchmarks. Evaluating the coherence of segmented components shows its competitive performance on the unsupervised segmentation task.">
+        <tr id="Link prediction models can benefit from incorporating textual descriptions of entities and relations, enabling fully inductive learning and flexibility in dynamic graphs. We address the challenge of also capturing rich structured information about the local neighbourhood of entities and their relations, by introducing a Transformer-based approach that effectively integrates textual descriptions with graph structure, reducing the reliance on resource-intensive text encoders. Our experiments on three challenging datasets show that our Fast-and-Frugal Text-Graph (FnF-TG) Transformers achieve superior performance compared to the previous state-of-the-art methods, while maintaining efficiency and scalability.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0f550adb5e176a948a8df78a459210a01fa137a7" target='_blank'>
-              Capturing Temporal Components for Time Series Classification
+          <td><a href="https://www.semanticscholar.org/paper/749af11854db6b02422c6073e34d6bcae5781e0d" target='_blank'>
+              Fast-and-Frugal Text-Graph Transformers are Effective Link Predictors
               </a>
             </td>
           <td>
-            Venkata Ragavendra Vavilthota, Ranjith Ramanathan, Sathyanarayanan N. Aakur
+            Andrei Catalin Coman, Christos Theodoropoulos, M. Moens, James Henderson
           </td>
-          <td>2024-06-20</td>
+          <td>2024-08-13</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Transformer, a deep neural network architecture, has long dominated the field of natural language processing and beyond. Nevertheless, the recent introduction of Mamba challenges its supremacy, sparks considerable interest among researchers, and gives rise to a series of Mamba-based models that have exhibited notable potential. This survey paper orchestrates a comprehensive discussion, diving into essential research dimensions, covering: (i) the functioning of the Mamba mechanism and its foundation on the principles of structured state space models; (ii) the proposed improvements and the integration of Mamba with various networks, exploring its potential as a substitute for Transformers; (iii) the combination of Transformers and Mamba to compensate for each other's shortcomings. We have also made efforts to interpret Mamba and Transformer in the framework of kernel functions, allowing for a comparison of their mathematical nature within a unified context. Our paper encompasses the vast majority of improvements related to Mamba to date.">
+        <tr id="Analyzing time-series data that may contain personal information, particularly in the medical field, presents serious privacy concerns. Sensitive health data from patients is often used to train machine-learning models for diagnostics and ongoing care. Assessing the privacy risk of such models is crucial to making knowledgeable decisions on whether to use a model in production, share it with third parties, or deploy it in patients homes. Membership Inference Attacks (MIA) are a key method for this kind of evaluation, however time-series prediction models have not been thoroughly studied in this context. We explore existing MIA techniques on time-series models, and introduce new features, focusing on the seasonality and trend components of the data. Seasonality is estimated using a multivariate Fourier transform, and a low-degree polynomial is used to approximate trends. We applied these techniques to various types of time-series models, using datasets from the health domain. Our results demonstrate that these new features enhance the effectiveness of MIAs in identifying membership, improving the understanding of privacy risks in medical data applications.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7343105953d6b67d9b94dc891649fb7197a33776" target='_blank'>
-              Venturing into Uncharted Waters: The Navigation Compass from Transformer to Mamba
+          <td><a href="https://www.semanticscholar.org/paper/fc26ca37aef313f1b2c96b71c1f95662bfd7a6e2" target='_blank'>
+              Membership Inference Attacks Against Time-Series Models
               </a>
             </td>
           <td>
-            Yuchen Zou, Yineng Chen, Z. Li, Lefei Zhang, Hai Zhao
+            Noam Koren, Abigail Goldsteen, Ariel Farkash, Guy Amit
           </td>
-          <td>2024-06-24</td>
+          <td>2024-07-03</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>20</td>
+          <td>8</td>
         </tr>
 
-        <tr id="Irregular and asynchronous event sequences are prevalent in many domains, such as social media, finance, and healthcare. Traditional temporal point processes (TPPs), like Hawkes processes, often struggle to model mutual inhibition and nonlinearity effectively. While recent neural network models, including RNNs and Transformers, address some of these issues, they still face challenges with long-term dependencies and computational efficiency. In this paper, we introduce the Mamba Hawkes Process (MHP), which leverages the Mamba state space architecture to capture long-range dependencies and dynamic event interactions. Our results show that MHP outperforms existing models across various datasets. Additionally, we propose the Mamba Hawkes Process Extension (MHP-E), which combines Mamba and Transformer models to enhance predictive capabilities. We present the novel application of the Mamba architecture to Hawkes processes, a flexible and extensible model structure, and a theoretical analysis of the synergy between state space models and Hawkes processes. Experimental results demonstrate the superior performance of both MHP and MHP-E, advancing the field of temporal point process modeling.">
+        <tr id="Large language models (LLMs) and their fine-tuning techniques have demonstrated superior performance in various language understanding and generation tasks. This paper explores fine-tuning LLMs for stock return forecasting with financial newsflow. In quantitative investing, return forecasting is fundamental for subsequent tasks like stock picking, portfolio optimization, etc. We formulate the model to include text representation and forecasting modules. We propose to compare the encoder-only and decoder-only LLMs, considering they generate text representations in distinct ways. The impact of these different representations on forecasting performance remains an open question. Meanwhile, we compare two simple methods of integrating LLMs' token-level representations into the forecasting module. The experiments on real news and investment universes reveal that: (1) aggregated representations from LLMs' token-level embeddings generally produce return predictions that enhance the performance of long-only and long-short portfolios; (2) in the relatively large investment universe, the decoder LLMs-based prediction model leads to stronger portfolios, whereas in the small universes, there are no consistent winners. Among the three LLMs studied (DeBERTa, Mistral, Llama), Mistral performs more robustly across different universes; (3) return predictions derived from LLMs' text representations are a strong signal for portfolio construction, outperforming conventional sentiment scores.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/01159bef23c8f357e01445fe63b05caff1959dc5" target='_blank'>
-              Mamba Hawkes Process
+          <td><a href="https://www.semanticscholar.org/paper/f6c0a84ac1f1fe79cfde96f4e163d0d69f9c06cb" target='_blank'>
+              Fine-Tuning Large Language Models for Stock Return Prediction Using Newsflow
               </a>
             </td>
           <td>
-            Anningzhe Gao, Shan Dai, Yan Hu
+            Tian Guo, E. Hauptmann
           </td>
-          <td>2024-07-07</td>
+          <td>2024-07-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Graph neural networks (GNNs) for graph classification or representation learning require a pooling operation to convert the nodes' embeddings of each graph to a vector as the graph-level representation and the operation has a significant impact on model accuracy. The paper presents a novel graph pooling method called Kernel Readout (KerRead). KerRead maps the node embeddings from the sample space with limited nodes to an augmented sample space with infinite nodes, and then calculates the inner product between some learnable adaptive centers and the augmented node embeddings, which forms a final graph-level feature vector. We apply the proposed strategy to six supervised and two unsupervised graph neural networks such as GCN, GIN, GUNet, InfoGraph, and GraphCL, and the experiments on eight benchmark datasets show that the proposed readout outperforms classical pooling methods such as Sum and seven state-of-the-art pooling methods such as SRead and Janossy GRU. Code and Appendix are both available at https://github.com/jiajunCAU/KerRead.">
+        <tr id="Despite the success of Heterogeneous Graph Neural Networks (HGNNs) in modeling real-world Heterogeneous Information Networks (HINs), challenges such as expressiveness limitations and over-smoothing have prompted researchers to explore Graph Transformers (GTs) for enhanced HIN representation learning. However, research on GT in HINs remains limited, with two key shortcomings in existing work: (1) A node's neighbors at different distances in HINs convey diverse semantics. Unfortunately, existing methods ignore such differences and uniformly treat neighbors within a given distance in a coarse manner, which results in semantic confusion. (2) Nodes in HINs have various types, each with unique semantics. Nevertheless, existing methods mix nodes of different types during neighbor aggregation, hindering the capture of proper correlations between nodes of diverse types. To bridge these gaps, we design an innovative structure named (k,t)-ring neighborhood, where nodes are initially organized by their distance, forming different non-overlapping k-ring neighborhoods for each distance. Within each k-ring structure, nodes are further categorized into different groups according to their types, thus emphasizing the heterogeneity of both distances and types in HINs naturally. Based on this structure, we propose a novel Hierarchical Heterogeneous Graph Transformer (HHGT) model, which seamlessly integrates a Type-level Transformer for aggregating nodes of different types within each k-ring neighborhood, followed by a Ring-level Transformer for aggregating different k-ring neighborhoods in a hierarchical manner. Extensive experiments are conducted on downstream tasks to verify HHGT's superiority over 14 baselines, with a notable improvement of up to 24.75% in NMI and 29.25% in ARI for node clustering task on the ACM dataset compared to the best baseline.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eb7eaa32c2656851204eea6a4172f373fc0c723a" target='_blank'>
-              Kernel Readout for Graph Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/7df2a6f12ecfee64aedb6236102e133b9f02264e" target='_blank'>
+              HHGT: Hierarchical Heterogeneous Graph Transformer for Heterogeneous Graph Representation Learning
               </a>
             </td>
           <td>
-            Jiajun Yu, Zhihao Wu, Jinyu Cai, Adele Lu Jia, Jicong Fan
+            Qiuyu Zhu, Liang Zhang, Qianxiong Xu, Kaijun Liu, Cheng Long, Xiaoyang Wang
           </td>
-          <td>2024-08-01</td>
-          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
+          <td>2024-07-18</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Graph Neural Networks (GNNs) have achieved notable success in the analysis of non-Euclidean data across a wide range of domains. However, their applicability is constrained by the dependence on the observed graph structure. To solve this problem, Latent Graph Inference (LGI) is proposed to infer a task-specific latent structure by computing similarity or edge probability of node features and then apply a GNN to produce predictions. Even so, existing approaches neglect the noise from node features, which affects generated graph structure and performance. In this work, we introduce a novel method called Probability Passing to refine the generated graph structure by aggregating edge probabilities of neighboring nodes based on observed graph. Furthermore, we continue to utilize the LGI framework, inputting the refined graph structure and node features into GNNs to obtain predictions. We name the proposed scheme as Probability Passing-based Graph Neural Network (PPGNN). Moreover, the anchor-based technique is employed to reduce complexity and improve efficiency. Experimental results demonstrate the effectiveness of the proposed method.">
+        <tr id="Time series classification with missing data is a prevalent issue in time series analysis, as temporal data often contain missing values in practical applications. The traditional two-stage approach, which handles imputation and classification separately, can result in sub-optimal performance as label information is not utilized in the imputation process. On the other hand, a one-stage approach can learn features under missing information, but feature representation is limited as imputed errors are propagated in the classification process. To overcome these challenges, this study proposes an end-to-end neural network that unifies data imputation and representation learning within a single framework, allowing the imputation process to take advantage of label information. Differing from previous methods, our approach places less emphasis on the accuracy of imputation data and instead prioritizes classification performance. A specifically designed multi-scale feature learning module is implemented to extract useful information from the noise-imputation data. The proposed model is evaluated on 68 univariate time series datasets from the UCR archive, as well as a multivariate time series dataset with various missing data ratios and 4 real-world datasets with missing information. The results indicate that the proposed model outperforms state-of-the-art approaches for incomplete time series classification, particularly in scenarios with high levels of missing data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/68942a69e4eac01516b5b152a6cbf1a3dfd57c2c" target='_blank'>
-              Probability Passing for Graph Neural Networks: Graph Structure and Representations Joint Learning
+          <td><a href="https://www.semanticscholar.org/paper/5eecace8149eba147315a0809afa377389f6ba24" target='_blank'>
+              An End-to-End Model for Time Series Classification In the Presence of Missing Values
               </a>
             </td>
           <td>
-            Ziteng Wang, YaXuan He, Bin Liu
+            Pengshuai Yao, Mengna Liu, Xu Cheng, Fan Shi, Huan Li, Xiufeng Liu, Shengyong Chen
           </td>
-          <td>2024-07-15</td>
+          <td>2024-08-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>14</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Hierarchical time-series forecasting (HTSF) is an important problem for many real-world business applications where the goal is to simultaneously forecast multiple time-series that are related to each other via a hierarchical relation. Recent works, however, do not address two important challenges that are typically observed in many demand forecasting applications at large companies. First, many time-series at lower levels of the hierarchy have high sparsity i.e., they have a significant number of zeros. Most HTSF methods do not address this varying sparsity across the hierarchy. Further, they do not scale well to the large size of the real-world hierarchy typically unseen in benchmarks used in literature. We resolve both these challenges by proposing HAILS, a novel probabilistic hierarchical model that enables accurate and calibrated probabilistic forecasts across the hierarchy by adaptively modeling sparse and dense time-series with different distributional assumptions and reconciling them to adhere to hierarchical constraints. We show the scalability and effectiveness of our methods by evaluating them against real-world demand forecasting datasets. We deploy HAILS at a large chemical manufacturing company for a product demand forecasting application with over ten thousand products and observe a significant 8.5\% improvement in forecast accuracy and 23% better improvement for sparse time-series. The enhanced accuracy and scalability make HAILS a valuable tool for improved business planning and customer experience.">
+        <tr id="Message-Passing Neural Networks (MPNNs) are extensively employed in graph learning tasks but suffer from limitations such as the restricted scope of information exchange, by being confined to neighboring nodes during each round of message passing. Various strategies have been proposed to address these limitations, including incorporating virtual nodes to facilitate global information exchange. In this study, we introduce the Hierarchical Support Graph (HSG), an extension of the virtual node concept created through recursive coarsening of the original graph. This approach provides a flexible framework for enhancing information flow in graphs, independent of the specific MPNN layers utilized. We present a theoretical analysis of HSGs, investigate their empirical performance, and demonstrate that HSGs can surpass other methods augmented with virtual nodes, achieving state-of-the-art results across multiple datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e7c76a66b9e8e91e00f152d5a723fd37775613e4" target='_blank'>
-              Large Scale Hierarchical Industrial Demand Time-Series Forecasting incorporating Sparsity
+          <td><a href="https://www.semanticscholar.org/paper/54d09e194436b08c9f64b0123db5f3a917f7a0fd" target='_blank'>
+              Next Level Message-Passing with Hierarchical Support Graphs
               </a>
             </td>
           <td>
-            Harshavardhan Kamarthi, Aditya B. Sasanur, Xinjie Tong, Xingyu Zhou, James Peters, Joe Czyzyk, B. A. Prakash
+            Carlos Vonessen, Florian Grötschla, R. Wattenhofer
           </td>
-          <td>2024-07-02</td>
+          <td>2024-06-22</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>19</td>
         </tr>
 
-        <tr id="The Variable Subset Forecasting (VSF) problem, where the majority of variables are unavailable in the inference stage of multivariate forecasting, has been an important but under-explored task with broad impacts in many real-world applications. Missing values, absent inter-correlation, and the impracticality of retraining largely hinder the ability of multivariate forecasting models to capture inherent relationships among variables, impacting their performance. However, existing approaches towards these issues either heavily rely on local temporal correlation or face limitations in fully recovering missing information from the unavailable subset, accompanied by notable computational expenses. To address these problems, we propose a novel density estimation solution to recover the information of missing variables via flows-based generative framework. In particular, a novel generative network for time series, namely Time-series Reconstruction Flows (TRF), is proposed to estimate and reconstruct the missing variable subset. In addition, a novel meta-training framework, Variable-Agnostic Meta Learning, has been developed to enhance the generalization ability of TRF, enabling it to adapt to diverse missing variables situations. Finally, extensive experiments are conducted to demonstrate the superiority of our proposed method compared with baseline methods.">
+        <tr id="The success of large pretrained models in natural language processing (NLP) and computer vision (CV) has opened new avenues for constructing foundation models for time series forecasting (TSF). Traditional TSF foundation models rely heavily on numerical data fitting. In contrast, the human brain is inherently skilled at processing visual information, prefer predicting future trends by observing visualized sequences. From a biomimetic perspective, utilizing models to directly process numerical sequences might not be the most effective route to achieving Artificial General Intelligence (AGI). This paper proposes ViTime, a novel Visual Intelligence-based foundation model for TSF. ViTime overcomes the limitations of numerical time series data fitting by utilizing visual data processing paradigms and employs a innovative data synthesis method during training, called Real Time Series (RealTS). Experiments on a diverse set of previously unseen forecasting datasets demonstrate that ViTime achieves state-of-the-art zero-shot performance, even surpassing the best individually trained supervised models in some situations. These findings suggest that visual intelligence can significantly enhance time series analysis and forecasting, paving the way for more advanced and versatile models in the field. The code for our framework is accessible at https://github.com/IkeYang/ViTime.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5dcee67fc3a8091cc9cc24057f5c0b9c933f4044" target='_blank'>
-              Reconstructing Missing Variables for Multivariate Time Series Forecasting via Conditional Generative Flows
+          <td><a href="https://www.semanticscholar.org/paper/e2db5afb441ca005fd6edc6249af583bf8df0634" target='_blank'>
+              ViTime: A Visual Intelligence-Based Foundation Model for Time Series Forecasting
               </a>
             </td>
           <td>
-            Xuanming Hu, Wei Fan, Haifeng Chen, Pengyang Wang, Yanjie Fu
+            Luoxiao Yang, Yun Wang, Xinqi Fan, Israel Cohen, Yue Zhao, Zijun Zhang
           </td>
-          <td>2024-08-01</td>
-          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
+          <td>2024-07-10</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>8</td>
         </tr>
 
-        <tr id="In the field of machine learning and artificial intelligence, time series forecasting plays a pivotal role across various domains such as finance, healthcare, and weather. However, the task of selecting the most suitable forecasting method for a given dataset is a complex task due to the diversity of data patterns and characteristics. This research aims to address this challenge by proposing a comprehensive benchmark for evaluating and ranking time series forecasting methods across a wide range of datasets. This study investigates the comparative performance of many methods from two prominent time series forecasting frameworks, AutoGluon-Timeseries, and sktime to shed light on their applicability in different real-world scenarios. This research contributes to the field of time series forecasting by providing a robust benchmarking methodology and facilitating informed decision-making when choosing forecasting methods for achieving optimal prediction.">
+        <tr id="Time series generation is a crucial research topic in the area of deep learning, which can be used for data augmentation, imputing missing values, and forecasting. Currently, latent diffusion models are ascending to the forefront of generative modeling for many important data representations. Being the most pivotal in the computer vision domain, latent diffusion models have also recently attracted interest in other communities, including NLP, Speech, and Geometric Space. In this work, we propose TimeLDM, a novel latent diffusion model for high-quality time series generation. TimeLDM is composed of a variational autoencoder that encodes time series into an informative and smoothed latent content and a latent diffusion model operating in the latent space to generate latent information. We evaluate the ability of our method to generate synthetic time series with simulated and realistic datasets, benchmark the performance against existing state-of-the-art methods. Qualitatively and quantitatively, we find that the proposed TimeLDM persistently delivers high-quality generated time series. Sores from Context-FID and Discriminative indicate that TimeLDM consistently and significantly outperforms current state-of-the-art benchmarks with an average improvement of 3.4$\times$ and 3.8$\times$, respectively. Further studies demonstrate that our method presents better performance on different lengths of time series data generation. To the best of our knowledge, this is the first study to explore the potential of the latent diffusion model for unconditional time series generation and establish a new baseline for synthetic time series.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/52869870f9e404f4e69a10b76ca410b00d19088d" target='_blank'>
-              Can time series forecasting be automated? A benchmark and analysis
+          <td><a href="https://www.semanticscholar.org/paper/c127c4b179c7e5d61f7a4347e0003557a02536f1" target='_blank'>
+              TimeLDM: Latent Diffusion Model for Unconditional Time Series Generation
               </a>
             </td>
           <td>
-            Anvitha Thirthapura Sreedhara, Joaquin Vanschoren
+            Jian Qian, Miao Sun, Sifan Zhou, Biao Wan, Minhao Li, Patrick Chiang
           </td>
-          <td>2024-07-23</td>
+          <td>2024-07-05</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="Time series is a typical data type in numerous domains; however, labeling large amounts of time series data can be costly and time-consuming. Learning effective representation from unlabeled time series data is a challenging task. Contrastive learning stands out as a promising method to acquire representations of unlabeled time series data. Therefore, we propose a self-supervised time-series representation learning framework via Time-Frequency Fusion Contrasting (TF-FC) to learn time-series representation from unlabeled data. Specifically, TF-FC combines time-domain augmentation with frequency-domain augmentation to generate the diverse samples. For time-domain augmentation, the raw time series data pass through the time-domain augmentation bank (such as jitter, scaling, permutation, and masking) and get time-domain augmentation data. For frequency-domain augmentation, first, the raw time series undergoes conversion into frequency domain data following Fast Fourier Transform (FFT) analysis. Then, the frequency data passes through the frequency-domain augmentation bank (such as low pass filter, remove frequency, add frequency, and phase shift) and gets frequency-domain augmentation data. The fusion method of time-domain augmentation data and frequency-domain augmentation data is kernel PCA, which is useful for extracting nonlinear features in high-dimensional spaces. By capturing both the time and frequency domains of the time series, the proposed approach is able to extract more informative features from the data, enhancing the model's capacity to distinguish between different time series. To verify the effectiveness of the TF-FC method, we conducted experiments on four time series domain datasets (i.e., SleepEEG, HAR, Gesture, and Epilepsy). Experimental results show that TF-FC significantly improves in recognition accuracy compared with other SOTA methods.">
+        <tr id="Causal discovery from time-series data aims to capture both intra-slice (contemporaneous) and inter-slice (time-lagged) causality between variables within the temporal chain, which is crucial for various scientific disciplines. Compared to causal discovery from non-time-series data, causal discovery from time-series data necessitates more serialized samples with a larger amount of observed time steps. To address the challenges, we propose a novel gradient-based causal discovery approach STIC, which focuses on \textbf{S}hort-\textbf{T}erm \textbf{I}nvariance using \textbf{C}onvolutional neural networks to uncover the causal relationships from time-series data. Specifically, STIC leverages both the short-term time and mechanism invariance of causality within each window observation, which possesses the property of independence, to enhance sample efficiency. Furthermore, we construct two causal convolution kernels, which correspond to the short-term time and mechanism invariance respectively, to estimate the window causal graph. To demonstrate the necessity of convolutional neural networks for causal discovery from time-series data, we theoretically derive the equivalence between convolution and the underlying generative principle of time-series data under the assumption that the additive noise model is identifiable. Experimental evaluations conducted on both synthetic and FMRI benchmark datasets demonstrate that our STIC outperforms baselines significantly and achieves the state-of-the-art performance, particularly when the datasets contain a limited number of observed time steps. Code is available at \url{https://github.com/HITshenrj/STIC}.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/51190de29ec8ff369f3082560caa7c46fc2885b5" target='_blank'>
-              Time-series representation learning via Time-Frequency Fusion Contrasting
+          <td><a href="https://www.semanticscholar.org/paper/801fe20484b5bf27c8c2899d947656d8aa4dff2e" target='_blank'>
+              Causal Discovery from Time-Series Data with Short-Term Invariance-Based Convolutional Neural Networks
               </a>
             </td>
           <td>
-            Wenbo Zhao, Ling Fan
+            Rujia Shen, Boran Wang, Chao Zhao, Yi Guan, Jingchi Jiang
           </td>
-          <td>2024-06-12</td>
-          <td>Frontiers in Artificial Intelligence</td>
+          <td>2024-08-15</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the oversmoothing of learned embeddings and long-range dependency being more pronounced in dynamic graphs, as features are aggregated both across neighborhood and time, no prior work has proposed an implicit graph neural model in a dynamic setting. In this paper, we present Implicit Dynamic Graph Neural Network (IDGNN) a novel implicit neural network for dynamic graphs which is the first of its kind. A key characteristic of IDGNN is that it demonstrably is well-posed, i.e., it is theoretically guaranteed to have a fixed-point representation. We then demonstrate that the standard iterative algorithm often used to train implicit models is computationally expensive in our dynamic setting as it involves computing gradients, which themselves have to be estimated in an iterative manner. To overcome this, we pose an equivalent bilevel optimization problem and propose an efficient single-loop training algorithm that avoids iterative computation by maintaining moving averages of key components of the gradients. We conduct extensive experiments on real-world datasets on both classification and regression tasks to demonstrate the superiority of our approach over the state-of-the-art baselines. We also demonstrate that our bi-level optimization framework maintains the performance of the expensive iterative algorithm while obtaining up to \textbf{1600x} speed-up.">
+        <tr id="Time series forecasting has played an important role in different industries, including economics, energy, weather, and healthcare. RNN-based methods have shown promising potential due to their strong ability to model the interaction of time and variables. However, they are prone to gradient issues like gradient explosion and vanishing gradients. And the prediction accuracy is not high. To address the above issues, this paper proposes a Fractional-order Lipschitz Recurrent Neural Network with a Frequency-domain Gated Attention mechanism (FLRNN-FGA). There are three major components: the Fractional-order Lipschitz Recurrent Neural Network (FLRNN), frequency module, and gated attention mechanism. In the FLRNN, fractional-order integration is employed to describe the dynamic systems accurately. It can capture long-term dependencies and improve prediction accuracy. Lipschitz weight matrices are applied to alleviate the gradient issues. In the frequency module, temporal data are transformed into the frequency domain by Fourier transform. Frequency domain processing can reduce the computational complexity of the model. In the gated attention mechanism, the gated structure can regulate attention information transmission to reduce the number of model parameters. Extensive experimental results on five real-world benchmark datasets demonstrate the effectiveness of FLRNN-FGA compared with the state-of-the-art methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3093322772df05295e0448968c691f9fa9b30d06" target='_blank'>
-              Efficient and Effective Implicit Dynamic Graph Neural Network
+          <td><a href="https://www.semanticscholar.org/paper/df8abef5d3a79df25da8495db7434b86114030b4" target='_blank'>
+              FLRNN-FGA: Fractional-Order Lipschitz Recurrent Neural Network with Frequency-Domain Gated Attention Mechanism for Time Series Forecasting
               </a>
             </td>
           <td>
-            Yongjian Zhong, Hieu Vu, Tianbao Yang, Bijaya Adhikari
+            Chunna Zhao, Junjie Ye, Zelong Zhu, Yaqun Huang
           </td>
-          <td>2024-06-25</td>
-          <td>ArXiv</td>
+          <td>2024-07-22</td>
+          <td>Fractal and Fractional</td>
           <td>0</td>
-          <td>4</td>
+          <td>7</td>
         </tr>
 
-        <tr id="This paper introduces BiLSTM-MLAM, a novel multi-scale time series prediction model. Initially, the approach utilizes bidirectional long short-term memory to capture information from both forward and backward directions in time series data. Subsequently, a multi-scale patch segmentation module generates various long sequences composed of equal-length segments, enabling the model to capture data patterns across multiple time scales by adjusting segment lengths. Finally, the local attention mechanism enhances feature extraction by accurately identifying and weighting important time segments, thereby strengthening the model’s understanding of the local features of the time series, followed by feature fusion. The model demonstrates outstanding performance in time series prediction tasks by effectively capturing sequence information across various time scales. Experimental validation illustrates the superior performance of BiLSTM-MLAM compared to six baseline methods across multiple datasets. When predicting the remaining life of aircraft engines, BiLSTM-MLAM outperforms the best baseline model by 6.66% in RMSE and 11.50% in MAE. In the LTE dataset, it achieves RMSE improvements of 12.77% and MAE enhancements of 3.06%, while in the load dataset, it demonstrates RMSE enhancements of 17.96% and MAE improvements of 30.39%. Additionally, ablation experiments confirm the positive impact of each module on prediction accuracy. Through segment length parameter tuning experiments, combining different segment lengths has resulted in lower prediction errors, affirming the effectiveness of the multi-scale fusion strategy in enhancing prediction accuracy by integrating information from multiple time scales.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ea6da7e837a4e1fc91974188bf6ea513a85abf72" target='_blank'>
-              BiLSTM-MLAM: A Multi-Scale Time Series Prediction Model for Sensor Data Based on Bi-LSTM and Local Attention Mechanisms
-              </a>
-            </td>
-          <td>
-            Yongxin Fan, Qian Tang, Yangming Guo, Yifei Wei
-          </td>
-          <td>2024-06-01</td>
-          <td>Sensors (Basel, Switzerland)</td>
-          <td>0</td>
-          <td>1</td>
-        </tr>
-
-        <tr id="Graph Neural Networks (GNNs) have emerged as the predominant method for analyzing graph-structured data. However, canonical GNNs have limited expressive power and generalization capability, thus triggering the development of more expressive yet computationally intensive methods. One such approach is to create a series of perturbed versions of input graphs and then repeatedly conduct multiple message-passing operations on all variations during training. Despite their expressive power, this approach does not scale well on larger graphs. To address this scalability issue, we introduce Scalable Expressiveness through Preprocessed Graph Perturbation (SE2P). This model offers a flexible, configurable balance between scalability and generalizability with four distinct configuration classes. At one extreme, the configuration prioritizes scalability through minimal learnable feature extraction and extensive preprocessing; at the other extreme, it enhances generalizability with more learnable feature extractions, though this increases scalability costs. We conduct extensive experiments on real-world datasets to evaluate the generalizability and scalability of SE2P variants compared to various state-of-the-art benchmarks. Our results indicate that, depending on the chosen SE2P configuration, the model can enhance generalizability compared to benchmarks while achieving significant speed improvements of up to 8-fold.">
+        <tr id="Multi-agent trajectory prediction is crucial to autonomous driving and understanding the surrounding environment. Learning-based approaches for multi-agent trajectory prediction, such as primarily relying on graph neural networks, graph transformers, and hypergraph neural networks, have demonstrated outstanding performance on real-world datasets in recent years. However, the hypergraph transformer-based method for trajectory prediction is yet to be explored. Therefore, we present a MultiscAle Relational Transformer (MART) network for multi-agent trajectory prediction. MART is a hypergraph transformer architecture to consider individual and group behaviors in transformer machinery. The core module of MART is the encoder, which comprises a Pair-wise Relational Transformer (PRT) and a Hyper Relational Transformer (HRT). The encoder extends the capabilities of a relational transformer by introducing HRT, which integrates hyperedge features into the transformer mechanism, promoting attention weights to focus on group-wise relations. In addition, we propose an Adaptive Group Estimator (AGE) designed to infer complex group relations in real-world environments. Extensive experiments on three real-world datasets (NBA, SDD, and ETH-UCY) demonstrate that our method achieves state-of-the-art performance, enhancing ADE/FDE by 3.9%/11.8% on the NBA dataset. Code is available at https://github.com/gist-ailab/MART.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1c648ab6b5b577ffafcd8c618af2b5f95c5f4019" target='_blank'>
-              Scalable Expressiveness through Preprocessed Graph Perturbations
+          <td><a href="https://www.semanticscholar.org/paper/6d30fe4d8196a1c8f984e6dc8d8f3783c98168cb" target='_blank'>
+              MART: MultiscAle Relational Transformer Networks for Multi-agent Trajectory Prediction
               </a>
             </td>
           <td>
-            Danial Saber, Amirali Salehi-Abari
+            Seongju Lee, Junseok Lee, Yeonguk Yu, Taeri Kim, Kyoobin Lee
           </td>
-          <td>2024-06-17</td>
+          <td>2024-07-31</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>13</td>
+          <td>16</td>
         </tr>
 
-        <tr id="Traffic forecasting is crucial for smart cities and intelligent transportation initiatives, where deep learning has made significant progress in modeling complex spatio-temporal patterns in recent years. However, current public datasets have limitations in reflecting the ultra-dynamic nature of real-world scenarios, characterized by continuously evolving infrastructures, varying temporal distributions, and temporal gaps due to sensor downtimes or changes in traffic patterns. These limitations inevitably restrict the practical applicability of existing traffic forecasting datasets. To bridge this gap, we present XXLTraffic, the largest available public traffic dataset with the longest timespan and increasing number of sensor nodes over the multiple years observed in the data, curated to support research in ultra-dynamic forecasting. Our benchmark includes both typical time-series forecasting settings with hourly and daily aggregated data and novel configurations that introduce gaps and down-sample the training size to better simulate practical constraints. We anticipate the new XXLTraffic will provide a fresh perspective for the time-series and traffic forecasting communities. It would also offer a robust platform for developing and evaluating models designed to tackle ultra-dynamic and extremely long forecasting problems. Our dataset supplements existing spatio-temporal data resources and leads to new research directions in this domain.">
+        <tr id="Graphs have emerged as critical data structures for content analysis in various domains, such as social network analysis, bioinformatics, and recommendation systems. Node classification, a fundamental task in this context, is typically tackled using graph neural networks (GNNs). Unfortunately, conventional GNNs still face challenges in scenarios with few labeled nodes, despite the prevalence of few-shot node classification tasks in real-world applications. To address this challenge, various approaches have been proposed, including graph meta-learning, transfer learning, and methods based on Large Language Models (LLMs). However, traditional meta-learning and transfer learning methods often require prior knowledge from base classes or fail to exploit the potential advantages of unlabeled nodes. Meanwhile, LLM-based methods may overlook the zero-shot capabilities of LLMs and rely heavily on the quality of generated contexts. In this paper, we propose a novel approach that integrates LLMs and GNNs, leveraging the zero-shot inference and reasoning capabilities of LLMs and employing a Graph-LLM-based active learning paradigm to enhance GNNs' performance. Extensive experiments demonstrate the effectiveness of our model in improving node classification accuracy with considerably limited labeled data, surpassing state-of-the-art baselines by significant margins.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/11aaf60abe4ce0825c53f16f0d34e6f3d8d20624" target='_blank'>
-              XXLTraffic: Expanding and Extremely Long Traffic Dataset for Ultra-Dynamic Forecasting Challenges
+          <td><a href="https://www.semanticscholar.org/paper/d41329cb9c08fef08379c558db5a09f412a506ad" target='_blank'>
+              Enhancing Data-Limited Graph Neural Networks by Actively Distilling Knowledge from Large Language Models
               </a>
             </td>
           <td>
-            Du Yin, Hao Xue, Arian Prabowo, Shuang Ao, Flora D. Salim
+            Quan Li, Tianxiang Zhao, Lingwei Chen, Junjie Xu, Suhang Wang
           </td>
-          <td>2024-06-18</td>
+          <td>2024-07-19</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>6</td>
+          <td>11</td>
         </tr>
 
-        <tr id="Accurate evaluation of forecasting models is essential for ensuring reliable predictions. Current practices for evaluating and comparing forecasting models focus on summarising performance into a single score, using metrics such as SMAPE. We hypothesize that averaging performance over all samples dilutes relevant information about the relative performance of models. Particularly, conditions in which this relative performance is different than the overall accuracy. We address this limitation by proposing a novel framework for evaluating univariate time series forecasting models from multiple perspectives, such as one-step ahead forecasting versus multi-step ahead forecasting. We show the advantages of this framework by comparing a state-of-the-art deep learning approach with classical forecasting techniques. While classical methods (e.g. ARIMA) are long-standing approaches to forecasting, deep neural networks (e.g. NHITS) have recently shown state-of-the-art forecasting performance in benchmark datasets. We conducted extensive experiments that show NHITS generally performs best, but its superiority varies with forecasting conditions. For instance, concerning the forecasting horizon, NHITS only outperforms classical approaches for multi-step ahead forecasting. Another relevant insight is that, when dealing with anomalies, NHITS is outperformed by methods such as Theta. These findings highlight the importance of aspect-based model evaluation.">
+        <tr id="Causal discovery on event sequences holds a pivotal significance across domains such as healthcare, finance, and industrial systems. The crux of this endeavor lies in unraveling causal structures among event types, typically portrayed as directed acyclic graphs (DAGs). Nonetheless, prevailing methodologies often grapple with untenable assumptions and intricate optimization hurdles. To address these challenges, we present a novel model named CausalNET. At the heart of CausalNET is a special prediction module based on the Transformer architecture, which prognosticates forthcoming events by leveraging historical occurrences, with its predictive prowess amplified by a trainable causal graph engineered to fathom causal relationships among event types. Further, to augment the predictive paradigm, we devise a causal decay matrix to encapsulate the reciprocal influence of events upon each other within the topological network. During training, we alternatively refine the prediction module and fine-tune the causal graph. Comprehensive evaluation on a spectrum of real-world and synthetic datasets underscores the superior performance and scalability of CausalNET, which marks a promising step forward in the realm of causal discovery. Code and Appendix are available at https://github.com/CGCL-codes/CausalNET.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/11c0631ee5b9502a277f7561c809f6a420e0df60" target='_blank'>
-              Forecasting with Deep Learning: Beyond Average of Average of Average Performance
+          <td><a href="https://www.semanticscholar.org/paper/7b393ee640bb697584ae62c868cc019ed098b961" target='_blank'>
+              CausalNET: Unveiling Causal Structures on Event Sequences by Topology-Informed Causal Attention
               </a>
             </td>
           <td>
-            Vítor Cerqueira, Luis Roque, Carlos Soares
+            Hua Zhu, Hong Huang, Kehan Yin, Zejun Fan, Hai Jin, Bang Liu
           </td>
-          <td>2024-06-24</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>13</td>
+          <td>1</td>
         </tr>
 
-        <tr id="While tokenized graph Transformers have demonstrated strong performance in node classification tasks, their reliance on a limited subset of nodes with high similarity scores for constructing token sequences overlooks valuable information from other nodes, hindering their ability to fully harness graph information for learning optimal node representations. To address this limitation, we propose a novel graph Transformer called GCFormer. Unlike previous approaches, GCFormer develops a hybrid token generator to create two types of token sequences, positive and negative, to capture diverse graph information. And a tailored Transformer-based backbone is adopted to learn meaningful node representations from these generated token sequences. Additionally, GCFormer introduces contrastive learning to extract valuable information from both positive and negative token sequences, enhancing the quality of learned node representations. Extensive experimental results across various datasets, including homophily and heterophily graphs, demonstrate the superiority of GCFormer in node classification, when compared to representative graph neural networks (GNNs) and graph Transformers.">
+        <tr id="In this paper, we leverage the power of latent diffusion models to generate synthetic time series tabular data. Along with the temporal and feature correlations, the heterogeneous nature of the feature in the table has been one of the main obstacles in time series tabular data modeling. We tackle this problem by combining the ideas of the variational auto-encoder (VAE) and the denoising diffusion probabilistic model (DDPM). Our model named as \texttt{TimeAutoDiff} has several key advantages including (1) Generality: the ability to handle the broad spectrum of time series tabular data from single to multi-sequence datasets; (2) Good fidelity and utility guarantees: numerical experiments on six publicly available datasets demonstrating significant improvements over state-of-the-art models in generating time series tabular data, across four metrics measuring fidelity and utility; (3) Fast sampling speed: entire time series data generation as opposed to the sequential data sampling schemes implemented in the existing diffusion-based models, eventually leading to significant improvements in sampling speed, (4) Entity conditional generation: the first implementation of conditional generation of multi-sequence time series tabular data with heterogenous features in the literature, enabling scenario exploration across multiple scientific and engineering domains. Codes are in preparation for release to the public, but available upon request.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e5e10bd5b694099c88e649d9502adecd0acd52f7" target='_blank'>
-              Leveraging Contrastive Learning for Enhanced Node Representations in Tokenized Graph Transformers
+          <td><a href="https://www.semanticscholar.org/paper/78a04be6d94e77047c3251e4480cd08d1194dbd1" target='_blank'>
+              TimeAutoDiff: Combining Autoencoder and Diffusion model for time series tabular data synthesizing
               </a>
             </td>
           <td>
-            Jinsong Chen, Hanpeng Liu, J. Hopcroft, Kun He
+            Namjoon Suh, Yuning Yang, Din-Yin Hsieh, Qitong Luan, Shi Xu, Shixiang Zhu, Guang Cheng
           </td>
-          <td>2024-06-27</td>
+          <td>2024-06-23</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>75</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Dynamic knowledge graphs (DKGs) are popular structures to express different types of connections between objects over time. They can also serve as an efficient mathematical tool to represent information extracted from complex unstructured data sources, such as text or images. Within financial applications, DKGs could be used to detect trends for strategic thematic investing, based on information obtained from financial news articles. In this work, we explore the properties of large language models (LLMs) as dynamic knowledge graph generators, proposing a novel open-source fine-tuned LLM for this purpose, called the Integrated Contextual Knowledge Graph Generator (ICKG). We use ICKG to produce a novel open-source DKG from a corpus of financial news articles, called FinDKG, and we propose an attention-based GNN architecture for analysing it, called KGTransformer. We test the performance of the proposed model on benchmark datasets and FinDKG, demonstrating superior performance on link prediction tasks. Additionally, we evaluate the performance of the KGTransformer on FinDKG for thematic investing, showing it can outperform existing thematic ETFs.">
+        <tr id="Evaluating the contribution of individual data points to a model's prediction is critical for interpreting model predictions and improving model performance. Existing data contribution methods have been applied to various data types, including tabular data, images, and texts; however, their primary focus has been on i.i.d. settings. Despite the pressing need for principled approaches tailored to time series datasets, the problem of estimating data contribution in such settings remains unexplored, possibly due to challenges associated with handling inherent temporal dependencies. This paper introduces TimeInf, a data contribution estimation method for time-series datasets. TimeInf uses influence functions to attribute model predictions to individual time points while preserving temporal structures. Our extensive empirical results demonstrate that TimeInf outperforms state-of-the-art methods in identifying harmful anomalies and helpful time points for forecasting. Additionally, TimeInf offers intuitive and interpretable attributions of data values, allowing us to easily distinguish diverse anomaly patterns through visualizations.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/330623f783928b9d552d3a29b263f002d30599c2" target='_blank'>
-              FinDKG: Dynamic Knowledge Graphs with Large Language Models for Detecting Global Trends in Financial Markets
+          <td><a href="https://www.semanticscholar.org/paper/3cf948c645144f6d8565608c19f9779114df6df2" target='_blank'>
+              TimeInf: Time Series Data Contribution via Influence Functions
               </a>
             </td>
           <td>
-            Xiaohui Victor Li, Francesco Sanna Passino
+            Yizi Zhang, Jingyan Shen, Xiaoxue Xiong, Yongchan Kwon
           </td>
-          <td>2024-07-15</td>
+          <td>2024-07-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>6</td>
-        </tr>
-
-        <tr id="In terms of accuracy, Graph Neural Networks (GNNs) are the best architectural choice for the node classification task. Their drawback in real-world deployment is the latency that emerges from the neighbourhood processing operation. One solution to the latency issue is to perform knowledge distillation from a trained GNN to a Multi-Layer Perceptron (MLP), where the MLP processes only the features of the node being classified (and possibly some pre-computed structural information). However, the performance of such MLPs in both transductive and inductive settings remains inconsistent for existing knowledge distillation techniques. We propose to address the performance concerns by using a specially-designed student model instead of an MLP. Our model, named Routing-by-Memory (RbM), is a form of Mixture-of-Experts (MoE), with a design that enforces expert specialization. By encouraging each expert to specialize on a certain region on the hidden representation space, we demonstrate experimentally that it is possible to derive considerably more consistent performance across multiple datasets.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7f18e0dfbe199a633e1163b88913387f19535125" target='_blank'>
-              Graph Knowledge Distillation to Mixture of Experts
-              </a>
-            </td>
-          <td>
-            P. Rumiantsev, Mark Coates
-          </td>
-          <td>2024-06-17</td>
-          <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
         </tr>
 
-        <tr id="Despite the success of Heterogeneous Graph Neural Networks (HGNNs) in modeling real-world Heterogeneous Information Networks (HINs), challenges such as expressiveness limitations and over-smoothing have prompted researchers to explore Graph Transformers (GTs) for enhanced HIN representation learning. However, research on GT in HINs remains limited, with two key shortcomings in existing work: (1) A node's neighbors at different distances in HINs convey diverse semantics. Unfortunately, existing methods ignore such differences and uniformly treat neighbors within a given distance in a coarse manner, which results in semantic confusion. (2) Nodes in HINs have various types, each with unique semantics. Nevertheless, existing methods mix nodes of different types during neighbor aggregation, hindering the capture of proper correlations between nodes of diverse types. To bridge these gaps, we design an innovative structure named (k,t)-ring neighborhood, where nodes are initially organized by their distance, forming different non-overlapping k-ring neighborhoods for each distance. Within each k-ring structure, nodes are further categorized into different groups according to their types, thus emphasizing the heterogeneity of both distances and types in HINs naturally. Based on this structure, we propose a novel Hierarchical Heterogeneous Graph Transformer (HHGT) model, which seamlessly integrates a Type-level Transformer for aggregating nodes of different types within each k-ring neighborhood, followed by a Ring-level Transformer for aggregating different k-ring neighborhoods in a hierarchical manner. Extensive experiments are conducted on downstream tasks to verify HHGT's superiority over 14 baselines, with a notable improvement of up to 24.75% in NMI and 29.25% in ARI for node clustering task on the ACM dataset compared to the best baseline.">
+        <tr id="Temporal causal discovery is a crucial task aimed at uncovering the causal relations within time series data. The latest temporal causal discovery methods usually train deep learning models on prediction tasks to uncover the causality between time series. They capture causal relations by analyzing the parameters of some components of the trained models, e.g., attention weights and convolution weights. However, this is an incomplete mapping process from the model parameters to the causality and fails to investigate the other components, e.g., fully connected layers and activation functions, that are also significant for causal discovery. To facilitate the utilization of the whole deep learning models in temporal causal discovery, we proposed an interpretable transformer-based causal discovery model termed CausalFormer, which consists of the causality-aware transformer and the decomposition-based causality detector. The causality-aware transformer learns the causal representation of time series data using a prediction task with the designed multi-kernel causal convolution which aggregates each input time series along the temporal dimension under the temporal priority constraint. Then, the decomposition-based causality detector interprets the global structure of the trained causality-aware transformer with the proposed regression relevance propagation to identify potential causal relations and finally construct the causal graph. Experiments on synthetic, simulated, and real datasets demonstrate the state-of-the-art performance of CausalFormer on discovering temporal causality. Our code is available at https://github.com/lingbai-kong/CausalFormer.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7df2a6f12ecfee64aedb6236102e133b9f02264e" target='_blank'>
-              HHGT: Hierarchical Heterogeneous Graph Transformer for Heterogeneous Graph Representation Learning
+          <td><a href="https://www.semanticscholar.org/paper/0298589ffc3502a8f8731583d6ed34241baab0de" target='_blank'>
+              CausalFormer: An Interpretable Transformer for Temporal Causal Discovery
               </a>
             </td>
           <td>
-            Qiuyu Zhu, Liang Zhang, Qianxiong Xu, Kaijun Liu, Cheng Long, Xiaoyang Wang
+            Lingbai Kong, Wengen Li, Hanchen Yang, Yichao Zhang, J. Guan, Shuigeng Zhou
           </td>
-          <td>2024-07-18</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>49</td>
         </tr>
 
-        <tr id="Analyzing time-series data that may contain personal information, particularly in the medical field, presents serious privacy concerns. Sensitive health data from patients is often used to train machine-learning models for diagnostics and ongoing care. Assessing the privacy risk of such models is crucial to making knowledgeable decisions on whether to use a model in production, share it with third parties, or deploy it in patients homes. Membership Inference Attacks (MIA) are a key method for this kind of evaluation, however time-series prediction models have not been thoroughly studied in this context. We explore existing MIA techniques on time-series models, and introduce new features, focusing on the seasonality and trend components of the data. Seasonality is estimated using a multivariate Fourier transform, and a low-degree polynomial is used to approximate trends. We applied these techniques to various types of time-series models, using datasets from the health domain. Our results demonstrate that these new features enhance the effectiveness of MIAs in identifying membership, improving the understanding of privacy risks in medical data applications.">
+        <tr id="The application of deep learning techniques for predicting stock market prices is a prominent and widely researched topic in the field of data science. To effectively predict market trends, it is essential to utilize a diversified dataset. In this paper, we give a graph neural network based convolutional neural network (CNN) model, that can be applied on diverse source of data, in the attempt to extract features to predict the trends of indices of \text{S}\&\text{P} 500, NASDAQ, DJI, NYSE, and RUSSEL. The experiments show that the associated models improve the performance of prediction in all indices over the baseline algorithms by about $4\% \text{ to } 15\%$, in terms of F-measure. A trading simulation is generated from predictions and gained a Sharpe ratio of over 3.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fc26ca37aef313f1b2c96b71c1f95662bfd7a6e2" target='_blank'>
-              Membership Inference Attacks Against Time-Series Models
+          <td><a href="https://www.semanticscholar.org/paper/db9f0abbc8601da414d831f4eef6626e555a4457" target='_blank'>
+              GraphCNNpred: A stock market indices prediction using a Graph based deep learning system
               </a>
             </td>
           <td>
-            Noam Koren, Abigail Goldsteen, Ariel Farkash, Guy Amit
+            Yuhui Jin
           </td>
-          <td>2024-07-03</td>
+          <td>2024-07-04</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>8</td>
+          <td>2</td>
+          <td>1</td>
         </tr>
 
-        <tr id="The most fundamental capability of modern AI methods such as Large Language Models (LLMs) is the ability to predict the next token in a long sequence of tokens, known as ``sequence modeling."Although the Transformers model is the current dominant approach to sequence modeling, its quadratic computational cost with respect to sequence length is a significant drawback. State-space models (SSMs) offer a promising alternative due to their linear decoding efficiency and high parallelizability during training. However, existing SSMs often rely on seemingly ad hoc linear recurrence designs. In this work, we explore SSM design through the lens of online learning, conceptualizing SSMs as meta-modules for specific online learning problems. This approach links SSM design to formulating precise online learning objectives, with state transition rules derived from optimizing these objectives. Based on this insight, we introduce a novel deep SSM architecture based on the implicit update for optimizing an online regression objective. Our experimental results show that our models outperform state-of-the-art SSMs, including the Mamba model, on standard sequence modeling benchmarks and language modeling tasks.">
+        <tr id="Continuous-Time Dynamic Graph (CTDG) precisely models evolving real-world relationships, drawing heightened interest in dynamic graph learning across academia and industry. However, existing CTDG models encounter challenges stemming from noise and limited historical data. Graph Data Augmentation (GDA) emerges as a critical solution, yet current approaches primarily focus on static graphs and struggle to effectively address the dynamics inherent in CTDGs. Moreover, these methods often demand substantial domain expertise for parameter tuning and lack theoretical guarantees for augmentation efficacy. To address these issues, we propose Conda, a novel latent diffusion-based GDA method tailored for CTDGs. Conda features a sandwich-like architecture, incorporating a Variational Auto-Encoder (VAE) and a conditional diffusion model, aimed at generating enhanced historical neighbor embeddings for target nodes. Unlike conventional diffusion models trained on entire graphs via pre-training, Conda requires historical neighbor sequence embeddings of target nodes for training, thus facilitating more targeted augmentation. We integrate Conda into the CTDG model and adopt an alternating training strategy to optimize performance. Extensive experimentation across six widely used real-world datasets showcases the consistent performance improvement of our approach, particularly in scenarios with limited historical data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/af4e8a4bf3effaf04a141e1048276c77ea8585a9" target='_blank'>
-              Longhorn: State Space Models are Amortized Online Learners
+          <td><a href="https://www.semanticscholar.org/paper/eb15255bdb2698993e5ad0223454abd6a732d2e7" target='_blank'>
+              Latent Conditional Diffusion-based Data Augmentation for Continuous-Time Dynamic Graph Model
               </a>
             </td>
           <td>
-            Bo Liu, Rui Wang, Lemeng Wu, Yihao Feng, Peter Stone, Qian Liu
+            Yuxing Tian, Yiyan Qi, Aiwen Jiang, Qi Huang, Jian Guo
           </td>
-          <td>2024-07-19</td>
+          <td>2024-07-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>16</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Sequential recommender systems aims to predict the users' next interaction through user behavior modeling with various operators like RNNs and attentions. However, existing models generally fail to achieve the three golden principles for sequential recommendation simultaneously, i.e., training efficiency, low-cost inference, and strong performance. To this end, we propose RecBLR, an Efficient Sequential Recommendation Model based on Behavior-Dependent Linear Recurrent Units to accomplish the impossible triangle of the three principles. By incorporating gating mechanisms and behavior-dependent designs into linear recurrent units, our model significantly enhances user behavior modeling and recommendation performance. Furthermore, we unlock the parallelizable training as well as inference efficiency for our model by designing a hardware-aware scanning acceleration algorithm with a customized CUDA kernel. Extensive experiments on real-world datasets with varying lengths of user behavior sequences demonstrate RecBLR's remarkable effectiveness in simultaneously achieving all three golden principles - strong recommendation performance, training efficiency, and low-cost inference, while exhibiting excellent scalability to datasets with long user interaction histories.">
+        <tr id="Time Series Anomaly Detection (TSAD) finds widespread applications across various domains such as financial markets, industrial production, and healthcare. Its primary objective is to learn the normal patterns of time series data, thereby identifying deviations in test samples. Most existing TSAD methods focus on modeling data from the temporal dimension, while ignoring the semantic information in the spatial dimension. To address this issue, we introduce a novel approach, called Spatial-Temporal Normality learning (STEN). STEN is composed of a sequence Order prediction-based Temporal Normality learning (OTN) module that captures the temporal correlations within sequences, and a Distance prediction-based Spatial Normality learning (DSN) module that learns the relative spatial relations between sequences in a feature space. By synthesizing these two modules, STEN learns expressive spatial-temporal representations for the normal patterns hidden in the time series data. Extensive experiments on five popular TSAD benchmarks show that STEN substantially outperforms state-of-the-art competing methods. Our code is available at https://github.com/mala-lab/STEN.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d72edbeb87b586ca8920971c462f7305db003a65" target='_blank'>
-              Behavior-Dependent Linear Recurrent Units for Efficient Sequential Recommendation
+          <td><a href="https://www.semanticscholar.org/paper/6136ae3b84b2b1b9e6215a5c67a3153abd0eedc2" target='_blank'>
+              Self-Supervised Spatial-Temporal Normality Learning for Time Series Anomaly Detection
               </a>
             </td>
           <td>
-            Chengkai Liu, Jianghao Lin, Hanzhou Liu, Jianling Wang, James Caverlee
+            Yutong Chen, Hongzuo Xu, Guansong Pang, Hezhe Qiao, Yuan Zhou, Mingsheng Shang
           </td>
-          <td>2024-06-18</td>
+          <td>2024-06-28</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>44</td>
+          <td>5</td>
         </tr>
 
-        <tr id="One of the fundamental representation learning tasks is unsupervised sequential disentanglement, where latent codes of inputs are decomposed to a single static factor and a sequence of dynamic factors. To extract this latent information, existing methods condition the static and dynamic codes on the entire input sequence. Unfortunately, these models often suffer from information leakage, i.e., the dynamic vectors encode both static and dynamic information, or vice versa, leading to a non-disentangled representation. Attempts to alleviate this problem via reducing the dynamic dimension and auxiliary loss terms gain only partial success. Instead, we propose a novel and simple architecture that mitigates information leakage by offering a simple and effective subtraction inductive bias while conditioning on a single sample. Remarkably, the resulting variational framework is simpler in terms of required loss terms, hyperparameters, and data augmentation. We evaluate our method on multiple data-modality benchmarks including general time series, video, and audio, and we show beyond state-of-the-art results on generation and prediction tasks in comparison to several strong baselines.">
+        <tr id="How to capture dynamic spatial-temporal dependencies remains an open question in multivariate time series (MTS) forecasting. Although recent advanced spatial-temporal graph neural networks (STGNNs) achieve superior forecasting performance, they either consider pre-defined spatial correlations or simply learn static graphs. Some research has tried to learn many adjacent matrices to reveal time-varying spatial correlations, but they generate discrete graphs which cannot encode evolutionary information and also face computational complexity problem. In this paper, we propose two significant plugins to help automatically learn enhanced dynamic spatial-temporal embedding of MTS data: (1) a novel neural conditional random field (CRF) layer. We find that the implicit time-varying spatial dependencies are reflected by the explicit changeable links between edges, and we propose the neural CRF to encode such pairwise changeable evolutionary inter-dependencies; (2) a structure adaptive graph convolution (SAGC) that does not require pre-defined graphs to capture semantically richer spatial correlations. Then, we integrate the neural CRF, SAGC with recurrent neural network to develop a new STGNN paradigm termed Adaptive Spatial-Temporal graph neural network with Conditional Random Field (ASTCRF), which can be trained in an end-to-end fashion. We validate the effectiveness, efficiency and scalability of ASTCRF on five public benchmark MTS datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/242344a5e543a645d5f761b0120f90be23c91b95" target='_blank'>
-              Sequential Disentanglement by Extracting Static Information From A Single Sequence Element
+          <td><a href="https://www.semanticscholar.org/paper/667940911f90cfd6980e5e1731731f7c2af49b08" target='_blank'>
+              Dynamic Spatial-Temporal Embedding via Neural Conditional Random Field for Multivariate Time Series Forecasting
               </a>
             </td>
           <td>
-            Nimrod Berman, Ilan Naiman, Idan Arbiv, Gal Fadlon, Omri Azencot
+            Peiyu Yi, Feihu Huang, Jian Peng, Zhifeng Bao
           </td>
-          <td>2024-06-26</td>
-          <td>ArXiv</td>
+          <td>2024-06-27</td>
+          <td>ACM Transactions on Spatial Algorithms and Systems</td>
           <td>0</td>
-          <td>11</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Foundation Models (FMs) serve as a general class for the development of artificial intelligence systems, offering broad potential for generalization across a spectrum of downstream tasks. Despite extensive research into self-supervised learning as the cornerstone of FMs, several outstanding issues persist in Graph Foundation Models that rely on graph self-supervised learning, namely: 1) Homogenization. The extent of generalization capability on downstream tasks remains unclear. 2) Scalability. It is unknown how effectively these models can scale to large datasets. 3) Efficiency. The training time and memory usage of these models require evaluation. 4) Training Stop Criteria. Determining the optimal stopping strategy for pre-training across multiple tasks to maximize performance on downstream tasks. To address these questions, we have constructed a rigorous benchmark that thoroughly analyzes and studies the generalization and scalability of self-supervised Graph Neural Network (GNN) models. Regarding generalization, we have implemented and compared the performance of various self-supervised GNN models, trained to generate node representations, across tasks such as node classification, link prediction, and node clustering. For scalability, we have compared the performance of various models after training using full-batch and mini-batch strategies. Additionally, we have assessed the training efficiency of these models by conducting experiments to test their GPU memory usage and throughput. Through these experiments, we aim to provide insights to motivate future research. The code for this benchmark is publicly available at https://github.com/NYUSHCS/GraphFM.">
+        <tr id="Modern recurrent layers are emerging as a promising path toward edge deployment of foundation models, especially in the context of large language models (LLMs). Compressing the whole input sequence in a finite-dimensional representation enables recurrent layers to model long-range dependencies while maintaining a constant inference cost for each token and a fixed memory requirement. However, the practical deployment of LLMs in resource-limited environments often requires further model compression, such as quantization and pruning. While these techniques are well-established for attention-based models, their effects on recurrent layers remain underexplored. In this preliminary work, we focus on post-training quantization for recurrent LLMs and show that Mamba models exhibit the same pattern of outlier channels observed in attention-based LLMs. We show that the reason for the difficulty of quantizing SSMs is caused by activation outliers, similar to those observed in transformer-based LLMs. We report baseline results for post-training quantization of Mamba that do not take into account the activation outliers and suggest first steps for outlier-aware quantization.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c3aa14a646b929f15b13615e0112fef502e61d85" target='_blank'>
-              GraphFM: A Comprehensive Benchmark for Graph Foundation Model
+          <td><a href="https://www.semanticscholar.org/paper/3d553478d06f751f872a82c774c8262ce66d47fd" target='_blank'>
+              Mamba-PTQ: Outlier Channels in Recurrent Large Language Models
               </a>
             </td>
           <td>
-            Yuhao Xu, Xinqi Liu, Keyu Duan, Yi Fang, Yu-Neng Chuang, D. Zha, Qiaoyu Tan
+            Alessandro Pierro, Steven Abreu
           </td>
-          <td>2024-06-12</td>
+          <td>2024-07-17</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>22</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Time series data are ubiquitous across a wide range of real-world domains. While real-world time series analysis (TSA) requires human experts to integrate numerical series data with multimodal domain-specific knowledge, most existing TSA models rely solely on numerical data, overlooking the significance of information beyond numerical series. This oversight is due to the untapped potential of textual series data and the absence of a comprehensive, high-quality multimodal dataset. To overcome this obstacle, we introduce Time-MMD, the first multi-domain, multimodal time series dataset covering 9 primary data domains. Time-MMD ensures fine-grained modality alignment, eliminates data contamination, and provides high usability. Additionally, we develop MM-TSFlib, the first multimodal time-series forecasting (TSF) library, seamlessly pipelining multimodal TSF evaluations based on Time-MMD for in-depth analyses. Extensive experiments conducted on Time-MMD through MM-TSFlib demonstrate significant performance enhancements by extending unimodal TSF to multimodality, evidenced by over 15% mean squared error reduction in general, and up to 40% in domains with rich textual data. More importantly, our datasets and library revolutionize broader applications, impacts, research topics to advance TSA. The dataset and library are available at https://github.com/AdityaLab/Time-MMD and https://github.com/AdityaLab/MM-TSFlib.">
+        <tr id="The modelling of temporal patterns in dynamic graphs is an important current research issue in the development of time-aware GNNs. Whether or not a specific sequence of events in a temporal graph constitutes a temporal pattern not only depends on the frequency of its occurrence. We consider whether it deviates from what is expected in a temporal graph where timestamps are randomly shuffled. While accounting for such a random baseline is important to model temporal patterns, it has mostly been ignored by current temporal graph neural networks. To address this issue we propose HYPA-DBGNN, a novel two-step approach that combines (i) the inference of anomalous sequential patterns in time series data on graphs based on a statistically principled null model, with (ii) a neural message passing approach that utilizes a higher-order De Bruijn graph whose edges capture overrepresented sequential patterns. Our method leverages hypergeometric graph ensembles to identify anomalous edges within both first- and higher-order De Bruijn graphs, which encode the temporal ordering of events. The model introduces an inductive bias that enhances model interpretability. We evaluate our approach for static node classification using benchmark datasets and a synthetic dataset that showcases its ability to incorporate the observed inductive bias regarding over- and under-represented temporal edges. We demonstrate the framework's effectiveness in detecting similar patterns within empirical datasets, resulting in superior performance compared to baseline methods in node classification tasks. To the best of our knowledge, our work is the first to introduce statistically informed GNNs that leverage temporal and causal sequence anomalies. HYPA-DBGNN represents a path for bridging the gap between statistical graph inference and neural graph representation learning, with potential applications to static GNNs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ef5ed58b37b4760ed1f5f89a06442f47d376aa90" target='_blank'>
-              Time-MMD: A New Multi-Domain Multimodal Dataset for Time Series Analysis
+          <td><a href="https://www.semanticscholar.org/paper/e06e0cb47d2e0afba3b7c9bbfa9d5c33b0375133" target='_blank'>
+              Inference of Sequential Patterns for Neural Message Passing in Temporal Graphs
               </a>
             </td>
           <td>
-            Haoxin Liu, Shangqing Xu, Zhiyuan Zhao, Lingkai Kong, Harshavardhan Kamarthi, Aditya B. Sasanur, Megha Sharma, Jiaming Cui, Qingsong Wen, Chao Zhang, B. A. Prakash
+            J. V. Pichowski, Vincenzo Perri, Lisi Qarkaxhija, Ingo Scholtes
           </td>
-          <td>2024-06-12</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>9</td>
+          <td>8</td>
         </tr>
 
-        <tr id="Time series generation is a crucial research topic in the area of deep learning, which can be used for data augmentation, imputing missing values, and forecasting. Currently, latent diffusion models are ascending to the forefront of generative modeling for many important data representations. Being the most pivotal in the computer vision domain, latent diffusion models have also recently attracted interest in other communities, including NLP, Speech, and Geometric Space. In this work, we propose TimeLDM, a novel latent diffusion model for high-quality time series generation. TimeLDM is composed of a variational autoencoder that encodes time series into an informative and smoothed latent content and a latent diffusion model operating in the latent space to generate latent information. We evaluate the ability of our method to generate synthetic time series with simulated and realistic datasets, benchmark the performance against existing state-of-the-art methods. Qualitatively and quantitatively, we find that the proposed TimeLDM persistently delivers high-quality generated time series. Sores from Context-FID and Discriminative indicate that TimeLDM consistently and significantly outperforms current state-of-the-art benchmarks with an average improvement of 3.4$\times$ and 3.8$\times$, respectively. Further studies demonstrate that our method presents better performance on different lengths of time series data generation. To the best of our knowledge, this is the first study to explore the potential of the latent diffusion model for unconditional time series generation and establish a new baseline for synthetic time series.">
+        <tr id="Sequential recommendation systems aim to provide personalized recommendations by analyzing dynamic preferences and dependencies within user behavior sequences. Recently, Transformer models can effectively capture user preferences. However, their quadratic computational complexity limits recommendation performance on long interaction sequence data. Inspired by the State Space Model (SSM)representative model, Mamba, which efficiently captures user preferences in long interaction sequences with linear complexity, we find that Mamba's recommendation effectiveness is limited in short interaction sequences, with failing to recall items of actual interest to users and exacerbating the data sparsity cold start problem. To address this issue, we innovatively propose a new model, MaTrRec, which combines the strengths of Mamba and Transformer. This model fully leverages Mamba's advantages in handling long-term dependencies and Transformer's global attention advantages in short-term dependencies, thereby enhances predictive capabilities on both long and short interaction sequence datasets while balancing model efficiency. Notably, our model significantly improves the data sparsity cold start problem, with an improvement of up to 33% on the highly sparse Amazon Musical Instruments dataset. We conducted extensive experimental evaluations on five widely used public datasets. The experimental results show that our model outperforms the current state-of-the-art sequential recommendation models on all five datasets. The code is available at https://github.com/Unintelligentmumu/MaTrRec.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c127c4b179c7e5d61f7a4347e0003557a02536f1" target='_blank'>
-              TimeLDM: Latent Diffusion Model for Unconditional Time Series Generation
+          <td><a href="https://www.semanticscholar.org/paper/412e6c60b2d5426ebf3724e770876d116c398984" target='_blank'>
+              MaTrRec: Uniting Mamba and Transformer for Sequential Recommendation
               </a>
             </td>
           <td>
-            Jian Qian, Miao Sun, Sifan Zhou, Biao Wan, Minhao Li, Patrick Chiang
+            Shun Zhang, Runsen Zhang, Zhirong Yang
           </td>
-          <td>2024-07-05</td>
+          <td>2024-07-27</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="The success of large pretrained models in natural language processing (NLP) and computer vision (CV) has opened new avenues for constructing foundation models for time series forecasting (TSF). Traditional TSF foundation models rely heavily on numerical data fitting. In contrast, the human brain is inherently skilled at processing visual information, prefer predicting future trends by observing visualized sequences. From a biomimetic perspective, utilizing models to directly process numerical sequences might not be the most effective route to achieving Artificial General Intelligence (AGI). This paper proposes ViTime, a novel Visual Intelligence-based foundation model for TSF. ViTime overcomes the limitations of numerical time series data fitting by utilizing visual data processing paradigms and employs a innovative data synthesis method during training, called Real Time Series (RealTS). Experiments on a diverse set of previously unseen forecasting datasets demonstrate that ViTime achieves state-of-the-art zero-shot performance, even surpassing the best individually trained supervised models in some situations. These findings suggest that visual intelligence can significantly enhance time series analysis and forecasting, paving the way for more advanced and versatile models in the field. The code for our framework is accessible at https://github.com/IkeYang/ViTime.">
+        <tr id="Recently, Large Language Models (LLMs) have demonstrated great potential in various data mining tasks, such as knowledge question answering, mathematical reasoning, and commonsense reasoning. However, the reasoning capability of LLMs on temporal event forecasting has been under-explored. To systematically investigate their abilities in temporal event forecasting, we conduct a comprehensive evaluation of LLM-based methods for temporal event forecasting. Due to the lack of a high-quality dataset that involves both graph and textual data, we first construct a benchmark dataset, named MidEast-TE-mini. Based on this dataset, we design a series of baseline methods, characterized by various input formats and retrieval augmented generation(RAG) modules. From extensive experiments, we find that directly integrating raw texts into the input of LLMs does not enhance zero-shot extrapolation performance. In contrast, incorporating raw texts in specific complex events and fine-tuning LLMs significantly improves performance. Moreover, enhanced with retrieval modules, LLM can effectively capture temporal relational patterns hidden in historical events. Meanwhile, issues such as popularity bias and the long-tail problem still persist in LLMs, particularly in the RAG-based method. These findings not only deepen our understanding of LLM-based event forecasting methods but also highlight several promising research directions.We consider that this comprehensive evaluation, along with the identified research opportunities, will significantly contribute to future research on temporal event forecasting through LLMs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e2db5afb441ca005fd6edc6249af583bf8df0634" target='_blank'>
-              ViTime: A Visual Intelligence-Based Foundation Model for Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/425b541ff4168e921c54ca9c3b449c1fcf985c55" target='_blank'>
+              A Comprehensive Evaluation of Large Language Models on Temporal Event Forecasting
               </a>
             </td>
           <td>
-            Luoxiao Yang, Yun Wang, Xinqi Fan, Israel Cohen, Yue Zhao, Zijun Zhang
+            He Chang, Chenchen Ye, Zhulin Tao, Jie Wu, Zhengmao Yang, Yunshan Ma, Xianglin Huang, Tat-Seng Chua
           </td>
-          <td>2024-07-10</td>
+          <td>2024-07-16</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>8</td>
+          <td>10</td>
         </tr>
 
-        <tr id="Dynamic link prediction is an important problem considered by many recent works proposing various approaches for learning temporal edge patterns. To assess their efficacy, models are evaluated on publicly available benchmark datasets involving continuous-time and discrete-time temporal graphs. However, as we show in this work, the suitability of common batch-oriented evaluation depends on the datasets' characteristics, which can cause two issues: First, for continuous-time temporal graphs, fixed-size batches create time windows with different durations, resulting in an inconsistent dynamic link prediction task. Second, for discrete-time temporal graphs, the sequence of batches can additionally introduce temporal dependencies that are not present in the data. In this work, we empirically show that this common evaluation approach leads to skewed model performance and hinders the fair comparison of methods. We mitigate this problem by reformulating dynamic link prediction as a link forecasting task that better accounts for temporal information present in the data. We provide implementations of our new evaluation method for commonly used graph learning frameworks.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/99a91aad86790ddad48ba2e88b8ff319dd2eb4a1" target='_blank'>
-              From Link Prediction to Forecasting: Information Loss in Batch-based Temporal Graph Learning
+          <td><a href="https://www.semanticscholar.org/paper/c6b30fb9799602bf4dfd68fdcf16333cb2b7ff18" target='_blank'>
+              CliqueFluxNet: Unveiling EHR Insights with Stochastic Edge Fluxing and Maximal Clique Utilisation Using Graph Neural Networks
               </a>
             </td>
           <td>
-            Moritz Lampert, Christopher Blöcker, Ingo Scholtes
+            Soheila Molaei, Nima Ghanbari Bousejin, Ghadeer O. Ghosheh, Anshul Thakur, V. Chauhan, Tingting Zhu, David A. Clifton
           </td>
-          <td>2024-06-07</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>Journal of Healthcare Informatics Research</td>
           <td>0</td>
-          <td>1</td>
+          <td>11</td>
         </tr>
 
-        <tr id="In recent years, graph neural networks (GNNs) have emerged as a potent tool for learning on graph-structured data and won fruitful successes in varied fields. The majority of GNNs follow the message-passing paradigm, where representations of each node are learned by recursively aggregating features of its neighbors. However, this mechanism brings severe over-smoothing and efficiency issues over high-degree graphs (HDGs), wherein most nodes have dozens (or even hundreds) of neighbors, such as social networks, transaction graphs, power grids, etc. Additionally, such graphs usually encompass rich and complex structure semantics, which are hard to capture merely by feature aggregations in GNNs. Motivated by the above limitations, we propose TADA, an efficient and effective front-mounted data augmentation framework for GNNs on HDGs. Under the hood, TADA includes two key modules: (i) feature expansion with structure embeddings, and (ii) topology- and attribute-aware graph sparsification. The former obtains augmented node features and enhanced model capacity by encoding the graph structure into high-quality structure embeddings with our highly-efficient sketching method. Further, by exploiting task-relevant features extracted from graph structures and attributes, the second module enables the accurate identification and reduction of numerous redundant/noisy edges from the input graph, thereby alleviating over-smoothing and facilitating faster feature aggregations over HDGs. Empirically, TADA considerably improves the predictive performance of mainstream GNN models on 8 real homophilic/heterophilic HDGs in terms of node classification, while achieving efficient training and inference processes.">
+        <tr id="Time-series classification is vital in health monitoring and human activity recognition, as well as in areas such as financial forecasting, process control, and a wide array of forecasting tasks. Traditional time-series models segment data into windows and assign one label per window, often missing label transitions within those windows. This paper presents a novel many-to-many time-series model and post-processing using hybrid recurrent neural networks with attention mechanisms, which more effectively captures label transitions over traditional many-to-one models. Further, unlike typical other many-to-many models, our approach doesn’t require a decoder. Instead, it employs an RNN, generating a label for every input time step. During inference, a weighted voting scheme consolidates overlapping predictions into one label per time step. Experiments show our model remains effective on time-series with sparse label shifts, but particularly excels in detecting frequent transitions. This model is ideal for tasks demanding accurate pinpointing of rapid label changes in time-series data, such as gesture recognition, making it ideal for fast-paced human activity recognition. 1">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b1607eceee9f94b8a186afb4d12f18e6b04e5466" target='_blank'>
-              Efficient Topology-aware Data Augmentation for High-Degree Graph Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/d206e88758c3992f96eaf77f9ddd4f0e63779b32" target='_blank'>
+              Many-to-Many Prediction for Effective Modeling of Frequent Label Transitions in Time Series
               </a>
             </td>
           <td>
-            Yurui Lai, Xiaoyang Lin, Renchi Yang, Hongtao Wang
+            Alexander Katrompas, V. Metsis
           </td>
-          <td>2024-06-08</td>
-          <td>ArXiv</td>
+          <td>2024-06-26</td>
+          <td>Proceedings of the 17th International Conference on PErvasive Technologies Related to Assistive Environments</td>
           <td>0</td>
-          <td>10</td>
+          <td>18</td>
         </tr>
 
-        <tr id="Large language models (LLMs) and their fine-tuning techniques have demonstrated superior performance in various language understanding and generation tasks. This paper explores fine-tuning LLMs for stock return forecasting with financial newsflow. In quantitative investing, return forecasting is fundamental for subsequent tasks like stock picking, portfolio optimization, etc. We formulate the model to include text representation and forecasting modules. We propose to compare the encoder-only and decoder-only LLMs, considering they generate text representations in distinct ways. The impact of these different representations on forecasting performance remains an open question. Meanwhile, we compare two simple methods of integrating LLMs' token-level representations into the forecasting module. The experiments on real news and investment universes reveal that: (1) aggregated representations from LLMs' token-level embeddings generally produce return predictions that enhance the performance of long-only and long-short portfolios; (2) in the relatively large investment universe, the decoder LLMs-based prediction model leads to stronger portfolios, whereas in the small universes, there are no consistent winners. Among the three LLMs studied (DeBERTa, Mistral, Llama), Mistral performs more robustly across different universes; (3) return predictions derived from LLMs' text representations are a strong signal for portfolio construction, outperforming conventional sentiment scores.">
+        <tr id="Dynamic link prediction is a critical task in the analysis of evolving networks, with applications ranging from recommender systems to economic exchanges. However, the concept of the temporal receptive field, which refers to the temporal context that models use for making predictions, has been largely overlooked and insufficiently analyzed in existing research. In this study, we present a comprehensive analysis of the temporal receptive field in dynamic graph learning. By examining multiple datasets and models, we formalize the role of temporal receptive field and highlight their crucial influence on predictive accuracy. Our results demonstrate that appropriately chosen temporal receptive field can significantly enhance model performance, while for some models, overly large windows may introduce noise and reduce accuracy. We conduct extensive benchmarking to validate our findings, ensuring that all experiments are fully reproducible. Code is available at https://github.com/ykrmm/BenchmarkTW .">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f6c0a84ac1f1fe79cfde96f4e163d0d69f9c06cb" target='_blank'>
-              Fine-Tuning Large Language Models for Stock Return Prediction Using Newsflow
+          <td><a href="https://www.semanticscholar.org/paper/31f09be25a90f0bff93ee2f78d85164a62f24094" target='_blank'>
+              Temporal receptive field in dynamic graph learning: A comprehensive analysis
               </a>
             </td>
           <td>
-            Tian Guo, E. Hauptmann
+            Yannis Karmim, Leshanshui Yang, Raphael Fournier S'Niehotta, Cl'ement Chatelain, S'ebastien Adam, Nicolas Thome
           </td>
-          <td>2024-07-25</td>
+          <td>2024-07-17</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Multi-agent trajectory prediction is crucial to autonomous driving and understanding the surrounding environment. Learning-based approaches for multi-agent trajectory prediction, such as primarily relying on graph neural networks, graph transformers, and hypergraph neural networks, have demonstrated outstanding performance on real-world datasets in recent years. However, the hypergraph transformer-based method for trajectory prediction is yet to be explored. Therefore, we present a MultiscAle Relational Transformer (MART) network for multi-agent trajectory prediction. MART is a hypergraph transformer architecture to consider individual and group behaviors in transformer machinery. The core module of MART is the encoder, which comprises a Pair-wise Relational Transformer (PRT) and a Hyper Relational Transformer (HRT). The encoder extends the capabilities of a relational transformer by introducing HRT, which integrates hyperedge features into the transformer mechanism, promoting attention weights to focus on group-wise relations. In addition, we propose an Adaptive Group Estimator (AGE) designed to infer complex group relations in real-world environments. Extensive experiments on three real-world datasets (NBA, SDD, and ETH-UCY) demonstrate that our method achieves state-of-the-art performance, enhancing ADE/FDE by 3.9%/11.8% on the NBA dataset. Code is available at https://github.com/gist-ailab/MART.">
+        <tr id="Accurate traffic flow forecasting is a crucial component of intelligent transportation systems, playing a pivotal role in enhancing transportation intelligence. The integration of Graph Neural Networks (GNNs) and Transformers in traffic flow forecasting has gained significant adoption for enhancing prediction accuracy. Yet, the complex spatial and temporal dependencies present in traffic data continue to pose substantial challenges: (1) Most GNN-based methods assume that the graph structure reflects the actual dependencies between nodes, overlooking the complex dependencies present in the real-world context. (2) Standard time-series models are unable to effectively model complex temporal dependencies, hindering prediction accuracy. To tackle these challenges, the authors propose a novel Transformer-based Spatiotemporal Graph Diffusion Convolution Network (TSGDC) for Traffic Flow Forecasting, which leverages graph diffusion and transformer to capture the complexity and dynamics of spatial and temporal patterns, thereby enhancing prediction performance. The authors designed an Efficient Channel Attention (ECA) that learns separately from the feature dimensions collected by traffic sensors and the temporal dimensions of traffic data, aiding in spatiotemporal modeling. Chebyshev Graph Diffusion Convolution (GDC) is used to capture the complex dependencies within the spatial distribution. Sequence decomposition blocks, as internal operations of transformers, are employed to gradually extract long-term stable trends from hidden complex variables. Additionally, by integrating multi-scale dependencies, including recent, daily, and weekly patterns, accurate traffic flow predictions are achieved. Experimental results on various public datasets show that TSGDC outperforms conventional traffic forecasting models, particularly in accuracy and robustness.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6d30fe4d8196a1c8f984e6dc8d8f3783c98168cb" target='_blank'>
-              MART: MultiscAle Relational Transformer Networks for Multi-agent Trajectory Prediction
+          <td><a href="https://www.semanticscholar.org/paper/f28ffc0b410cb4e7b7c33a98e7941875942be67a" target='_blank'>
+              Transformer-Based Spatiotemporal Graph Diffusion Convolution Network for Traffic Flow Forecasting
               </a>
             </td>
           <td>
-            Seongju Lee, Junseok Lee, Yeonguk Yu, Taeri Kim, Kyoobin Lee
+            Siwei Wei, Yang Yang, Donghua Liu, Ke Deng, Chunzhi Wang
           </td>
-          <td>2024-07-31</td>
-          <td>ArXiv</td>
+          <td>2024-08-09</td>
+          <td>Electronics</td>
           <td>0</td>
-          <td>16</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Recent advancements in graph learning have revolutionized the way to understand and analyze data with complex structures. Notably, Graph Neural Networks (GNNs), i.e. neural network architectures designed for learning graph representations, have become a popular paradigm. With these models being usually characterized by intuition-driven design or highly intricate components, placing them within the theoretical analysis framework to distill the core concepts, helps understand the key principles that drive the functionality better and guide further development. Given this surge in interest, this article provides a comprehensive summary of the theoretical foundations and breakthroughs concerning the approximation and learning behaviors intrinsic to prevalent graph learning models. Encompassing discussions on fundamental aspects such as expressiveness power, generalization, optimization, and unique phenomena such as over-smoothing and over-squashing, this piece delves into the theoretical foundations and frontier driving the evolution of graph learning. In addition, this article also presents several challenges and further initiates discussions on possible solutions.">
+        <tr id="Many empirical studies of labor market questions rely on estimating relatively simple predictive models using small, carefully constructed longitudinal survey datasets based on hand-engineered features. Large Language Models (LLMs), trained on massive datasets, encode vast quantities of world knowledge and can be used for the next job prediction problem. However, while an off-the-shelf LLM produces plausible career trajectories when prompted, the probability with which an LLM predicts a particular job transition conditional on career history will not, in general, align with the true conditional probability in a given population. Recently, Vafa et al. (2024) introduced a transformer-based"foundation model", CAREER, trained using a large, unrepresentative resume dataset, that predicts transitions between jobs; it further demonstrated how transfer learning techniques can be used to leverage the foundation model to build better predictive models of both transitions and wages that reflect conditional transition probabilities found in nationally representative survey datasets. This paper considers an alternative where the fine-tuning of the CAREER foundation model is replaced by fine-tuning LLMs. For the task of next job prediction, we demonstrate that models trained with our approach outperform several alternatives in terms of predictive performance on the survey data, including traditional econometric models, CAREER, and LLMs with in-context learning, even though the LLM can in principle predict job titles that are not allowed in the survey data. Further, we show that our fine-tuned LLM-based models' predictions are more representative of the career trajectories of various workforce subpopulations than off-the-shelf LLM models and CAREER. We conduct experiments and analyses that highlight the sources of the gains in the performance of our models for representative predictions.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a1981788eb330bae203bdc08c63d1dbcb0c13d07" target='_blank'>
-              Foundations and Frontiers of Graph Learning Theory
+          <td><a href="https://www.semanticscholar.org/paper/8553495cea575792c19bf8e77ac26d3a92afd7c5" target='_blank'>
+              LABOR-LLM: Language-Based Occupational Representations with Large Language Models
               </a>
             </td>
           <td>
-            Yu Huang, Min Zhou, Menglin Yang, Zhen Wang, Muhan Zhang, Jie Wang, Hong Xie, Hao Wang, Defu Lian, Enhong Chen
+            Tianyu Du, Ayush Kanodia, Herman Brunborg, Keyon Vafa, Susan Athey
           </td>
-          <td>2024-07-03</td>
+          <td>2024-06-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>37</td>
+          <td>13</td>
         </tr>
 
-        <tr id="Evaluating the contribution of individual data points to a model's prediction is critical for interpreting model predictions and improving model performance. Existing data contribution methods have been applied to various data types, including tabular data, images, and texts; however, their primary focus has been on i.i.d. settings. Despite the pressing need for principled approaches tailored to time series datasets, the problem of estimating data contribution in such settings remains unexplored, possibly due to challenges associated with handling inherent temporal dependencies. This paper introduces TimeInf, a data contribution estimation method for time-series datasets. TimeInf uses influence functions to attribute model predictions to individual time points while preserving temporal structures. Our extensive empirical results demonstrate that TimeInf outperforms state-of-the-art methods in identifying harmful anomalies and helpful time points for forecasting. Additionally, TimeInf offers intuitive and interpretable attributions of data values, allowing us to easily distinguish diverse anomaly patterns through visualizations.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3cf948c645144f6d8565608c19f9779114df6df2" target='_blank'>
-              TimeInf: Time Series Data Contribution via Influence Functions
+          <td><a href="https://www.semanticscholar.org/paper/0084b07c9c1f87776c162af58347aa0ba6767f3d" target='_blank'>
+              DyHANE: dynamic heterogeneous attributed network embedding through experience node replay
               </a>
             </td>
           <td>
-            Yizi Zhang, Jingyan Shen, Xiaoxue Xiong, Yongchan Kwon
+            Liliana Martirano, D. Ienco, R. Interdonato, Andrea Tagarelli
           </td>
-          <td>2024-07-21</td>
-          <td>ArXiv</td>
-          <td>0</td>
+          <td>2024-07-05</td>
+          <td>Appl. Netw. Sci.</td>
           <td>0</td>
+          <td>29</td>
         </tr>
 
-        <tr id="Temporal Graph Networks (TGNs) have demonstrated their remarkable performance in modeling temporal interaction graphs. These works can generate temporal node representations by encoding the surrounding neighborhoods for the target node. However, an inherent limitation of existing TGNs is their reliance on fixed, hand-crafted rules for neighborhood encoding, overlooking the necessity for an adaptive and learnable neighborhood that can accommodate both personalization and temporal evolution across different timestamps. In this paper, we aim to enhance existing TGNs by introducing an adaptive neighborhood encoding mechanism. We present SEAN, a flexible plug-and-play model that can be seamlessly integrated with existing TGNs, effectively boosting their performance. To achieve this, we decompose the adaptive neighborhood encoding process into two phases: (i) representative neighbor selection, and (ii) temporal-aware neighborhood information aggregation. Specifically, we propose the Representative Neighbor Selector component, which automatically pinpoints the most important neighbors for the target node. It offers a tailored understanding of each node's unique surrounding context, facilitating personalization. Subsequently, we propose a Temporal-aware Aggregator, which synthesizes neighborhood aggregation by selectively determining the utilization of aggregation routes and decaying the outdated information, allowing our model to adaptively leverage both the contextually significant and current information during aggregation. We conduct extensive experiments by integrating SEAN into three representative TGNs, evaluating their performance on four public datasets and one financial benchmark dataset introduced in this paper. The results demonstrate that SEAN consistently leads to performance improvements across all models, achieving SOTA performance and exceptional robustness.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fa81e2dd5b5b24060e39ae56d528880b3e10f261" target='_blank'>
-              Towards Adaptive Neighborhood for Advancing Temporal Interaction Graph Modeling
-              </a>
-            </td>
-          <td>
-            Siwei Zhang, Xi Chen, Yun Xiong, Xixi Wu, Yao Zhang, Yongrui Fu, Yinglong Zhao, Jiawei Zhang
-          </td>
-          <td>2024-06-14</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>3</td>
-        </tr>
-
-        <tr id="Graphs have emerged as critical data structures for content analysis in various domains, such as social network analysis, bioinformatics, and recommendation systems. Node classification, a fundamental task in this context, is typically tackled using graph neural networks (GNNs). Unfortunately, conventional GNNs still face challenges in scenarios with few labeled nodes, despite the prevalence of few-shot node classification tasks in real-world applications. To address this challenge, various approaches have been proposed, including graph meta-learning, transfer learning, and methods based on Large Language Models (LLMs). However, traditional meta-learning and transfer learning methods often require prior knowledge from base classes or fail to exploit the potential advantages of unlabeled nodes. Meanwhile, LLM-based methods may overlook the zero-shot capabilities of LLMs and rely heavily on the quality of generated contexts. In this paper, we propose a novel approach that integrates LLMs and GNNs, leveraging the zero-shot inference and reasoning capabilities of LLMs and employing a Graph-LLM-based active learning paradigm to enhance GNNs' performance. Extensive experiments demonstrate the effectiveness of our model in improving node classification accuracy with considerably limited labeled data, surpassing state-of-the-art baselines by significant margins.">
+        <tr id="Stock price forecasting is a challenging area of research, particularly due to the complexity and unpredictability of financial markets. The accuracy of prediction models is influenced by various factors, including nonlinearity, seasonality, and economic shocks. Deep learning has demonstrated better forecasts of stock prices than traditional approaches. This study, therefore, proposed a new approach to improve forecasting system based on an end-to-end convolutional recurrent neural network (CRNN) with attention mechanism. Our approach first investigates local stock price features using 1D convolutional neural network, and then employs a bidirectional long short-term memory (Bi-LSTM) network for forecasting. This model stands out by effectively utilizing contextual data and representing the temporal character of data. The Bi-LSTM is helpful for understanding the history and future contextual information since it uncovers both past and future contexts of stock data. Furthermore, integrating attention mechanism within the CRNN represents a significant improvement. This allows our model to handle long input sequences more effectively and capture the inherent stochasticity in stock prices, which is often missed by traditional models. The effectiveness of our approach is investigated using data on 10 stock indexes from Yahoo Finance. The results show that our method outperforms ARIMA, LSTM, and conventional methods. ">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d41329cb9c08fef08379c558db5a09f412a506ad" target='_blank'>
-              Enhancing Data-Limited Graph Neural Networks by Actively Distilling Knowledge from Large Language Models
+          <td><a href="https://www.semanticscholar.org/paper/d308e58a2b17825f4c41dbf390403ee62eb1a34c" target='_blank'>
+              An improved convolutional recurrent neural network for stock price forecasting
               </a>
             </td>
           <td>
-            Quan Li, Tianxiang Zhao, Lingwei Chen, Junjie Xu, Suhang Wang
+            Hoang Vuong Pham, Hung Phu Lam, Le Nhat Duy, T. Pham, T. Trinh
           </td>
-          <td>2024-07-19</td>
-          <td>ArXiv</td>
+          <td>2024-09-01</td>
+          <td>IAES International Journal of Artificial Intelligence (IJ-AI)</td>
           <td>0</td>
-          <td>11</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Time Series Anomaly Detection (TSAD) finds widespread applications across various domains such as financial markets, industrial production, and healthcare. Its primary objective is to learn the normal patterns of time series data, thereby identifying deviations in test samples. Most existing TSAD methods focus on modeling data from the temporal dimension, while ignoring the semantic information in the spatial dimension. To address this issue, we introduce a novel approach, called Spatial-Temporal Normality learning (STEN). STEN is composed of a sequence Order prediction-based Temporal Normality learning (OTN) module that captures the temporal correlations within sequences, and a Distance prediction-based Spatial Normality learning (DSN) module that learns the relative spatial relations between sequences in a feature space. By synthesizing these two modules, STEN learns expressive spatial-temporal representations for the normal patterns hidden in the time series data. Extensive experiments on five popular TSAD benchmarks show that STEN substantially outperforms state-of-the-art competing methods. Our code is available at https://github.com/mala-lab/STEN.">
+        <tr id="An emerging topic in large language models (LLMs) is their application to time series forecasting, characterizing mainstream and patternable characteristics of time series. A relevant but rarely explored and more challenging question is whether LLMs can detect and explain time series anomalies, a critical task across various real-world applications. In this paper, we investigate the capabilities of LLMs, specifically GPT-4 and LLaMA3, in detecting and explaining anomalies in time series. Our studies reveal that: 1) LLMs cannot be directly used for time series anomaly detection. 2) By designing prompt strategies such as in-context learning and chain-of-thought prompting, GPT-4 can detect time series anomalies with results competitive to baseline methods. 3) We propose a synthesized dataset to automatically generate time series anomalies with corresponding explanations. By applying instruction fine-tuning on this dataset, LLaMA3 demonstrates improved performance in time series anomaly detection tasks. In summary, our exploration shows the promising potential of LLMs as time series anomaly detectors.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6136ae3b84b2b1b9e6215a5c67a3153abd0eedc2" target='_blank'>
-              Self-Supervised Spatial-Temporal Normality Learning for Time Series Anomaly Detection
+          <td><a href="https://www.semanticscholar.org/paper/12b073694ad8cf460d1e74a34b68d07536e0db14" target='_blank'>
+              Can LLMs Serve As Time Series Anomaly Detectors?
               </a>
             </td>
           <td>
-            Yutong Chen, Hongzuo Xu, Guansong Pang, Hezhe Qiao, Yuan Zhou, Mingsheng Shang
+            Manqing Dong, Hao Huang, Longbing Cao
           </td>
-          <td>2024-06-28</td>
+          <td>2024-08-06</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>5</td>
-        </tr>
-
-        <tr id="In this paper, we leverage the power of latent diffusion models to generate synthetic time series tabular data. Along with the temporal and feature correlations, the heterogeneous nature of the feature in the table has been one of the main obstacles in time series tabular data modeling. We tackle this problem by combining the ideas of the variational auto-encoder (VAE) and the denoising diffusion probabilistic model (DDPM). Our model named as \texttt{TimeAutoDiff} has several key advantages including (1) Generality: the ability to handle the broad spectrum of time series tabular data from single to multi-sequence datasets; (2) Good fidelity and utility guarantees: numerical experiments on six publicly available datasets demonstrating significant improvements over state-of-the-art models in generating time series tabular data, across four metrics measuring fidelity and utility; (3) Fast sampling speed: entire time series data generation as opposed to the sequential data sampling schemes implemented in the existing diffusion-based models, eventually leading to significant improvements in sampling speed, (4) Entity conditional generation: the first implementation of conditional generation of multi-sequence time series tabular data with heterogenous features in the literature, enabling scenario exploration across multiple scientific and engineering domains. Codes are in preparation for release to the public, but available upon request.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/78a04be6d94e77047c3251e4480cd08d1194dbd1" target='_blank'>
-              TimeAutoDiff: Combining Autoencoder and Diffusion model for time series tabular data synthesizing
-              </a>
-            </td>
-          <td>
-            Namjoon Suh, Yuning Yang, Din-Yin Hsieh, Qitong Luan, Shi Xu, Shixiang Zhu, Guang Cheng
-          </td>
-          <td>2024-06-23</td>
-          <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
         </tr>
 
-        <tr id="Continuous-Time Dynamic Graph (CTDG) precisely models evolving real-world relationships, drawing heightened interest in dynamic graph learning across academia and industry. However, existing CTDG models encounter challenges stemming from noise and limited historical data. Graph Data Augmentation (GDA) emerges as a critical solution, yet current approaches primarily focus on static graphs and struggle to effectively address the dynamics inherent in CTDGs. Moreover, these methods often demand substantial domain expertise for parameter tuning and lack theoretical guarantees for augmentation efficacy. To address these issues, we propose Conda, a novel latent diffusion-based GDA method tailored for CTDGs. Conda features a sandwich-like architecture, incorporating a Variational Auto-Encoder (VAE) and a conditional diffusion model, aimed at generating enhanced historical neighbor embeddings for target nodes. Unlike conventional diffusion models trained on entire graphs via pre-training, Conda requires historical neighbor sequence embeddings of target nodes for training, thus facilitating more targeted augmentation. We integrate Conda into the CTDG model and adopt an alternating training strategy to optimize performance. Extensive experimentation across six widely used real-world datasets showcases the consistent performance improvement of our approach, particularly in scenarios with limited historical data.">
+        <tr id="Crime forecasting is a critical component of urban analysis and essential for stabilizing society today. Unlike other time series forecasting problems, crime incidents are sparse, particularly in small regions and within specific time periods. Traditional spatial-temporal deep learning models often struggle with this sparsity, as they typically cannot effectively handle the non-Gaussian nature of crime data, which is characterized by numerous zeros and over-dispersed patterns. To address these challenges, we introduce a novel approach termed Spatial Temporal Multivariate Zero-Inflated Negative Binomial Graph Neural Networks (STMGNN-ZINB). This framework leverages diffusion and convolution networks to analyze spatial, temporal, and multivariate correlations, enabling the parameterization of probabilistic distributions of crime incidents. By incorporating a Zero-Inflated Negative Binomial model, STMGNN-ZINB effectively manages the sparse nature of crime data, enhancing prediction accuracy and the precision of confidence intervals. Our evaluation on real-world datasets confirms that STMGNN-ZINB outperforms existing models, providing a more reliable tool for predicting and understanding crime dynamics.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/eb15255bdb2698993e5ad0223454abd6a732d2e7" target='_blank'>
-              Latent Conditional Diffusion-based Data Augmentation for Continuous-Time Dynamic Graph Model
+          <td><a href="https://www.semanticscholar.org/paper/24c426aeaad4d19ac16a0dbe2914166f1ee8d9da" target='_blank'>
+              Uncertainty-Aware Crime Prediction With Spatial Temporal Multivariate Graph Neural Networks
               </a>
             </td>
           <td>
-            Yuxing Tian, Yiyan Qi, Aiwen Jiang, Qi Huang, Jian Guo
+            Zepu Wang, Xiaobo Ma, Huajie Yang, Weimin Lvu, Peng Sun, Sharath Chandra Guntuku
           </td>
-          <td>2024-07-11</td>
+          <td>2024-08-08</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>27</td>
         </tr>
 
-        <tr id="Limited by the scale and diversity of time series data, the neural networks trained on time series data often overfit and show unsatisfacotry performances. In comparison, large language models (LLMs) recently exhibit impressive generalization in diverse fields. Although massive LLM based approaches are proposed for time series tasks, these methods require to load the whole LLM in both training and reference. This high computational demands limit practical applications in resource-constrained settings, like edge-computing and IoT devices. To address this issue, we propose Knowledge Pruning (KP), a novel paradigm for time series learning in this paper. For a specific downstream task, we argue that the world knowledge learned by LLMs is much redundant and only the related knowledge termed as"pertinent knowledge"is useful. Unlike other methods, our KP targets to prune the redundant knowledge and only distill the pertinent knowledge into the target model. This reduces model size and computational costs significantly. Additionally, different from existing LLM based approaches, our KP does not require to load the LLM in the process of training and testing, further easing computational burdens. With our proposed KP, a lightweight network can effectively learn the pertinent knowledge, achieving satisfactory performances with a low computation cost. To verify the effectiveness of our KP, two fundamental tasks on edge-computing devices are investigated in our experiments, where eight diverse environments or benchmarks with different networks are used to verify the generalization of our KP. Through experiments, our KP demonstrates effective learning of pertinent knowledge, achieving notable performance improvements in regression (19.7% on average) and classification (up to 13.7%) tasks, showcasing state-of-the-art results.">
+        <tr id="In accordance with the findings presented in [34], this study examines the applicability of Machine Learning (ML) models and training strategies from the Natural Language Processing (NLP) domain in addressing time series problems, emphasizing the structural and operational aspects of these models and strategies. Recognizing the structural congruence within the data, we opt for Stock Price Prediction (SPP) as the designated domain to assess the transferability of NLP models and strategies. Building upon initial positive outcomes derived from quantitative SPP models in our ongoing research endeavors, we provide a rationale for exploring a range of additional methods and conducting subsequent research experiments. The outlined research aims to elucidate the efficacy of leveraging NLP models and techniques for addressing time series problems exemplified as SPP.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/818750ab091d9a798766931f53aad7bf0581bccb" target='_blank'>
-              LLM-based Knowledge Pruning for Time Series Data Analytics on Edge-computing Devices
+          <td><a href="https://www.semanticscholar.org/paper/7c4f1f32caa4d520f1b1d66244227ab9df24a38e" target='_blank'>
+              Assessment of the Applicability of Large Language Models for Quantitative Stock Price Prediction
               </a>
             </td>
           <td>
-            Ruibing Jin, Qing Xu, Min Wu, Yuecong Xu, Dan Li, Xiaoli Li, Zhenghua Chen
+            Frederic Voigt, Kai von Luck, Peer Stelldinger
           </td>
-          <td>2024-06-13</td>
-          <td>ArXiv</td>
+          <td>2024-06-26</td>
+          <td>Proceedings of the 17th International Conference on PErvasive Technologies Related to Assistive Environments</td>
           <td>0</td>
-          <td>13</td>
+          <td>12</td>
         </tr>
 
-        <tr id="Graph neural networks (GNNs) excel in learning from network-like data but often lack interpretability, making their application challenging in domains requiring transparent decision-making. We propose the Graph Kolmogorov-Arnold Network (GKAN), a novel GNN model leveraging spline-based activation functions on edges to enhance both accuracy and interpretability. Our experiments on five benchmark datasets demonstrate that GKAN outperforms state-of-the-art GNN models in node classification, link prediction, and graph classification tasks. In addition to the improved accuracy, GKAN's design inherently provides clear insights into the model's decision-making process, eliminating the need for post-hoc explainability techniques. This paper discusses the methodology, performance, and interpretability of GKAN, highlighting its potential for applications in domains where interpretability is crucial.">
+        <tr id="Graphs are crucial for representing interrelated data and aiding predictive modeling by capturing complex relationships. Achieving high-quality graph representation is important for identifying linked patterns, leading to improvements in Graph Neural Networks (GNNs) to better capture data structures. However, challenges such as data scarcity, high collection costs, and ethical concerns limit progress. As a result, generative models and data augmentation have become more and more popular. This study explores using generated graphs for data augmentation, comparing the performance of combining generated graphs with real graphs, and examining the effect of different quantities of generated graphs on graph classification tasks. The experiments show that balancing scalability and quality requires different generators based on graph size. Our results introduce a new approach to graph data augmentation, ensuring consistent labels and enhancing classification performance.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ce82880f5527b26fdb12cd1fa13d4cbc45c9e012" target='_blank'>
-              Kolmogorov-Arnold Graph Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/f4641fc657af2ab1a0c304535fd1f2caa9ccc97f" target='_blank'>
+              Data Augmentation in Graph Neural Networks: The Role of Generated Synthetic Graphs
               </a>
             </td>
           <td>
-            Gianluca De Carlo, A. Mastropietro, Aris Anagnostopoulos
+            Sumeyye Bas, Kıymet Kaya, Resul Tugay, S. G. Oguducu
           </td>
-          <td>2024-06-26</td>
+          <td>2024-07-20</td>
           <td>ArXiv</td>
-          <td>3</td>
+          <td>0</td>
           <td>4</td>
         </tr>
 
-        <tr id="Temporal causal discovery is a crucial task aimed at uncovering the causal relations within time series data. The latest temporal causal discovery methods usually train deep learning models on prediction tasks to uncover the causality between time series. They capture causal relations by analyzing the parameters of some components of the trained models, e.g., attention weights and convolution weights. However, this is an incomplete mapping process from the model parameters to the causality and fails to investigate the other components, e.g., fully connected layers and activation functions, that are also significant for causal discovery. To facilitate the utilization of the whole deep learning models in temporal causal discovery, we proposed an interpretable transformer-based causal discovery model termed CausalFormer, which consists of the causality-aware transformer and the decomposition-based causality detector. The causality-aware transformer learns the causal representation of time series data using a prediction task with the designed multi-kernel causal convolution which aggregates each input time series along the temporal dimension under the temporal priority constraint. Then, the decomposition-based causality detector interprets the global structure of the trained causality-aware transformer with the proposed regression relevance propagation to identify potential causal relations and finally construct the causal graph. Experiments on synthetic, simulated, and real datasets demonstrate the state-of-the-art performance of CausalFormer on discovering temporal causality. Our code is available at https://github.com/lingbai-kong/CausalFormer.">
+        <tr id="Fluctuations in the financial market are influenced by various driving forces and numerous factors. Traditional financial research aims to identify the factors influencing stock prices, and existing works construct a common neural network learning framework that learns temporal dependency using a fixed time window of historical information, such as RNN and LSTM models. However, these models only consider the short-term and point-to-point relationships within stock series. The financial market is a complex and dynamic system with many unobservable temporal patterns. Therefore, we propose an adaptive period-aggregation model called the Latent Period-Aggregated Stock Transformer (LPAST). The model integrates a variational autoencoder (VAE) with a period-to-period attention mechanism for multistep prediction in the financial time series. Additionally, we introduce a self-correlation learning method and routing mechanism to handle complex multi-period aggregations and information distribution. Main contributions include proposing a novel period-aggregation representation scheme, introducing a new attention mechanism, and validating the model’s superiority in long-horizon prediction tasks. The LPAST model demonstrates its potential and effectiveness in financial market prediction, highlighting its relevance in financial research and predictive analytics.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0298589ffc3502a8f8731583d6ed34241baab0de" target='_blank'>
-              CausalFormer: An Interpretable Transformer for Temporal Causal Discovery
+          <td><a href="https://www.semanticscholar.org/paper/c8b56ca8a213a228fe44d00254f0cbca7f9209bd" target='_blank'>
+              Period-aggregated transformer for learning latent seasonalities in long-horizon financial time series
               </a>
             </td>
           <td>
-            Lingbai Kong, Wengen Li, Hanchen Yang, Yichao Zhang, J. Guan, Shuigeng Zhou
+            Zhenyang Tang, Jinshui Huang, Denisa Rinprasertmeechai
           </td>
-          <td>2024-06-24</td>
-          <td>ArXiv</td>
+          <td>2024-08-08</td>
+          <td>PLOS ONE</td>
           <td>0</td>
-          <td>49</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Sequential recommendation systems aim to provide personalized recommendations by analyzing dynamic preferences and dependencies within user behavior sequences. Recently, Transformer models can effectively capture user preferences. However, their quadratic computational complexity limits recommendation performance on long interaction sequence data. Inspired by the State Space Model (SSM)representative model, Mamba, which efficiently captures user preferences in long interaction sequences with linear complexity, we find that Mamba's recommendation effectiveness is limited in short interaction sequences, with failing to recall items of actual interest to users and exacerbating the data sparsity cold start problem. To address this issue, we innovatively propose a new model, MaTrRec, which combines the strengths of Mamba and Transformer. This model fully leverages Mamba's advantages in handling long-term dependencies and Transformer's global attention advantages in short-term dependencies, thereby enhances predictive capabilities on both long and short interaction sequence datasets while balancing model efficiency. Notably, our model significantly improves the data sparsity cold start problem, with an improvement of up to 33% on the highly sparse Amazon Musical Instruments dataset. We conducted extensive experimental evaluations on five widely used public datasets. The experimental results show that our model outperforms the current state-of-the-art sequential recommendation models on all five datasets. The code is available at https://github.com/Unintelligentmumu/MaTrRec.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/412e6c60b2d5426ebf3724e770876d116c398984" target='_blank'>
-              MaTrRec: Uniting Mamba and Transformer for Sequential Recommendation
+          <td><a href="https://www.semanticscholar.org/paper/916b0fd6c75c26229a6b648ba316e3bdb9f99ea6" target='_blank'>
+              PMANet: a time series forecasting model for Chinese stock price prediction
               </a>
             </td>
           <td>
-            Shun Zhang, Runsen Zhang, Zhirong Yang
+            Wenke Zhu, Weisi Dai, Chunling Tang, Guoxiong Zhou, Zewei Liu, Yunjing Zhao
           </td>
-          <td>2024-07-27</td>
-          <td>ArXiv</td>
-          <td>0</td>
+          <td>2024-08-07</td>
+          <td>Scientific Reports</td>
           <td>0</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Time-series classification is vital in health monitoring and human activity recognition, as well as in areas such as financial forecasting, process control, and a wide array of forecasting tasks. Traditional time-series models segment data into windows and assign one label per window, often missing label transitions within those windows. This paper presents a novel many-to-many time-series model and post-processing using hybrid recurrent neural networks with attention mechanisms, which more effectively captures label transitions over traditional many-to-one models. Further, unlike typical other many-to-many models, our approach doesn’t require a decoder. Instead, it employs an RNN, generating a label for every input time step. During inference, a weighted voting scheme consolidates overlapping predictions into one label per time step. Experiments show our model remains effective on time-series with sparse label shifts, but particularly excels in detecting frequent transitions. This model is ideal for tasks demanding accurate pinpointing of rapid label changes in time-series data, such as gesture recognition, making it ideal for fast-paced human activity recognition. 1">
+        <tr id="Ensemble forecasts from numerical weather prediction models show systematic errors that require correction via post-processing. While there has been substantial progress in flexible neural network-based post-processing methods over the past years, most station-based approaches still treat every input data point separately which limits the capabilities for leveraging spatial structures in the forecast errors. In order to improve information sharing across locations, we propose a graph neural network architecture for ensemble post-processing, which represents the station locations as nodes on a graph and utilizes an attention mechanism to identify relevant predictive information from neighboring locations. In a case study on 2-m temperature forecasts over Europe, the graph neural network model shows substantial improvements over a highly competitive neural network-based post-processing method.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d206e88758c3992f96eaf77f9ddd4f0e63779b32" target='_blank'>
-              Many-to-Many Prediction for Effective Modeling of Frequent Label Transitions in Time Series
+          <td><a href="https://www.semanticscholar.org/paper/1fe4b1eeac90174d97c76b0869c2c1e6f138febe" target='_blank'>
+              Graph Neural Networks and Spatial Information Learning for Post-Processing Ensemble Weather Forecasts
               </a>
             </td>
           <td>
-            Alexander Katrompas, V. Metsis
+            Moritz Feik, Sebastian Lerch, Jan Stuhmer
           </td>
-          <td>2024-06-26</td>
-          <td>Proceedings of the 17th International Conference on PErvasive Technologies Related to Assistive Environments</td>
+          <td>2024-07-08</td>
+          <td>ArXiv</td>
+          <td>0</td>
           <td>0</td>
-          <td>17</td>
         </tr>
 
-        <tr id="Recurrent neural network-based sequence-to-sequence models have been extensively applied for multi-step-ahead time series forecasting. These models typically involve a decoder trained using either its previous forecasts or the actual observed values as the decoder inputs. However, relying on self-generated predictions can lead to the rapid accumulation of errors over multiple steps, while using the actual observations introduces exposure bias as these values are unavailable during the extrapolation stage. In this regard, this study proposes a novel training approach called reinforced decoder, which introduces auxiliary models to generate alternative decoder inputs that remain accessible when extrapolating. Additionally, a reinforcement learning algorithm is utilized to dynamically select the optimal inputs to improve accuracy. Comprehensive experiments demonstrate that our approach outperforms representative training methods over several datasets. Furthermore, the proposed approach also exhibits promising performance when generalized to self-attention-based sequence-to-sequence forecasting models.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ecdcef5ef150ad893f080cafe211f505c559753a" target='_blank'>
-              Reinforced Decoder: Towards Training Recurrent Neural Networks for Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/a8f0842a1540b91ce53047bb74813c3d07827909" target='_blank'>
+              Fine-scale deep learning model for time series forecasting
               </a>
             </td>
           <td>
-            Qi Sima, Xinze Zhang, Yukun Bao, Siyue Yang, Liang Shen
+            Yuwei Chen, Wenjing Jia, Qiang Wu
           </td>
-          <td>2024-06-14</td>
-          <td>ArXiv</td>
-          <td>0</td>
+          <td>2024-08-06</td>
+          <td>Applied Intelligence</td>
           <td>0</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Recent advances in large language models (LLMs) have unlocked novel opportunities for machine learning applications in the financial domain. These models have demonstrated remarkable capabilities in understanding context, processing vast amounts of data, and generating human-preferred contents. In this survey, we explore the application of LLMs on various financial tasks, focusing on their potential to transform traditional practices and drive innovation. We provide a discussion of the progress and advantages of LLMs in financial contexts, analyzing their advanced technologies as well as prospective capabilities in contextual understanding, transfer learning flexibility, complex emotion detection, etc. We then highlight this survey for categorizing the existing literature into key application areas, including linguistic tasks, sentiment analysis, financial time series, financial reasoning, agent-based modeling, and other applications. For each application area, we delve into specific methodologies, such as textual analysis, knowledge-based analysis, forecasting, data augmentation, planning, decision support, and simulations. Furthermore, a comprehensive collection of datasets, model assets, and useful codes associated with mainstream applications are presented as resources for the researchers and practitioners. Finally, we outline the challenges and opportunities for future research, particularly emphasizing a number of distinctive aspects in this field. We hope our work can help facilitate the adoption and further development of LLMs in the financial sector.">
+        <tr id="We introduce NodeFlow, a flexible framework for probabilistic regression on tabular data that combines Neural Oblivious Decision Ensembles (NODEs) and Conditional Continuous Normalizing Flows (CNFs). It offers improved modeling capabilities for arbitrary probabilistic distributions, addressing the limitations of traditional parametric approaches. In NodeFlow, the NODE captures complex relationships in tabular data through a tree-like structure, while the conditional CNF utilizes the NODE’s output space as a conditioning factor. The training process of NodeFlow employs standard gradient-based learning, facilitating the end-to-end optimization of the NODEs and CNF-based density estimation. This approach ensures outstanding performance, ease of implementation, and scalability, making NodeFlow an appealing choice for practitioners and researchers. Comprehensive assessments on benchmark datasets underscore NodeFlow’s efficacy, revealing its achievement of state-of-the-art outcomes in multivariate probabilistic regression setup and its strong performance in univariate regression tasks. Furthermore, ablation studies are conducted to justify the design choices of NodeFlow. In conclusion, NodeFlow’s end-to-end training process and strong performance make it a compelling solution for practitioners and researchers. Additionally, it opens new avenues for research and application in the field of probabilistic regression on tabular data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8663871588271b4f20645fefcc7d25d9bd1547cf" target='_blank'>
-              A Survey of Large Language Models for Financial Applications: Progress, Prospects and Challenges
+          <td><a href="https://www.semanticscholar.org/paper/7b7ef3bf708e12014b3094d7f3efb36a9d8eb2f4" target='_blank'>
+              NodeFlow: Towards End-to-End Flexible Probabilistic Regression on Tabular Data
               </a>
             </td>
           <td>
-            Yuqi Nie, Yaxuan Kong, Xiaowen Dong, John M. Mulvey, H. Poor, Qingsong Wen, Stefan Zohren
+            Patryk Wielopolski, Oleksii Furman, Maciej Zięba
           </td>
-          <td>2024-06-15</td>
-          <td>ArXiv</td>
+          <td>2024-07-01</td>
+          <td>Entropy</td>
+          <td>0</td>
           <td>2</td>
-          <td>3</td>
         </tr>
 
-        <tr id="The modelling of temporal patterns in dynamic graphs is an important current research issue in the development of time-aware GNNs. Whether or not a specific sequence of events in a temporal graph constitutes a temporal pattern not only depends on the frequency of its occurrence. We consider whether it deviates from what is expected in a temporal graph where timestamps are randomly shuffled. While accounting for such a random baseline is important to model temporal patterns, it has mostly been ignored by current temporal graph neural networks. To address this issue we propose HYPA-DBGNN, a novel two-step approach that combines (i) the inference of anomalous sequential patterns in time series data on graphs based on a statistically principled null model, with (ii) a neural message passing approach that utilizes a higher-order De Bruijn graph whose edges capture overrepresented sequential patterns. Our method leverages hypergeometric graph ensembles to identify anomalous edges within both first- and higher-order De Bruijn graphs, which encode the temporal ordering of events. The model introduces an inductive bias that enhances model interpretability. We evaluate our approach for static node classification using benchmark datasets and a synthetic dataset that showcases its ability to incorporate the observed inductive bias regarding over- and under-represented temporal edges. We demonstrate the framework's effectiveness in detecting similar patterns within empirical datasets, resulting in superior performance compared to baseline methods in node classification tasks. To the best of our knowledge, our work is the first to introduce statistically informed GNNs that leverage temporal and causal sequence anomalies. HYPA-DBGNN represents a path for bridging the gap between statistical graph inference and neural graph representation learning, with potential applications to static GNNs.">
+        <tr id="The prediction of time series is a challenging task relevant in such diverse applications as analyzing financial data, forecasting flow dynamics or understanding biological processes. Especially chaotic time series that depend on a long history pose an exceptionally difficult problem. While machine learning has shown to be a promising approach for predicting such time series, it either demands long training time and much training data when using deep recurrent neural networks. Alternative, when using a reservoir computing approach it comes with high uncertainty and typically a high number of random initializations and extensive hyper-parameter tuning when using a reservoir computing approach. In this paper, we focus on the reservoir computing approach and propose a new mapping of input data into the reservoir's state space. Furthermore, we incorporate this method in two novel network architectures increasing parallelizability, depth and predictive capabilities of the neural network while reducing the dependence on randomness. For the evaluation, we approximate a set of time series from the Mackey-Glass equation, inhabiting non-chaotic as well as chaotic behavior and compare our approaches in regard to their predictive capabilities to echo state networks and gated recurrent units. For the chaotic time series, we observe an error reduction of up to $85.45\%$ and up to $87.90\%$ in contrast to echo state networks and gated recurrent units respectively. Furthermore, we also observe tremendous improvements for non-chaotic time series of up to $99.99\%$ in contrast to existing approaches.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e06e0cb47d2e0afba3b7c9bbfa9d5c33b0375133" target='_blank'>
-              Inference of Sequential Patterns for Neural Message Passing in Temporal Graphs
+          <td><a href="https://www.semanticscholar.org/paper/d488897997df288927a73befa218f42726e3f36d" target='_blank'>
+              Temporal Convolution Derived Multi-Layered Reservoir Computing
               </a>
             </td>
           <td>
-            J. V. Pichowski, Vincenzo Perri, Lisi Qarkaxhija, Ingo Scholtes
+            Johannes Viehweg, Dominik Walther, Patrick Mäder
           </td>
-          <td>2024-06-24</td>
+          <td>2024-07-09</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>8</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Although most graph neural networks (GNNs) can operate on graphs of any size, their classification performance often declines on graphs larger than those encountered during training. Existing methods insufficiently address the removal of size information from graph representations, resulting in sub-optimal performance and reliance on backbone models. In response, we propose DISGEN, a novel and model-agnostic framework designed to disentangle size factors from graph representations. DISGEN employs size- and task-invariant augmentations and introduces a decoupling loss that minimizes shared information in hidden representations, with theoretical guarantees for its effectiveness. Our empirical results show that DISGEN outperforms the state-of-the-art models by up to 6% on real-world datasets, underscoring its effectiveness in enhancing the size generalizability of GNNs. Our codes are available at: https://github.com/GraphmindDartmouth/DISGEN.">
+        <tr id="Graph-level anomaly detection (GLAD) has already gained significant importance and has become a popular field of study, attracting considerable attention across numerous downstream works. The core focus of this domain is to capture and highlight the anomalous information within given graph datasets. In most existing studies, anomalies are often the instances of few. The stark imbalance misleads current GLAD methods to focus on learning the patterns of normal graphs more, further impacting anomaly detection performance. Moreover, existing methods predominantly utilize the inherent features of nodes to identify anomalous graph patterns which is approved suboptimal according to our experiments. In this work, we propose an imbalanced GLAD method via counterfactual augmentation and feature learning. Specifically, we first construct anomalous samples based on counterfactual learning, aiming to expand and balance the datasets. Additionally, we construct a module based on Graph Neural Networks (GNNs), which allows us to utilize degree attributes to complement the inherent attribute features of nodes. Then, we design an adaptive weight learning module to integrate features tailored to different datasets effectively to avoid indiscriminately treating all features as equivalent. Furthermore, extensive baseline experiments conducted on public datasets substantiate the robustness and effectiveness. Besides, we apply the model to brain disease datasets, which can prove the generalization capability of our work. The source code of our work is available online.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/625920dff26468f86c9bb3b13e31538496bf222e" target='_blank'>
-              Enhancing Size Generalization in Graph Neural Networks through Disentangled Representation Learning
+          <td><a href="https://www.semanticscholar.org/paper/f75be7b79dc5b02dfc1845486489956beb059786" target='_blank'>
+              Imbalanced Graph-Level Anomaly Detection via Counterfactual Augmentation and Feature Learning
               </a>
             </td>
           <td>
-            Zheng Huang, Qihui Yang, Dawei Zhou, Yujun Yan
+            Zitong Wang, Xuexiong Luo, Enfeng Song, Qiuqing Bai, Fu Lin
           </td>
-          <td>2024-06-07</td>
+          <td>2024-07-13</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Recently, Large Language Models (LLMs) have demonstrated great potential in various data mining tasks, such as knowledge question answering, mathematical reasoning, and commonsense reasoning. However, the reasoning capability of LLMs on temporal event forecasting has been under-explored. To systematically investigate their abilities in temporal event forecasting, we conduct a comprehensive evaluation of LLM-based methods for temporal event forecasting. Due to the lack of a high-quality dataset that involves both graph and textual data, we first construct a benchmark dataset, named MidEast-TE-mini. Based on this dataset, we design a series of baseline methods, characterized by various input formats and retrieval augmented generation(RAG) modules. From extensive experiments, we find that directly integrating raw texts into the input of LLMs does not enhance zero-shot extrapolation performance. In contrast, incorporating raw texts in specific complex events and fine-tuning LLMs significantly improves performance. Moreover, enhanced with retrieval modules, LLM can effectively capture temporal relational patterns hidden in historical events. Meanwhile, issues such as popularity bias and the long-tail problem still persist in LLMs, particularly in the RAG-based method. These findings not only deepen our understanding of LLM-based event forecasting methods but also highlight several promising research directions.We consider that this comprehensive evaluation, along with the identified research opportunities, will significantly contribute to future research on temporal event forecasting through LLMs.">
+        <tr id="Time series forecasting is an important task in many fields ranging from supply chain management to weather forecasting. Recently, Transformer neural network architectures have shown promising results in forecasting on common time series benchmark datasets. However, application to supply chain demand forecasting, which can have challenging characteristics such as sparsity and cross-series effects, has been limited. In this work, we explore the application of Transformer-based models to supply chain demand forecasting. In particular, we develop a new Transformer-based forecasting approach using a shared, multi-task per-time series network with an initial component applying attention across time series, to capture interactions and help address sparsity. We provide a case study applying our approach to successfully improve demand prediction for a medical device manufacturing company. To further validate our approach, we also apply it to public demand forecasting datasets as well and demonstrate competitive to superior performance compared to a variety of baseline and state-of-the-art forecast methods across the private and public datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/425b541ff4168e921c54ca9c3b449c1fcf985c55" target='_blank'>
-              A Comprehensive Evaluation of Large Language Models on Temporal Event Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/c560b5bcb4b68fabfa9a99f94896b217ce52a3f6" target='_blank'>
+              Inter-Series Transformer: Attending to Products in Time Series Forecasting
               </a>
             </td>
           <td>
-            He Chang, Chenchen Ye, Zhulin Tao, Jie Wu, Zhengmao Yang, Yunshan Ma, Xianglin Huang, Tat-Seng Chua
+            Rares Cristian, P. Harsha, Clemente Ocejo, Georgia Perakis, Brian Quanz, Ioannis Spantidakis, Hamza Zerhouni
           </td>
-          <td>2024-07-16</td>
+          <td>2024-08-07</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>10</td>
+          <td>12</td>
         </tr>
 
-        <tr id="Effective utilization of time series data is often constrained by the scarcity of data quantity that reflects complex dynamics, especially under the condition of distributional shifts. Existing datasets may not encompass the full range of statistical properties required for robust and comprehensive analysis. And privacy concerns can further limit their accessibility in domains such as finance and healthcare. This paper presents an approach that utilizes large language models and data source interfaces to explore and collect time series datasets. While obtained from external sources, the collected data share critical statistical properties with primary time series datasets, making it possible to model and adapt to various scenarios. This method enlarges the data quantity when the original data is limited or lacks essential properties. It suggests that collected datasets can effectively supplement existing datasets, especially involving changes in data distribution. We demonstrate the effectiveness of the collected datasets through practical examples and show how time series forecasting foundation models fine-tuned on these datasets achieve comparable performance to those models without fine-tuning.">
+        <tr id="Temporal networks are effective in capturing the evolving interactions of networks over time, such as social networks and e-commerce networks. In recent years, researchers have primarily concentrated on developing specific model architectures for Temporal Graph Neural Networks (TGNNs) in order to improve the representation quality of temporal nodes and edges. However, limited attention has been given to the quality of negative samples during the training of TGNNs. When compared with static networks, temporal networks present two specific challenges for negative sampling: positive sparsity and positive shift. Positive sparsity refers to the presence of a single positive sample amidst numerous negative samples at each timestamp, while positive shift relates to the variations in positive samples across different timestamps. To robustly address these challenges in training TGNNs, we introduce Curriculum Negative Mining (CurNM), a model-aware curriculum learning framework that adaptively adjusts the difficulty of negative samples. Within this framework, we first establish a dynamically updated negative pool that balances random, historical, and hard negatives to address the challenges posed by positive sparsity. Secondly, we implement a temporal-aware negative selection module that focuses on learning from the disentangled factors of recently active edges, thus accurately capturing shifting preferences. Extensive experiments on 12 datasets and 3 TGNNs demonstrate that our method outperforms baseline methods by a significant margin. Additionally, thorough ablation studies and parameter sensitivity experiments verify the usefulness and robustness of our approach. Our code is available at https://github.com/zziyue83/CurNM.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d313d3981a7cc76c02a68fdca8a28be1b93f0235" target='_blank'>
-              A Language Model-Guided Framework for Mining Time Series with Distributional Shifts
+          <td><a href="https://www.semanticscholar.org/paper/56efc5b54a9beda670261028d60fe6056619863a" target='_blank'>
+              Curriculum Negative Mining For Temporal Networks
               </a>
             </td>
           <td>
-            Haibei Zhu, Yousef El-Laham, Elizabeth Fons, Svitlana Vyetrenko
+            Ziyue Chen, Tongya Zheng, Mingli Song
           </td>
-          <td>2024-06-07</td>
+          <td>2024-07-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>5</td>
         </tr>
 
-        <tr id="Modern recurrent layers are emerging as a promising path toward edge deployment of foundation models, especially in the context of large language models (LLMs). Compressing the whole input sequence in a finite-dimensional representation enables recurrent layers to model long-range dependencies while maintaining a constant inference cost for each token and a fixed memory requirement. However, the practical deployment of LLMs in resource-limited environments often requires further model compression, such as quantization and pruning. While these techniques are well-established for attention-based models, their effects on recurrent layers remain underexplored. In this preliminary work, we focus on post-training quantization for recurrent LLMs and show that Mamba models exhibit the same pattern of outlier channels observed in attention-based LLMs. We show that the reason for the difficulty of quantizing SSMs is caused by activation outliers, similar to those observed in transformer-based LLMs. We report baseline results for post-training quantization of Mamba that do not take into account the activation outliers and suggest first steps for outlier-aware quantization.">
+        <tr id="We propose a novel data-driven network framework for forecasting problems related to E-mini S\&P 500 and CBOE Volatility Index futures, in which products with different expirations act as distinct nodes. We provide visual demonstrations of the correlation structures of these products in terms of their returns, realized volatility, and trading volume. The resulting networks offer insights into the contemporaneous movements across the different products, illustrating how inherently connected the movements of the future products belonging to these two classes are. These networks are further utilized by a multi-channel Graph Convolutional Network to enhance the predictive power of a Long Short-Term Memory network, allowing for the propagation of forecasts of highly correlated quantities, combining the temporal with the spatial aspect of the term structure.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3d553478d06f751f872a82c774c8262ce66d47fd" target='_blank'>
-              Mamba-PTQ: Outlier Channels in Recurrent Large Language Models
+          <td><a href="https://www.semanticscholar.org/paper/250fe7baf3fd0aa1f684eedd3e76aeb1b17f89aa" target='_blank'>
+              A GCN-LSTM Approach for ES-mini and VX Futures Forecasting
               </a>
             </td>
           <td>
-            Alessandro Pierro, Steven Abreu
+            N. Michael, Mihai Cucuringu, Sam Howison
           </td>
-          <td>2024-07-17</td>
+          <td>2024-08-10</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>8</td>
         </tr>
 
-        <tr id="In recent years, Graph Neural Networks (GNNs) have become the de facto tool for learning node and graph representations. Most GNNs typically consist of a sequence of neighborhood aggregation (a.k.a., message passing) layers. Within each of these layers, the representation of each node is updated from an aggregation and transformation of its neighbours representations at the previous layer. The upper bound for the expressive power of message passing GNNs was reached through the use of MLPs as a transformation, due to their universal approximation capabilities. However, MLPs suffer from well-known limitations, which recently motivated the introduction of Kolmogorov-Arnold Networks (KANs). KANs rely on the Kolmogorov-Arnold representation theorem, rendering them a promising alternative to MLPs. In this work, we compare the performance of KANs against that of MLPs in graph learning tasks. We perform extensive experiments on node classification, graph classification and graph regression datasets. Our preliminary results indicate that while KANs are on-par with MLPs in classification tasks, they seem to have a clear advantage in the graph regression tasks. Code is available at https: //github.com/RomanBresson/KAGNN.">
+        <tr id="In the realm of event prediction, temporal knowledge graph forecasting (TKGF) stands as a pivotal technique. Previous approaches face the challenges of not utilizing experience during testing and relying on a single short-term history, which limits adaptation to evolving data. In this paper, we introduce the Online Neural-Symbolic Event Prediction (ONSEP) framework, which innovates by integrating dynamic causal rule mining (DCRM) and dual history augmented generation (DHAG). DCRM dynamically constructs causal rules from real-time data, allowing for swift adaptation to new causal relationships. In parallel, DHAG merges short-term and long-term historical contexts, leveraging a bi-branch approach to enrich event prediction. Our framework demonstrates notable performance enhancements across diverse datasets, with significant Hit@k (k=1,3,10) improvements, showcasing its ability to augment large language models (LLMs) for event prediction without necessitating extensive retraining. The ONSEP framework not only advances the field of TKGF but also underscores the potential of neural-symbolic approaches in adapting to dynamic data environments.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/78167a0578e995148dac629768e9495113c8babd" target='_blank'>
-              KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning
+          <td><a href="https://www.semanticscholar.org/paper/0f4e7c0661406c5e4a78a9aa8c2f70648662b630" target='_blank'>
+              ONSEP: A Novel Online Neural-Symbolic Framework for Event Prediction Based on Large Language Model
               </a>
             </td>
           <td>
-            Roman Bresson, Giannis Nikolentzos, G. Panagopoulos, Michail Chatzianastasis, Jun Pang, M. Vazirgiannis
+            Xuanqing Yu, Wangtao Sun, Jingwei Li, Kang Liu, Chengbao Liu, JieFu Tan
           </td>
-          <td>2024-06-26</td>
+          <td>2024-08-14</td>
           <td>ArXiv</td>
-          <td>5</td>
-          <td>54</td>
+          <td>0</td>
+          <td>8</td>
         </tr>
 
-        <tr id="Self-attention-based networks have achieved remarkable performance in sequential recommendation tasks. A crucial component of these models is positional encoding. In this study, we delve into the learned positional embedding, demonstrating that it often captures the distance between tokens. Building on this insight, we introduce novel attention models that directly learn positional relations. Extensive experiments reveal that our proposed models, \textbf{PARec} and \textbf{FPARec} outperform previous self-attention-based approaches.Our code is available at the link for anonymous review: https://anonymous.4open.science/ r/FPARec-2C55/">
+        <tr id="Accurately predicting PM2.5 is a crucial task for protecting public health and making policy decisions. In the meanwhile, it is also a challenging task, given the complex spatio-temporal patterns of PM2.5 concentrations. Recently, the utilization of graph neural network (GNN) models has emerged as a promising approach, demonstrating significant advantages in capturing the spatial and temporal dependencies associated with PM2.5 concentrations. In this work, we collected a comprehensive dataset spanning 308 cities in China, encompassing data on seven pollutants as well as meteorological variables from January 2015 to September 2022. To effectively predict the PM2.5 concentrations, we propose a graph attention recurrent neural network (GARNN) model by taking into account both meteorological and geographical information. Extensive experiments validated the efficiency of the proposed GARNN model, revealing its superior performance compared to other existing methods in terms of predictive capabilities. This study contributes to advancing the understanding and prediction of PM2.5 concentrations, providing a valuable tool for addressing environmental challenges.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/67b7eb42f7e350495d8d222d37cb87e85050d0c1" target='_blank'>
-              Learning Positional Attention for Sequential Recommendation
+          <td><a href="https://www.semanticscholar.org/paper/f0d3185a50e22682b8c650ceac52e70dd3a9849f" target='_blank'>
+              A Graph Attention Recurrent Neural Network Model for PM2.5 Prediction: A Case Study in China from 2015 to 2022
               </a>
             </td>
           <td>
-            Fangfang Luo, Juan Zhang, Shenghui Xu
+            Rui Pan, Tuozhen Liu, Lingfei Ma
           </td>
           <td>2024-07-03</td>
-          <td>ArXiv</td>
+          <td>Atmosphere</td>
           <td>0</td>
-          <td>2</td>
+          <td>19</td>
         </tr>
 
-        <tr id="How to capture dynamic spatial-temporal dependencies remains an open question in multivariate time series (MTS) forecasting. Although recent advanced spatial-temporal graph neural networks (STGNNs) achieve superior forecasting performance, they either consider pre-defined spatial correlations or simply learn static graphs. Some research has tried to learn many adjacent matrices to reveal time-varying spatial correlations, but they generate discrete graphs which cannot encode evolutionary information and also face computational complexity problem. In this paper, we propose two significant plugins to help automatically learn enhanced dynamic spatial-temporal embedding of MTS data: (1) a novel neural conditional random field (CRF) layer. We find that the implicit time-varying spatial dependencies are reflected by the explicit changeable links between edges, and we propose the neural CRF to encode such pairwise changeable evolutionary inter-dependencies; (2) a structure adaptive graph convolution (SAGC) that does not require pre-defined graphs to capture semantically richer spatial correlations. Then, we integrate the neural CRF, SAGC with recurrent neural network to develop a new STGNN paradigm termed Adaptive Spatial-Temporal graph neural network with Conditional Random Field (ASTCRF), which can be trained in an end-to-end fashion. We validate the effectiveness, efficiency and scalability of ASTCRF on five public benchmark MTS datasets.">
+        <tr id="In this study, we delve into the Structured State Space Model (S4), Change Point Detection methodologies, and the Switching Non-linear Dynamics System (SNLDS). Our central proposition is an enhanced inference technique and long-range dependency method for SNLDS. The cornerstone of our approach is the fusion of S4 and SNLDS, leveraging the strengths of both models to effectively address the intricacies of long-range dependencies in switching time series. Through rigorous testing, we demonstrate that our proposed methodology adeptly segments and reproduces long-range dependencies in both the 1-D Lorenz dataset and the 2-D bouncing ball dataset. Notably, our integrated approach outperforms the standalone SNLDS in these tasks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/667940911f90cfd6980e5e1731731f7c2af49b08" target='_blank'>
-              Dynamic Spatial-Temporal Embedding via Neural Conditional Random Field for Multivariate Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/737fccae30a52b719925aa3bdefbccf7758f66f5" target='_blank'>
+              Long Range Switching Time Series Prediction via State Space Model
               </a>
             </td>
           <td>
-            Peiyu Yi, Feihu Huang, Jian Peng, Zhifeng Bao
+            Jiaming Zhang, Yang Ding, Yunfeng Gao
           </td>
-          <td>2024-06-27</td>
-          <td>ACM Transactions on Spatial Algorithms and Systems</td>
+          <td>2024-07-27</td>
+          <td>ArXiv</td>
+          <td>0</td>
           <td>0</td>
-          <td>3</td>
         </tr>
 
-        <tr id="Global Station Weather Forecasting (GSWF) is crucial for various sectors, including aviation, agriculture, energy, and disaster preparedness. Recent advancements in deep learning have significantly improved the accuracy of weather predictions by optimizing models based on public meteorological data. However, existing public datasets for GSWF optimization and benchmarking still suffer from significant limitations, such as small sizes, limited temporal coverage, and a lack of comprehensive variables. These shortcomings prevent them from effectively reflecting the benchmarks of current forecasting methods and fail to support the real needs of operational weather forecasting. To address these challenges, we present the WEATHER-5K dataset. This dataset comprises a comprehensive collection of data from 5,672 weather stations worldwide, spanning a 10-year period with one-hour intervals. It includes multiple crucial weather elements, providing a more reliable and interpretable resource for forecasting. Furthermore, our WEATHER-5K dataset can serve as a benchmark for comprehensively evaluating existing well-known forecasting models, extending beyond GSWF methods to support future time-series research challenges and opportunities. The dataset and benchmark implementation are publicly available at: https://github.com/taohan10200/WEATHER-5K.">
+        <tr id="Deep neural networks (DNNs) are prominent in predictive analytics for accurately forecasting target variables. However, inherent uncertainties necessitate constructing prediction intervals for reliability. The existing literature often lacks practical methodologies for creating predictive intervals, especially for time series with trends and seasonal patterns. This paper explicitly details a practical approach integrating dual-output Monte Carlo Dropout (MCDO) with DNNs to approximate predictive means and variances within a Bayesian framework, enabling forecast interval construction. The dual-output architecture employs a custom loss function, combining mean squared error with Softplus-derived predictive variance, ensuring non-negative variance values. Hyperparameter optimization is performed through a grid search exploring activation functions, dropout rates, epochs, and batch sizes. Empirical distributions of predictive means and variances from the MCDO demonstrate the results of the dual-output MCDO DNNs. The proposed method achieves a significant improvement in forecast accuracy, with an RMSE reduction of about 10% compared to the seasonal autoregressive integrated moving average model. Additionally, the method provides more reliable forecast intervals, as evidenced by a higher coverage proportion and narrower interval widths. A case study on Thailand’s durian export data showcases the method’s utility and applicability to other datasets with trends and/or seasonal components.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5584976fb110e70abdb876f5f4bf7e68b532960d" target='_blank'>
-              WEATHER-5K: A Large-scale Global Station Weather Dataset Towards Comprehensive Time-series Forecasting Benchmark
+          <td><a href="https://www.semanticscholar.org/paper/48e9c93416cccc0d5c4d1f0646a11cd372d3ec5b" target='_blank'>
+              Time-Series Interval Forecasting with Dual-Output Monte Carlo Dropout: A Case Study on Durian Exports
               </a>
             </td>
           <td>
-            Tao Han, Song Guo, Zhenghao Chen, Wanghan Xu, Lei Bai
+            Unyamanee Kummaraka, Patchanok Srisuradetchai
           </td>
-          <td>2024-06-20</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>4</td>
+          <td>2024-08-02</td>
+          <td>Forecasting</td>
+          <td>0</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Predicting edge weights on graphs has various applications, from transportation systems to social networks. This paper describes a Graph Neural Network (GNN) approach for edge weight prediction with guaranteed coverage. We leverage conformal prediction to calibrate the GNN outputs and produce valid prediction intervals. We handle data heteroscedasticity through error reweighting and Conformalized Quantile Regression (CQR). We compare the performance of our method against baseline techniques on real-world transportation datasets. Our approach has better coverage and efficiency than all baselines and showcases robustness and adaptability.">
+        <tr id="With the remarkable success of generative models like ChatGPT, Artificial Intelligence Generated Content (AIGC) is undergoing explosive development. Not limited to text and images, generative models can generate industrial time series data, addressing challenges such as the difficulty of data collection and data annotation. Due to their outstanding generation ability, they have been widely used in Internet of Things, metaverse, and cyber-physical-social systems to enhance the efficiency of industrial production. In this paper, we present a comprehensive overview of generative models for industrial time series from deep generative models (DGMs) to large generative models (LGMs). First, a DGM-based AIGC framework is proposed for industrial time series generation. Within this framework, we survey advanced industrial DGMs and present a multi-perspective categorization. Furthermore, we systematically analyze the critical technologies required to construct industrial LGMs from four aspects: large-scale industrial dataset, LGMs architecture for complex industrial characteristics, self-supervised training for industrial time series, and fine-tuning of industrial downstream tasks. Finally, we conclude the challenges and future directions to enable the development of generative models in industry.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/45835fe65b9bb84b0790546bc24380a1931bc96d" target='_blank'>
-              Conformal Load Prediction with Transductive Graph Autoencoders
+          <td><a href="https://www.semanticscholar.org/paper/dc1ce4a6d24e82a1c9c05d41f69b1e606efa4115" target='_blank'>
+              AIGC for Industrial Time Series: From Deep Generative Models to Large Generative Models
               </a>
             </td>
           <td>
-            Rui Luo, Nicolo Colombo
+            Lei Ren, Haiteng Wang, Yang Tang, Chunhua Yang
           </td>
-          <td>2024-06-12</td>
+          <td>2024-07-16</td>
           <td>ArXiv</td>
-          <td>4</td>
           <td>0</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Financial assets exhibit complex dependency structures, which are crucial for investors to create diversified portfolios to mitigate risk in volatile financial markets. To explore the financial asset dependencies dynamics, we propose a novel approach that models the dependencies of assets as an Asset Dependency Matrix (ADM) and treats the ADM sequences as image sequences. This allows us to leverage deep learning-based video prediction methods to capture the spatiotemporal dependencies among assets. However, unlike images where neighboring pixels exhibit explicit spatiotemporal dependencies due to the natural continuity of object movements, assets in ADM do not have a natural order. This poses challenges to organizing the relational assets to reveal better the spatiotemporal dependencies among neighboring assets for ADM forecasting. To tackle the challenges, we propose the Asset Dependency Neural Network (ADNN), which employs the Convolutional Long Short-Term Memory (ConvLSTM) network, a highly successful method for video prediction. ADNN can employ static and dynamic transformation functions to optimize the representations of the ADM. Through extensive experiments, we demonstrate that our proposed framework consistently outperforms the baselines in the ADM prediction and downstream application tasks. This research contributes to understanding and predicting asset dependencies, offering valuable insights for financial market participants.">
+        <tr id="Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (Joint Adaptive predictioN-region Estimation for Time-series), a novel framework for constructing conformal prediction regions that are valid for both univariate and multivariate time series. JANET generalises the inductive conformal framework and efficiently produces joint prediction regions with controlled K-familywise error rates, enabling flexible adaptation to specific application needs. Our empirical evaluation demonstrates JANET's superior performance in multi-step prediction tasks across diverse time series datasets, highlighting its potential for reliable and interpretable uncertainty quantification in sequential data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c51f53bdd4ab87d20b8e0a174f968f4dcf42a6a3" target='_blank'>
-              Financial Assets Dependency Prediction Utilizing Spatiotemporal Patterns
+          <td><a href="https://www.semanticscholar.org/paper/b21605b67376e0377590d3cdfb99e3c43495b865" target='_blank'>
+              JANET: Joint Adaptive predictioN-region Estimation for Time-series
               </a>
             </td>
           <td>
-            Haoren Zhu, Pengfei Zhao, NG WilfredSiuHung, Dik Lun Lee
+            Eshant English, Eliot Wong-Toi, Matteo Fontana, Stephan Mandt, P. Smyth, Christoph Lippert
           </td>
-          <td>2024-06-13</td>
+          <td>2024-07-08</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>8</td>
         </tr>
 
-        <tr id="Sequential recommendation aims to recommend the next items that a target user may have interest in based on the user’s sequence of past behaviors, which has become a hot research topic in both academia and industry. In the literature, sequential recommendation adopts a Sequence-to-Item or Sequence-to-Sequence training strategy, which supervises a sequential model with a user’s next one or more behaviors as the labels and the sequence of the past behaviors as the input. However, existing powerful sequential recommendation approaches employ more and more complex deep structures such as Transformer in order to accurately capture the sequential patterns, which heavily rely on hand-crafted designs on key attention mechanism to achieve state-of-the-art performance, thus failing to automatically obtain the optimal design of attention representation architectures in various scenarios with different data. Other works on classic automated deep recommender systems only focus on traditional settings, ignoring the problem of sequential scenarios. In this paper, we study the problem of automated sequential recommendation, which faces two main challenges: i) How can we design a proper search space tailored for attention automation in sequential recommendation, and ii) How can we accurately search effective attention representation architectures considering multiple user interests reflected in the sequential behavior. To tackle these challenges, we propose an automated disentangled sequential recommendation (AutoDisenSeq) model. In particular, we employ neural architecture search (NAS) and design a search space tailored for automated attention representation in attentive intention-disentangled sequential recommendation with an expressive and efficient space complexity of \(O(n^{2})\) given \(n\) as the number of layers. We further propose a context-aware parameter sharing mechanism taking characteristics of each sub-architecture into account to enable accurate architecture performance estimations and great flexibility for disentanglement of latent intention representation. Moreover, we propose AutoDisenSeq-LLM, which utilizes the textual understanding power of large language model (LLM) as a guidance to refine the candidate list for recommendation from AutoDisenSeq. We conduct extensive experiments to show that our proposed AutoDisenSeq model and AutoDisenSeq-LLM model outperform existing baseline methods on four real-world datasets in both overall recommendation and cold-start recommendation scenarios.">
+        <tr id="Time series forecasting has been an essential field in many different application areas, including economic analysis, meteorology, and so forth. The majority of time series forecasting models are trained using the mean squared error (MSE). However, this training based on MSE causes a limitation known as prediction delay. The prediction delay, which implies the ground-truth precedes the prediction, can cause serious problems in a variety of fields, e.g., finance and weather forecasting -- as a matter of fact, predictions succeeding ground-truth observations are not practically meaningful although their MSEs can be low. This paper proposes a new perspective on traditional time series forecasting tasks and introduces a new solution to mitigate the prediction delay. We introduce a continuous-time gated recurrent unit (GRU) based on the neural ordinary differential equation (NODE) which can supervise explicit time-derivatives. We generalize the GRU architecture in a continuous-time manner and minimize the prediction delay through our time-derivative regularization. Our method outperforms in metrics such as MSE, Dynamic Time Warping (DTW) and Time Distortion Index (TDI). In addition, we demonstrate the low prediction delay of our method in a variety of datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bd9e2e3c45eedfffe777eb3211087d95e9353cf0" target='_blank'>
-              Automated Disentangled Sequential Recommendation with Large Language Models
+          <td><a href="https://www.semanticscholar.org/paper/cb1274dd33e80fab3c983829e9b94abcebe9e2a8" target='_blank'>
+              Addressing Prediction Delays in Time Series Forecasting: A Continuous GRU Approach with Derivative Regularization
               </a>
             </td>
           <td>
-            Xin Wang, Hong Chen, Zirui Pan, Yuwei Zhou, Chaoyu Guan, Lifeng Sun, Wenwu Zhu
+            Sheo Yon Jhin, Seojin Kim, Noseong Park
           </td>
           <td>2024-06-29</td>
-          <td>ACM Transactions on Information Systems</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>17</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Dynamic link prediction is a critical task in the analysis of evolving networks, with applications ranging from recommender systems to economic exchanges. However, the concept of the temporal receptive field, which refers to the temporal context that models use for making predictions, has been largely overlooked and insufficiently analyzed in existing research. In this study, we present a comprehensive analysis of the temporal receptive field in dynamic graph learning. By examining multiple datasets and models, we formalize the role of temporal receptive field and highlight their crucial influence on predictive accuracy. Our results demonstrate that appropriately chosen temporal receptive field can significantly enhance model performance, while for some models, overly large windows may introduce noise and reduce accuracy. We conduct extensive benchmarking to validate our findings, ensuring that all experiments are fully reproducible. Code is available at https://github.com/ykrmm/BenchmarkTW .">
+        <tr id="Self-supervised Pretrained Models (PTMs) have demonstrated remarkable performance in computer vision and natural language processing tasks. These successes have prompted researchers to design PTMs for time series data. In our experiments, most self-supervised time series PTMs were surpassed by simple supervised models. We hypothesize this undesired phenomenon may be caused by data scarcity. In response, we test six time series generation methods, use the generated data in pretraining in lieu of the real data, and examine the effects on classification performance. Our results indicate that replacing a real-data pretraining set with a greater volume of only generated samples produces noticeable improvement.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/31f09be25a90f0bff93ee2f78d85164a62f24094" target='_blank'>
-              Temporal receptive field in dynamic graph learning: A comprehensive analysis
+          <td><a href="https://www.semanticscholar.org/paper/bcb109299f76471af99ce2c8c40fc510cec2c1b0" target='_blank'>
+              A Systematic Evaluation of Generated Time Series and Their Effects in Self-Supervised Pretraining
               </a>
             </td>
           <td>
-            Yannis Karmim, Leshanshui Yang, Raphael Fournier S'Niehotta, Cl'ement Chatelain, S'ebastien Adam, Nicolas Thome
+            Audrey Der, Chin-Chia Michael Yeh, Xin Dai, Huiyuan Chen, Yan Zheng, Yujie Fan, Zhongfang Zhuang, Vivian Lai, Junpeng Wang, Liang Wang, Wei Zhang, Eamonn J. Keogh
           </td>
-          <td>2024-07-17</td>
+          <td>2024-08-15</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>22</td>
         </tr>
 
-        <tr id="Time Series Classification (TSC) encompasses two settings: classifying entire sequences or classifying segmented subsequences. The raw time series for segmented TSC usually contain Multiple classes with Varying Duration of each class (MVD). Therefore, the characteristics of MVD pose unique challenges for segmented TSC, yet have been largely overlooked by existing works. Specifically, there exists a natural temporal dependency between consecutive instances (segments) to be classified within MVD. However, mainstream TSC models rely on the assumption of independent and identically distributed (i.i.d.), focusing on independently modeling each segment. Additionally, annotators with varying expertise may provide inconsistent boundary labels, leading to unstable performance of noise-free TSC models. To address these challenges, we first formally demonstrate that valuable contextual information enhances the discriminative power of classification instances. Leveraging the contextual priors of MVD at both the data and label levels, we propose a novel consistency learning framework Con4m, which effectively utilizes contextual information more conducive to discriminating consecutive segments in segmented TSC tasks, while harmonizing inconsistent boundary labels for training. Extensive experiments across multiple datasets validate the effectiveness of Con4m in handling segmented TSC tasks on MVD.">
+        <tr id="Transformer-based methods have recently demonstrated their potential in time series forecasting problems. However, the mainstream approach, primarily utilizing attention to model inter-step correlation in the time domain, is constrained by two significant issues that lead to ineffective and inefficient multivariate forecasting. The first is that key representations in the time domain are scattered and sparse, resulting in parameter bloat and increased difficulty in capturing time dependencies. The second is that treating time step points as uniformly embedded tokens leads to the erasure of inter-variate correlations. To address these challenges, we propose a frequency-wise and variables-oriented transformer-based method. This method leverages the intrinsic conjugate symmetry in the frequency domain, enabling compact frequency domain representations that naturally mix information across time points while reducing spatio-temporal costs. Multivariate inter-correlations can also be captured from similar frequency domain components, which enhances the variables-oriented attention mechanism modeling capability. Further, we employ both polar and complex domain perspectives to enrich the frequency domain representations and decode complicated temporal patterns. We propose frequency-enhanced independent representation multi-head attention (FIR-Attention) to leverage these advantages for improved multivariate interaction. Techniques such as cutting-off frequency and equivalent mapping are used to ensure the model’s lightweight nature. Extensive experiments on eight mainstream datasets show that our approach achieves first-rate satisfactory results and, importantly, requires only one percent of the spatio-temporal cost of mainstream methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bf2d1773723caebef0ace7589e223775b9178a15" target='_blank'>
-              Con4m: Context-aware Consistency Learning Framework for Segmented Time Series Classification
+          <td><a href="https://www.semanticscholar.org/paper/36f87cbd5187e521184ddb319b132292cb8ae608" target='_blank'>
+              Frequency-Enhanced Transformer with Symmetry-Based Lightweight Multi-Representation for Multivariate Time Series Forecasting
               </a>
             </td>
           <td>
-            Junru Chen, Tianyu Cao, Jing Xu, Jiahe Li, Zhilong Chen, Tao Xiao, Yang Yang
+            Chenyue Wang, Zhouyuan Zhang, Xin Wang, Mingyang Liu, Lin Chen, Jiatian Pi
           </td>
-          <td>2024-07-31</td>
-          <td>ArXiv</td>
+          <td>2024-06-25</td>
+          <td>Symmetry</td>
           <td>0</td>
-          <td>2</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Stock price forecasting is a challenging area of research, particularly due to the complexity and unpredictability of financial markets. The accuracy of prediction models is influenced by various factors, including nonlinearity, seasonality, and economic shocks. Deep learning has demonstrated better forecasts of stock prices than traditional approaches. This study, therefore, proposed a new approach to improve forecasting system based on an end-to-end convolutional recurrent neural network (CRNN) with attention mechanism. Our approach first investigates local stock price features using 1D convolutional neural network, and then employs a bidirectional long short-term memory (Bi-LSTM) network for forecasting. This model stands out by effectively utilizing contextual data and representing the temporal character of data. The Bi-LSTM is helpful for understanding the history and future contextual information since it uncovers both past and future contexts of stock data. Furthermore, integrating attention mechanism within the CRNN represents a significant improvement. This allows our model to handle long input sequences more effectively and capture the inherent stochasticity in stock prices, which is often missed by traditional models. The effectiveness of our approach is investigated using data on 10 stock indexes from Yahoo Finance. The results show that our method outperforms ARIMA, LSTM, and conventional methods. ">
+        <tr id="We introduce the Robustness of Hierarchically Organized Time Series (RHiOTS) framework, designed to assess the robustness of hierarchical time series forecasting models and algorithms on real-world datasets. Hierarchical time series, where lower-level forecasts must sum to upper-level ones, are prevalent in various contexts, such as retail sales across countries. Current empirical evaluations of forecasting methods are often limited to a small set of benchmark datasets, offering a narrow view of algorithm behavior. RHiOTS addresses this gap by systematically altering existing datasets and modifying the characteristics of individual series and their interrelations. It uses a set of parameterizable transformations to simulate those changes in the data distribution. Additionally, RHiOTS incorporates an innovative visualization component, turning complex, multidimensional robustness evaluation results into intuitive, easily interpretable visuals. This approach allows an in-depth analysis of algorithm and model behavior under diverse conditions. We illustrate the use of RHiOTS by analyzing the predictive performance of several algorithms. Our findings show that traditional statistical methods are more robust than state-of-the-art deep learning algorithms, except when the transformation effect is highly disruptive. Furthermore, we found no significant differences in the robustness of the algorithms when applying specific reconciliation methods, such as MinT. RHiOTS provides researchers with a comprehensive tool for understanding the nuanced behavior of forecasting algorithms, offering a more reliable basis for selecting the most appropriate method for a given problem.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d308e58a2b17825f4c41dbf390403ee62eb1a34c" target='_blank'>
-              An improved convolutional recurrent neural network for stock price forecasting
+          <td><a href="https://www.semanticscholar.org/paper/525cf42ca049ecd3089189612e74d0df68dbcae0" target='_blank'>
+              RHiOTS: A Framework for Evaluating Hierarchical Time Series Forecasting Algorithms
               </a>
             </td>
           <td>
-            Hoang Vuong Pham, Hung Phu Lam, Le Nhat Duy, T. Pham, T. Trinh
+            Luis Roque, Carlos Soares, Luís Torgo
           </td>
-          <td>2024-09-01</td>
-          <td>IAES International Journal of Artificial Intelligence (IJ-AI)</td>
+          <td>2024-08-06</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>36</td>
         </tr>
 
-        <tr id="Deep learning-based time series forecasting has dominated the short-term precipitation forecasting field with the help of its ability to estimate motion flow in high-resolution datasets. The growing interest in precipitation nowcasting offers substantial opportunities for the advancement of current forecasting technologies. Nevertheless, there has been a scarcity of in-depth surveys of time series precipitation forecasting using deep learning. Thus, this paper systemically reviews recent progress in time series precipitation forecasting models. Specifically, we investigate the following key points within background components, covering: i) preprocessing, ii) objective functions, and iii) evaluation metrics. We then categorize forecasting models into \textit{recursive} and \textit{multiple} strategies based on their approaches to predict future frames, investigate the impacts of models using the strategies, and performance assessments. Finally, we evaluate current deep learning-based models for precipitation forecasting on a public benchmark, discuss their limitations and challenges, and present some promising research directions. Our contribution lies in providing insights for a better understanding of time series precipitation forecasting and in aiding the development of robust AI solutions for the future.">
+        <tr id="We study an emerging and intriguing problem of multimodal temporal event forecasting with large language models. Compared to using text or graph modalities, the investigation of utilizing images for temporal event forecasting has not been fully explored, especially in the era of large language models (LLMs). To bridge this gap, we are particularly interested in two key questions of: 1) why images will help in temporal event forecasting, and 2) how to integrate images into the LLM-based forecasting framework. To answer these research questions, we propose to identify two essential functions that images play in the scenario of temporal event forecasting, i.e., highlighting and complementary. Then, we develop a novel framework, named MM-Forecast. It employs an Image Function Identification module to recognize these functions as verbal descriptions using multimodal large language models (MLLMs), and subsequently incorporates these function descriptions into LLM-based forecasting models. To evaluate our approach, we construct a new multimodal dataset, MidEast-TE-mm, by extending an existing event dataset MidEast-TE-mini with images. Empirical studies demonstrate that our MM-Forecast can correctly identify the image functions, and further more, incorporating these verbal function descriptions significantly improves the forecasting performance. The dataset, code, and prompts are available at https://github.com/LuminosityX/MM-Forecast.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/af01a887c3cb3281eae5debf8f1c64aec2caa446" target='_blank'>
-              Deep learning for precipitation nowcasting: A survey from the perspective of time series forecasting
+          <td><a href="https://www.semanticscholar.org/paper/881bcfa9a1a54c64991dd08db8ba6dea916b5ef1" target='_blank'>
+              MM-Forecast: A Multimodal Approach to Temporal Event Forecasting with Large Language Models
               </a>
             </td>
           <td>
-            Sojung An, Tae-Jin Oh, Eunha Sohn, Donghyun Kim
+            Haoxuan Li, Zhengmao Yang, Yunshan Ma, Yi Bin, Yang Yang, Tat-Seng Chua
           </td>
-          <td>2024-06-07</td>
+          <td>2024-08-08</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>7</td>
         </tr>
 
-        <tr id="The Transformer architecture has significantly advanced deep learning, particularly in natural language processing, by effectively managing long-range dependencies. However, as the demand for understanding complex relationships grows, refining the Transformer's architecture becomes critical. This paper introduces Skip-Layer Attention (SLA) to enhance Transformer models by enabling direct attention between non-adjacent layers. This method improves the model's ability to capture dependencies between high-level abstract features and low-level details. By facilitating direct attention between these diverse feature levels, our approach overcomes the limitations of current Transformers, which often rely on suboptimal intra-layer attention. Our implementation extends the Transformer's functionality by enabling queries in a given layer to interact with keys and values from both the current layer and one preceding layer, thus enhancing the diversity of multi-head attention without additional computational burden. Extensive experiments demonstrate that our enhanced Transformer model achieves superior performance in language modeling tasks, highlighting the effectiveness of our skip-layer attention mechanism.">
+        <tr id="Message passing graph neural networks (GNNs) would appear to be powerful tools to learn distributed algorithms via gradient descent, but generate catastrophically incorrect predictions when nodes update asynchronously during inference. This failure under asynchrony effectively excludes these architectures from many potential applications, such as learning local communication policies between resource-constrained agents in, e.g., robotic swarms or sensor networks. In this work we explore why this failure occurs in common GNN architectures, and identify"implicitly-defined"GNNs as a class of architectures which is provably robust to partially asynchronous"hogwild"inference, adapting convergence guarantees from work in asynchronous and distributed optimization, e.g., Bertsekas (1982); Niu et al. (2011). We then propose a novel implicitly-defined GNN architecture, which we call an energy GNN. We show that this architecture outperforms other GNNs from this class on a variety of synthetic tasks inspired by multi-agent systems, and achieves competitive performance on real-world datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/937a377d5ac0f6a835b843615c5e94e71a34176e" target='_blank'>
-              Skip-Layer Attention: Bridging Abstract and Detailed Dependencies in Transformers
+          <td><a href="https://www.semanticscholar.org/paper/3d41f9e0bdc43fc19966e67aef4422bfb59a0315" target='_blank'>
+              Graph Neural Networks Gone Hogwild
               </a>
             </td>
           <td>
-            Qian Chen, Wen Wang, Qinglin Zhang, Siqi Zheng, Shiliang Zhang, Chong Deng, Hai Yu, Jiaqing Liu, Yukun Ma, Chong Zhang
+            Olga Solodova, Nick Richardson, Deniz Oktay, Ryan P. Adams
           </td>
-          <td>2024-06-17</td>
+          <td>2024-06-29</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>5</td>
         </tr>
 
-        <tr id="Accurate load forecasting is essential for maintaining the power balance between generators and consumers, especially with the increasing integration of renewable energy sources, which introduce significant intermittent volatility. With the development of data-driven methods, machine learning and deep learning-based models have become the predominant approach for load forecasting tasks. In recent years, pre-trained language models (PLMs) have made significant advancements, demonstrating superior performance in various fields. This paper proposes a load forecasting method based on PLMs, which offers not only accurate predictive ability but also general and flexible applicability. Additionally, a data modeling method is proposed to effectively transform load sequence data into natural language for PLM training. Furthermore, we introduce a data enhancement strategy that eliminate the impact of PLM hallucinations on forecasting results. The effectiveness of the proposed method has been validated on two real-world datasets. Compared with existing methods, our approach shows state-of-the-art performance across all validation metrics.">
+        <tr id="Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM).">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/01f84016326ad53ac67ec2299719090300765b73" target='_blank'>
-              LFPLM: A General and Flexible Load Forecasting Framework based on Pre-trained Language Model
+          <td><a href="https://www.semanticscholar.org/paper/c788a35c2dcda370161d8beda4525409126416c4" target='_blank'>
+              Parallelizing Autoregressive Generation with Variational State Space Models
               </a>
             </td>
           <td>
-            Mingyang Gao, Suyang Zhou, Wei Gu, Zhi Wu, Zijian Hu, Hong Zhu, Haiquan Liu
+            Gaspard Lambrechts, Yann Claes, Pierre Geurts, Damien Ernst
           </td>
-          <td>2024-06-17</td>
+          <td>2024-07-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>33</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Although traffic prediction has been receiving considerable attention with a number of successes in the context of intelligent transportation systems, the prediction of traffic states over a complex transportation network that contains different road types has remained a challenge. This study proposes a multi-scale graph wavelet temporal convolution network (MSGWTCN) to predict the traffic states in complex transportation networks. Specifically, a multi-scale spatial block is designed to simultaneously capture the spatial information at different levels, and the gated temporal convolution network is employed to extract the temporal dependencies of the data. The model jointly learns to mount multiple levels of the spatial interactions by stacking graph wavelets with different scales. Two real-world datasets are used in this study to investigate the model performance, including a highway network in Seattle and a dense road network of Manhattan in New York City. Experiment results show that the proposed model outperforms other baseline models. Furthermore, different scales of graph wavelets are found to be effective in extracting local, intermediate and global information at the same time and thus enable the model to learn a complex transportation network topology with various types of road segments. By carefully customizing the scales of wavelets, the model is able to improve the prediction performance and better adapt to different network configurations.">
+        <tr id="Modeling time series data has become a very at tractive research topic due to its wide application, such as human activity recognition, financial forecasting and sensor-based automatic system monitoring. Recently deep learning models have shown great advances in modeling the time series data but they heavily depend on a large amount of labeled data. To avoid costly labeling, this paper explores domain adaptation from a labeled source domain to the unlabeled target domain on time series data. To achieve the goal, we propose a disentangled representation learning framework named CADT to disentangle the domain-invariant features from the domain-specific ones. Particularly, CADT is injected with a novel class-wise hypersphere loss to improve the generalization of the classifier from the source domain to the target domain. Intuitively, it restricts the source data of the same class within the same hypersphere and minimizes the radius of it, which in turn enlarges the margin between different classes and makes the decision boundary of both domains easier. We further devise several kinds of domain-preserving data augmentation methods to better capture the domain-specific patterns. Extensive experiments on two public datasets and two real-world applications demonstrate the effectiveness of the proposed model against several state-of-the-art baselines.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4d5e11bf997ee82ceae16dc66b7c5ab1148908d6" target='_blank'>
-              Traffic Prediction considering Multiple Levels of Spatial-temporal Information: A Multi-scale Graph Wavelet-based Approach
+          <td><a href="https://www.semanticscholar.org/paper/a21870156817614d3af47fda7b03e99e6181a852" target='_blank'>
+              Disentangling Domain and General Representations for Time Series Classification
               </a>
             </td>
           <td>
-            Zilin Bian, Jingqin Gao, K. Ozbay, Zhenning Li
+            Youmin Chen, Xinyu Yan, Yang Yang, Jianfeng Zhang, Jing Zhang, Lujia Pan, Juren Li
           </td>
-          <td>2024-06-18</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>44</td>
+          <td>6</td>
         </tr>
 
-        <tr id="In accordance with the findings presented in [34], this study examines the applicability of Machine Learning (ML) models and training strategies from the Natural Language Processing (NLP) domain in addressing time series problems, emphasizing the structural and operational aspects of these models and strategies. Recognizing the structural congruence within the data, we opt for Stock Price Prediction (SPP) as the designated domain to assess the transferability of NLP models and strategies. Building upon initial positive outcomes derived from quantitative SPP models in our ongoing research endeavors, we provide a rationale for exploring a range of additional methods and conducting subsequent research experiments. The outlined research aims to elucidate the efficacy of leveraging NLP models and techniques for addressing time series problems exemplified as SPP.">
+        <tr id="Long-separated research has been conducted on two highly correlated tracks: traffic and incidents. Traffic track witnesses complicating deep learning models, e.g., to push the prediction a few percent more accurate, and the incident track only studies the incidents alone, e.g., to infer the incident risk. We, for the first time, spatiotemporally aligned the two tracks in a large-scale region (16,972 traffic nodes) over the whole year of 2023: our XTraffic dataset includes traffic, i.e., time-series indexes on traffic flow, lane occupancy, and average vehicle speed, and incidents, whose records are spatiotemporally-aligned with traffic data, with seven different incident classes. Additionally, each node includes detailed physical and policy-level meta-attributes of lanes. Our data can revolutionalize traditional traffic-related tasks towards higher interpretability and practice: instead of traditional prediction or classification tasks, we conduct: (1) post-incident traffic forecasting to quantify the impact of different incidents on traffic indexes; (2) incident classification using traffic indexes to determine the incidents types for precautions measures; (3) global causal analysis among the traffic indexes, meta-attributes, and incidents to give high-level guidance of the interrelations of various factors; (4) local causal analysis within road nodes to examine how different incidents affect the road segments' relations. The dataset is available at http://xaitraffic.github.io.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7c4f1f32caa4d520f1b1d66244227ab9df24a38e" target='_blank'>
-              Assessment of the Applicability of Large Language Models for Quantitative Stock Price Prediction
+          <td><a href="https://www.semanticscholar.org/paper/5b7ebd41f1ed8a8a78309e7df817ed2ca8c6f1fa" target='_blank'>
+              XTraffic: A Dataset Where Traffic Meets Incidents with Explainability and More
               </a>
             </td>
           <td>
-            Frederic Voigt, Kai von Luck, Peer Stelldinger
+            Xiaochuan Gou, Ziyue Li, Tian Lan, Junpeng Lin, Zhishuai Li, Bingyu Zhao, Chen Zhang, Di Wang, Xiangliang Zhang
           </td>
-          <td>2024-06-26</td>
-          <td>Proceedings of the 17th International Conference on PErvasive Technologies Related to Assistive Environments</td>
+          <td>2024-07-16</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>12</td>
+          <td>5</td>
         </tr>
 
-        <tr id="Many of today's data is time-series data originating from various sources, such as sensors, transaction systems, or production systems. Major challenges with such data include privacy and business sensitivity. Generative time-series models have the potential to overcome these problems, allowing representative synthetic data, such as people's movement in cities, to be shared openly and be used to the benefit of society at large. However, contemporary approaches are limited to prohibitively short sequences and small scales. Aside from major memory limitations, the models generate less accurate and less representative samples the longer the sequences are. This issue is further exacerbated by the lack of a comprehensive and accessible benchmark. Furthermore, a common need in practical applications is what-if analysis and dynamic adaptation to data distribution changes, for usage in decision making and to manage a changing world: What if this road is temporarily blocked or another road is added? The focus of this paper is on mobility data, such as people's movement in cities, requiring all these issues to be addressed. To this end, we propose a transformer-based diffusion model, TDDPM, for time-series which outperforms and scales substantially better than state-of-the-art. This is evaluated in a new comprehensive benchmark across several sequence lengths, standard datasets, and evaluation measures. We also demonstrate how the model can be conditioned on a prior over spatial occupancy frequency information, allowing the model to generate mobility data for previously unseen environments and for hypothetical scenarios where the underlying road network and its usage changes. This is evaluated by training on mobility data from part of a city. Then, using only aggregate spatial information as prior, we demonstrate out-of-distribution generalization to the unobserved remainder of the city.">
+        <tr id="In multivariate and multistep time series prediction research, we often face the problems of insufficient spatial feature extraction and insufficient time-dependent mining of historical series data, which also brings great challenges to multivariate time series analysis and prediction. Inspired by the attention mechanism and residual module, this study proposes a multivariate time series prediction method based on a convolutional-residual gated recurrent hybrid model (CNN-DA-RGRU) with a two-layer attention mechanism to solve the multivariate time series prediction problem in these two stages. Specifically, the convolution module of the proposed model is used to extract the relational features among the sequences, and the two-layer attention mechanism can pay more attention to the relevant variables and give them higher weights to eliminate the irrelevant features, while the residual gated loop module is used to extract the time-varying features of the sequences, in which the residual block is used to achieve the direct connectivity to enhance the expressive power of the model, to solve the gradient explosion and vanishing scenarios, and to facilitate gradient propagation. Experiments were conducted on two public datasets using the proposed model to determine the model hyperparameters, and ablation experiments were conducted to verify the effectiveness of the model; by comparing it with several models, the proposed model was found to achieve good results in multivariate time series-forecasting tasks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1d7a486a59e6327be349015918f17ee84f6c4776" target='_blank'>
-              Deep Temporal Deaggregation: Large-Scale Spatio-Temporal Generative Models
+          <td><a href="https://www.semanticscholar.org/paper/5b50ae3b720af720b3168b475e54d37b97e5e669" target='_blank'>
+              A Multivariate Time Series Prediction Method Based on Convolution-Residual Gated Recurrent Neural Network and Double-Layer Attention
               </a>
             </td>
           <td>
-            David Bergstrom, Mattias Tiger, Fredrik Heintz
+            Chuxin Cao, Jianhong Huang, Man Wu, Zhizhe Lin, Yan Sun
           </td>
-          <td>2024-06-18</td>
-          <td>ArXiv</td>
+          <td>2024-07-18</td>
+          <td>Electronics</td>
           <td>0</td>
           <td>6</td>
         </tr>
 
-        <tr id="Knowledge tracing (KT) is the task of predicting students' future performance based on their historical learning interaction data. With the rapid advancement of attention mechanisms, many attention based KT models are developed. However, existing attention based KT models exhibit performance drops as the number of student interactions increases beyond the number of interactions on which the KT models are trained. We refer to this as the length generalization of KT model. In this paper, we propose stableKT to enhance length generalization that is able to learn from short sequences and maintain high prediction performance when generalizing on long sequences. Furthermore, we design a multi-head aggregation module to capture the complex relationships between questions and the corresponding knowledge components (KCs) by combining dot-product attention and hyperbolic attention. Experimental results on three public educational datasets show that our model exhibits robust capability of length generalization and outperforms all baseline models in terms of AUC. To encourage reproducible research, we make our data and code publicly available at https://pykt.org.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2ac13d53e452e6d6c24a6176c6fbeac0846ac5a0" target='_blank'>
-              Enhancing Length Generalization for Attention Based Knowledge Tracing Models with Linear Biases
+          <td><a href="https://www.semanticscholar.org/paper/debe0ee50d9dc6388d2e21ad87cbf672e2865ff3" target='_blank'>
+              Randomnet: clustering time series using untrained deep neural networks
               </a>
             </td>
           <td>
-            Xueyi Li, Youheng Bai, Teng Guo, Zitao Liu, Yaying Huang, Xiangyu Zhao, Feng Xia, Weiqi Luo, Jian Weng
+            Xiaosheng Li, Wenjie Xi, Jessica Lin
           </td>
-          <td>2024-08-01</td>
-          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
+          <td>2024-06-22</td>
+          <td>Data Mining and Knowledge Discovery</td>
           <td>0</td>
-          <td>1</td>
+          <td>5</td>
         </tr>
 
-        <tr id="Real-world data generation often involves certain geometries (e.g., graphs) that induce instance-level interdependence. This characteristic makes the generalization of learning models more difficult due to the intricate interdependent patterns that impact data-generative distributions and can vary from training to testing. In this work, we propose a geometric diffusion model with learnable divergence fields for the challenging generalization problem with interdependent data. We generalize the diffusion equation with stochastic diffusivity at each time step, which aims to capture the multi-faceted information flows among interdependent data. Furthermore, we derive a new learning objective through causal inference, which can guide the model to learn generalizable patterns of interdependence that are insensitive across domains. Regarding practical implementation, we introduce three model instantiations that can be considered as the generalized versions of GCN, GAT, and Transformers, respectively, which possess advanced robustness against distribution shifts. We demonstrate their promising efficacy for out-of-distribution generalization on diverse real-world datasets.">
+        <tr id="
+ Traffic forecasting problems involve jointly modeling the non-linear spatio-temporal dependencies at different scales. While Graph Neural Network models have been effectively used to capture the non-linear spatial dependencies, capturing the dynamic spatial dependencies between the locations remains a major challenge. The errors in capturing such dependencies propagate in modeling the temporal dependencies between the locations, thereby severely affecting the performance of long-term predictions. While transformer-based mechanisms have been recently proposed for capturing the dynamic spatial dependencies, these methods are susceptible to fluctuations in data brought on by unforeseen events like traffic congestion and accidents. To mitigate these issues we propose an improvised Spatio-temporal parallel transformer (STPT) based model for traffic prediction that uses multiple adjacency graphs passed through a pair of coupled graph transformer-convolution network units, operating in parallel, to generate more noise-resilient embeddings. We conduct extensive experiments on 4 real-world traffic datasets and compare the performance of STPT with several state-of-the-art baselines, in terms of measures like RMSE, MAE, and MAPE. We find that using STPT improves the performance by around
+
+ \(10-34\%\)
+
+ as compared to the baselines. We also investigate the applicability of the model on other spatio-temporal data in other domains. We use a covid-19 dataset to predict the number of future occurrences in different regions from a given set of historical occurrences. The results demonstrate the superiority of our model for such datasets.
+">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7666eb9e80743f9c6338661320051e51f14d92df" target='_blank'>
-              Learning Divergence Fields for Shift-Robust Graph Representations
+          <td><a href="https://www.semanticscholar.org/paper/d890dbf3502df2b73e7403abca6b1585a2a7bdd4" target='_blank'>
+              Spatio-Temporal Parallel Transformer based model for Traffic Prediction
               </a>
             </td>
           <td>
-            Qitian Wu, Fan Nie, Chenxiao Yang, Junchi Yan
+            Rahul Kumar, João Mendes‐Moreira, Joydeep Chandra
           </td>
-          <td>2024-06-07</td>
-          <td>ArXiv</td>
+          <td>2024-07-19</td>
+          <td>ACM Transactions on Knowledge Discovery from Data</td>
           <td>0</td>
-          <td>17</td>
+          <td>5</td>
         </tr>
 
-        <tr id="To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that unobserved variables can be recovered from the history of only a handful of observed variables. To test whether language models are effectively constructing delay embeddings, we measure the capacities of sequence models to reconstruct unobserved dynamics. We trained 1-layer transformer decoders and state-space sequence models on next-step prediction from noisy, partially-observed time series data. We found that each sequence layer can learn a viable embedding of the underlying system. However, state-space models have a stronger inductive bias than transformers-in particular, they more effectively reconstruct unobserved information at initialization, leading to more parameter-efficient models and lower error on dynamics tasks. Our work thus forges a novel connection between dynamical systems and deep learning sequence models via delay embedding theory.">
+        <tr id="Large Language Models (LLMs) have been shown to perform well for many downstream tasks. Transfer learning can enable LLMs to acquire skills that were not targeted during pre-training. In financial contexts, LLMs can sometimes beat well-established benchmarks. This paper investigates how well LLMs perform in the task of forecasting corporate credit ratings. We show that while LLMs are very good at encoding textual information, traditional methods are still very competitive when it comes to encoding numeric and multimodal data. For our task, current LLMs perform worse than a more traditional XGBoost architecture that combines fundamental and macroeconomic data with high-density text-based embedding features.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/de9997857d06f20ea1332b1569e9abd7f837abca" target='_blank'>
-              Delay Embedding Theory of Neural Sequence Models
+          <td><a href="https://www.semanticscholar.org/paper/95e12933c0081864ec2a7b4cc64d936843bb0493" target='_blank'>
+              Traditional Methods Outperform Generative LLMs at Forecasting Credit Ratings
               </a>
             </td>
           <td>
-            Mitchell Ostrow, Adam J. Eisen, I. Fiete
+            Felix Drinkall, J. Pierrehumbert, Stefan Zohren
           </td>
-          <td>2024-06-17</td>
+          <td>2024-07-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>30</td>
+          <td>45</td>
         </tr>
 
-        <tr id="Rethink convolution-based graph neural networks (GNN) -- they characteristically suffer from limited expressiveness, over-smoothing, and over-squashing, and require specialized sparse kernels for efficient computation. Here, we design a simple graph learning module entirely free of convolution operators, coined \textit{random walk with unifying memory} (RUM) neural network, where an RNN merges the topological and semantic graph features along the random walks terminating at each node. Relating the rich literature on RNN behavior and graph topology, we theoretically show and experimentally verify that RUM attenuates the aforementioned symptoms and is more expressive than the Weisfeiler-Lehman (WL) isomorphism test. On a variety of node- and graph-level classification and regression tasks, RUM not only achieves competitive performance, but is also robust, memory-efficient, scalable, and faster than the simplest convolutional GNNs.">
+        <tr id=": Sales forecasting is crucial for business planning and resource allocation. Data-driven approaches have become popular in this field. This study compares the performance of three forecasting models: Autoregressive Integrated Moving Average (ARIMA), Long Short-Term Memory (LSTM) and Prophet within the context of specific sales categories derived from acquiring data provided by a bank. This study uses a time series dataset provided by Tink off data, which covers various sales categories and time intervals. These categories, including pharmacies, railway tickets, books, sporting goods and fuel stations, present unique forecasting challenges because of their distinct demand patterns and potential for high volatility. Through a comparative analysis focusing on accuracy, robustness and computational efficiency, the study reveals that while all models demonstrate efficacy in certain scenarios, their performance varies depending on the specific category and forecasting horizon. ARIMA exhibits consistent accuracy across categories, particularly for daily predictions, aligning with its strength in capturing trends and seasonality. LSTM, on the other hand, shows promise for hourly predictions in categories like fuel stations, leveraging its ability to learn long-term dependencies. However, the LSTM model shows inconsistent results, sometimes outperforming others, but with varying performance across runs. This study provides insights for practitioners within the banking and financial sectors seeking to select the most appropriate forecasting model based on their specific sales categories and forecasting needs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9b451516b9432318d81aef2a5bdc0135d2285a5d" target='_blank'>
-              Non-convolutional Graph Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/d18133f1dde33c5c7df061aac195fad8e9eac107" target='_blank'>
+              Sales Forecasting Models: Comparison between ARIMA, LSTM and Prophet
               </a>
             </td>
           <td>
-            Yuanqing Wang, Kyunghyun Cho
+            Dmitry Brykin
           </td>
-          <td>2024-07-31</td>
-          <td>ArXiv</td>
+          <td>2024-10-01</td>
+          <td>Journal of Computer Science</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="We introduce NodeFlow, a flexible framework for probabilistic regression on tabular data that combines Neural Oblivious Decision Ensembles (NODEs) and Conditional Continuous Normalizing Flows (CNFs). It offers improved modeling capabilities for arbitrary probabilistic distributions, addressing the limitations of traditional parametric approaches. In NodeFlow, the NODE captures complex relationships in tabular data through a tree-like structure, while the conditional CNF utilizes the NODE’s output space as a conditioning factor. The training process of NodeFlow employs standard gradient-based learning, facilitating the end-to-end optimization of the NODEs and CNF-based density estimation. This approach ensures outstanding performance, ease of implementation, and scalability, making NodeFlow an appealing choice for practitioners and researchers. Comprehensive assessments on benchmark datasets underscore NodeFlow’s efficacy, revealing its achievement of state-of-the-art outcomes in multivariate probabilistic regression setup and its strong performance in univariate regression tasks. Furthermore, ablation studies are conducted to justify the design choices of NodeFlow. In conclusion, NodeFlow’s end-to-end training process and strong performance make it a compelling solution for practitioners and researchers. Additionally, it opens new avenues for research and application in the field of probabilistic regression on tabular data.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7b7ef3bf708e12014b3094d7f3efb36a9d8eb2f4" target='_blank'>
-              NodeFlow: Towards End-to-End Flexible Probabilistic Regression on Tabular Data
+          <td><a href="https://www.semanticscholar.org/paper/f5525624998a69eda4aa0ec2d507973f15dabde2" target='_blank'>
+              SeeMore: a spatiotemporal predictive model with bidirectional distillation and level-specific meta-adaptation
               </a>
             </td>
           <td>
-            Patryk Wielopolski, Oleksii Furman, Maciej Zięba
+            Yuqing Ma, Wei Liu, Yajun Gao, Yang Yuan, Shihao Bai, Haotong Qin, Xianglong Liu
           </td>
-          <td>2024-07-01</td>
-          <td>Entropy</td>
+          <td>2024-07-22</td>
+          <td>Science China Information Sciences</td>
           <td>0</td>
-          <td>2</td>
+          <td>15</td>
         </tr>
 
-        <tr id="We present a conformal prediction method for time series using the Transformer architecture to capture long-memory and long-range dependencies. Specifically, we use the Transformer decoder as a conditional quantile estimator to predict the quantiles of prediction residuals, which are used to estimate the prediction interval. We hypothesize that the Transformer decoder benefits the estimation of the prediction interval by learning temporal dependencies across past prediction residuals. Our comprehensive experiments using simulated and real data empirically demonstrate the superiority of the proposed method compared to the existing state-of-the-art conformal prediction methods.">
+        <tr id="Accurate stock market predictions following earnings reports are crucial for investors. Traditional methods, particularly classical machine learning models, struggle with these predictions because they cannot effectively process and interpret extensive textual data contained in earnings reports and often overlook nuances that influence market movements. This paper introduces an advanced approach by employing Large Language Models (LLMs) instruction fine-tuned with a novel combination of instruction-based techniques and quantized low-rank adaptation (QLoRA) compression. Our methodology integrates 'base factors', such as financial metric growth and earnings transcripts, with 'external factors', including recent market indices performances and analyst grades, to create a rich, supervised dataset. This comprehensive dataset enables our models to achieve superior predictive performance in terms of accuracy, weighted F1, and Matthews correlation coefficient (MCC), especially evident in the comparison with benchmarks such as GPT-4. We specifically highlight the efficacy of the llama-3-8b-Instruct-4bit model, which showcases significant improvements over baseline models. The paper also discusses the potential of expanding the output capabilities to include a 'Hold' option and extending the prediction horizon, aiming to accommodate various investment styles and time frames. This study not only demonstrates the power of integrating cutting-edge AI with fine-tuned financial data but also paves the way for future research in enhancing AI-driven financial analysis tools.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c3a2546319ca34e4f2d616bbc95db8ca3452d022" target='_blank'>
-              Transformer Conformal Prediction for Time Series
+          <td><a href="https://www.semanticscholar.org/paper/31e6b91ed8eb6f5fe8703301fc439fd1af160132" target='_blank'>
+              Harnessing Earnings Reports for Stock Predictions: A QLoRA-Enhanced LLM Approach
               </a>
             </td>
           <td>
-            Junghwan Lee, Chen Xu, Yao Xie
+            Haowei Ni, Shuchen Meng, Xupeng Chen, Ziqing Zhao, Andi Chen, Panfeng Li, Shiyao Zhang, Qifu Yin, Yuanqing Wang, Yuxi Chan
           </td>
-          <td>2024-06-08</td>
+          <td>2024-08-13</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>7</td>
         </tr>
 
-        <tr id="Recently, Large Language Models (LLMs) have attracted significant attention for their exceptional performance across a broad range of tasks, particularly in text analysis. However, the finance sector presents a distinct challenge due to its dependence on time-series data for complex forecasting tasks. In this study, we introduce a novel framework called LLMFactor, which employs Sequential Knowledge-Guided Prompting (SKGP) to identify factors that influence stock movements using LLMs. Unlike previous methods that relied on keyphrases or sentiment analysis, this approach focuses on extracting factors more directly related to stock market dynamics, providing clear explanations for complex temporal changes. Our framework directs the LLMs to create background knowledge through a fill-in-the-blank strategy and then discerns potential factors affecting stock prices from related news. Guided by background knowledge and identified factors, we leverage historical stock prices in textual format to predict stock movement. An extensive evaluation of the LLMFactor framework across four benchmark datasets from both the U.S. and Chinese stock markets demonstrates its superiority over existing state-of-the-art methods and its effectiveness in financial time-series forecasting.">
+        <tr id="Distribution shift over time occurs in many settings. Leveraging historical data is necessary to learn a model for the last time point when limited data is available in the final period, yet few methods have been developed specifically for this purpose. In this work, we construct a benchmark with different sequences of synthetic shifts to evaluate the effectiveness of 3 classes of methods that 1) learn from all data without adapting to the final period, 2) learn from historical data with no regard to the sequential nature and then adapt to the final period, and 3) leverage the sequential nature of historical data when tailoring a model to the final period. We call this benchmark Seq-to-Final to highlight the focus on using a sequence of time periods to learn a model for the final time point. Our synthetic benchmark allows users to construct sequences with different types of shift and compare different methods. We focus on image classification tasks using CIFAR-10 and CIFAR-100 as the base images for the synthetic sequences. We also evaluate the same methods on the Portraits dataset to explore the relevance to real-world shifts over time. Finally, we create a visualization to contrast the initializations and updates from different methods at the final time step. Our results suggest that, for the sequences in our benchmark, methods that disregard the sequential structure and adapt to the final time point tend to perform well. The approaches we evaluate that leverage the sequential nature do not offer any improvement. We hope that this benchmark will inspire the development of new algorithms that are better at leveraging sequential historical data or a deeper understanding of why methods that disregard the sequential nature are able to perform well.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7185f24f33de547954baa0c71cafaf41786e81ba" target='_blank'>
-              LLMFactor: Extracting Profitable Factors through Prompts for Explainable Stock Movement Prediction
+          <td><a href="https://www.semanticscholar.org/paper/dff5247f9c46cb7745eb5c8b20a4225f15cd7d8a" target='_blank'>
+              Seq-to-Final: A Benchmark for Tuning from Sequential Distributions to a Final Time Point
               </a>
             </td>
           <td>
-            Meiyun Wang, Kiyoshi Izumi, Hiroki Sakaji
+            Christina X. Ji, Ahmed M. Alaa, David Sontag
           </td>
-          <td>2024-06-16</td>
+          <td>2024-07-12</td>
           <td>ArXiv</td>
-          <td>1</td>
-          <td>12</td>
+          <td>0</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Large Language Models (LLMs) have demonstrated remarkable performance across various natural language processing tasks. Recently, several LLMs-based pipelines have been developed to enhance learning on graphs with text attributes, showcasing promising performance. However, graphs are well-known to be susceptible to adversarial attacks and it remains unclear whether LLMs exhibit robustness in learning on graphs. To address this gap, our work aims to explore the potential of LLMs in the context of adversarial attacks on graphs. Specifically, we investigate the robustness against graph structural and textual perturbations in terms of two dimensions: LLMs-as-Enhancers and LLMs-as-Predictors. Through extensive experiments, we find that, compared to shallow models, both LLMs-as-Enhancers and LLMs-as-Predictors offer superior robustness against structural and textual attacks.Based on these findings, we carried out additional analyses to investigate the underlying causes. Furthermore, we have made our benchmark library openly available to facilitate quick and fair evaluations, and to encourage ongoing innovative research in this field.">
+        <tr id="In the rapidly evolving field of real estate economics, the prediction of house prices continues to be a complex challenge, intricately tied to a multitude of socio-economic factors. Traditional predictive models often overlook spatial interdependencies that significantly influence housing prices. The objective of this study is to leverage Graph Neural Networks (GNNs) on open statistics knowledge graphs to model these spatial dependencies and predict house prices across Scotland’s 2011 data zones. The methodology involves retrieving integrated statistical indicators from the official Scottish Open Government Data portal and applying three representative GNN algorithms: ChebNet, GCN, and GraphSAGE. These GNNs are compared against traditional models, including the tabular-based XGBoost and a simple Multi-Layer Perceptron (MLP), demonstrating superior prediction accuracy. Innovative contributions of this study include the use of GNNs to model spatial dependencies in real estate economics and the application of local and global explainability techniques to enhance transparency and trust in the predictions. The global feature importance is determined by a logistic regression surrogate model while the local, region-level understanding of the GNN predictions is achieved through the use of GNNExplainer. Explainability results are compared with those from a previous work that applied the XGBoost machine learning algorithm and the SHapley Additive exPlanations (SHAP) explainability framework on the same dataset. Interestingly, both the global surrogate model and the SHAP approach underscored the comparative illness factor, a health indicator, and the ratio of detached dwellings as the most crucial features in the global explainability. In the case of local explanations, while both methods showed similar results, the GNN approach provided a richer, more comprehensive understanding of the predictions for two specific data zones.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5fcfc60e2fdcf84c747a9b011282f20a7cd3fdfc" target='_blank'>
-              Learning on Graphs with Large Language Models(LLMs): A Deep Dive into Model Robustness
+          <td><a href="https://www.semanticscholar.org/paper/615cab34abada51059e7bf812011aa18b664bad3" target='_blank'>
+              Explainable Graph Neural Networks: An Application to Open Statistics Knowledge Graphs for Estimating House Prices
               </a>
             </td>
           <td>
-            Kai Guo, Zewen Liu, Zhikai Chen, Hongzhi Wen, Wei Jin, Jiliang Tang, Yi Chang
+            Areti Karamanou, Petros Brimos, E. Kalampokis, K. Tarabanis
           </td>
-          <td>2024-07-16</td>
-          <td>ArXiv</td>
+          <td>2024-08-06</td>
+          <td>Technologies</td>
           <td>0</td>
-          <td>21</td>
+          <td>36</td>
         </tr>
 
-        <tr id="Large Generative Models (LGMs) such as GPT, Stable Diffusion, Sora, and Suno are trained on a huge amount of language corpus, images, videos, and audio that are extremely diverse from numerous domains. This training paradigm over diverse well-curated data lies at the heart of generating creative and sensible content. However, all previous graph generative models (e.g., GraphRNN, MDVAE, MoFlow, GDSS, and DiGress) have been trained only on one dataset each time, which cannot replicate the revolutionary success achieved by LGMs in other fields. To remedy this crucial gap, we propose a new class of graph generative model called Large Graph Generative Model (LGGM) that is trained on a large corpus of graphs (over 5000 graphs) from 13 different domains. We empirically demonstrate that the pre-trained LGGM has superior zero-shot generative capability to existing graph generative models. Furthermore, our pre-trained LGGM can be easily fine-tuned with graphs from target domains and demonstrate even better performance than those directly trained from scratch, behaving as a solid starting point for real-world customization. Inspired by Stable Diffusion, we further equip LGGM with the capability to generate graphs given text prompts (Text-to-Graph), such as the description of the network name and domain (i.e.,"The power-1138-bus graph represents a network of buses in a power distribution system."), and network statistics (i.e.,"The graph has a low average degree, suitable for modeling social media interactions."). This Text-to-Graph capability integrates the extensive world knowledge in the underlying language model, offering users fine-grained control of the generated graphs. We release the code, the model checkpoint, and the datasets at https://lggm-lg.github.io/.">
+        <tr id="Multivariate time series modeling has been essential in sensor-based data mining tasks. However, capturing complex dynamics caused by intra-variable (temporal) and inter-variable (spatial) relationships while simultaneously taking into account evolving data distributions is a non-trivial task, which faces accumulated computational overhead and multiple temporal patterns or distribution modes. Most existing methods focus on the former direction without adaptive task-specific learning ability. To this end, we developed a holistic spatial-temporal meta-learning probabilistic inference framework, entitled ST-MeLaPI, for the efficient and versatile learning of complex dynamics. Specifically, first, a multivariate relationship recognition module is utilized to learn task-specific inter-variable dependencies. Then, a multiview meta-learning and probabilistic inference strategy was designed to learn shared parameters while enabling the fast and flexible learning of task-specific parameters for different batches. At the core are spatial dependency-oriented and temporal pattern-oriented meta-learning approximate probabilistic inference modules, which can quickly adapt to changing environments via stochastic neurons at each timestamp. Finally, a gated aggregation scheme is leveraged to realize appropriate information selection for the generative style prediction. We benchmarked our approach against state-of-the-art methods with real-world data. The experimental results demonstrate the superiority of our approach over the baselines.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/27cc05d2ad2f48123db8fb6b38690862b34ac75c" target='_blank'>
-              Large Generative Graph Models
+          <td><a href="https://www.semanticscholar.org/paper/4dea55e0f4c4c2f82b1128047a54ec3d4fccaa7f" target='_blank'>
+              Multiview Spatial-Temporal Meta-Learning for Multivariate Time Series Forecasting
               </a>
             </td>
           <td>
-            Yu Wang, Ryan Rossi, Namyong Park, Huiyuan Chen, Nesreen K. Ahmed, Puja Trivedi, Franck Dernoncourt, Danai Koutra, Tyler Derr
+            Liang Zhang, Jianping Zhu, Bo Jin, Xiaopeng Wei
           </td>
-          <td>2024-06-07</td>
-          <td>ArXiv</td>
+          <td>2024-07-01</td>
+          <td>Sensors (Basel, Switzerland)</td>
           <td>0</td>
-          <td>36</td>
+          <td>8</td>
         </tr>
 
-        <tr id="With the recent advancements in graph neural networks (GNNs), spectral GNNs have received increasing popularity by virtue of their specialty in capturing graph signals in the frequency domain, demonstrating promising capability in specific tasks. However, few systematic studies have been conducted on assessing their spectral characteristics. This emerging family of models also varies in terms of designs and settings, leading to difficulties in comparing their performance and deciding on the suitable model for specific scenarios, especially for large-scale tasks. In this work, we extensively benchmark spectral GNNs with a focus on the frequency perspective. We analyze and categorize over 30 GNNs with 27 corresponding filters. Then, we implement these spectral models under a unified framework with dedicated graph computations and efficient training schemes. Thorough experiments are conducted on the spectral models with inclusive metrics on effectiveness and efficiency, offering practical guidelines on evaluating and selecting spectral GNNs with desirable performance. Our implementation enables application on larger graphs with comparable performance and less overhead, which is available at: https://github.com/gdmnl/Spectral-GNN-Benchmark.">
+        <tr id="Conformal prediction offers a practical framework for distribution-free uncertainty quantification, providing finite-sample coverage guarantees under relatively mild assumptions on data exchangeability. However, these assumptions cease to hold for time series due to their temporally correlated nature. In this work, we present a novel use of conformal prediction for time series forecasting that incorporates time series decomposition. This approach allows us to model different temporal components individually. By applying specific conformal algorithms to each component and then merging the obtained prediction intervals, we customize our methods to account for the different exchangeability regimes underlying each component. Our decomposition-based approach is thoroughly discussed and empirically evaluated on synthetic and real-world data. We find that the method provides promising results on well-structured time series, but can be limited by factors such as the decomposition step for more complex data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2d1fb9cc0fea3df724772a0837dbb92a01f2ce67" target='_blank'>
-              Benchmarking Spectral Graph Neural Networks: A Comprehensive Study on Effectiveness and Efficiency
+          <td><a href="https://www.semanticscholar.org/paper/378cd3711a8103879551b49650e1ffcd928c112a" target='_blank'>
+              Conformal time series decomposition with component-wise exchangeability
               </a>
             </td>
           <td>
-            Ningyi Liao, Haoyu Liu, Zulun Zhu, Siqiang Luo, L. Lakshmanan
+            Derck W. E. Prinzhorn, Thijmen Nijdam, Putri A. van der Linden, Alexander Timans
           </td>
-          <td>2024-06-14</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>69</td>
+          <td>0</td>
         </tr>
 
-        <tr id="In this study, we delve into the Structured State Space Model (S4), Change Point Detection methodologies, and the Switching Non-linear Dynamics System (SNLDS). Our central proposition is an enhanced inference technique and long-range dependency method for SNLDS. The cornerstone of our approach is the fusion of S4 and SNLDS, leveraging the strengths of both models to effectively address the intricacies of long-range dependencies in switching time series. Through rigorous testing, we demonstrate that our proposed methodology adeptly segments and reproduces long-range dependencies in both the 1-D Lorenz dataset and the 2-D bouncing ball dataset. Notably, our integrated approach outperforms the standalone SNLDS in these tasks.">
+        <tr id="Summarizing web graphs is challenging due to the heterogeneity of the modeled information and its changes over time. We investigate the use of neural networks for lifelong graph summarization. Assuming we observe the web graph at a certain time, we train the networks to summarize graph vertices. We apply this trained network to summarize the vertices of the changed graph at the next point in time. Subsequently, we continue training and evaluating the network to perform lifelong graph summarization. We use the GNNs Graph-MLP and GraphSAINT, as well as an MLP baseline, to summarize the temporal graphs. We compare $1$-hop and $2$-hop summaries. We investigate the impact of reusing parameters from a previous snapshot by measuring the backward and forward transfer and the forgetting rate of the neural networks. Our extensive experiments on ten weekly snapshots of a web graph with over $100$M edges, sampled in 2012 and 2022, show that all networks predominantly use $1$-hop information to determine the summary, even when performing $2$-hop summarization. Due to the heterogeneity of web graphs, in some snapshots, the $2$-hop summary produces over ten times more vertex summaries than the $1$-hop summary. When using the network trained on the last snapshot from 2012 and applying it to the first snapshot of 2022, we observe a strong drop in accuracy. We attribute this drop over the ten-year time warp to the strongly increased heterogeneity of the web graph in 2022.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/737fccae30a52b719925aa3bdefbccf7758f66f5" target='_blank'>
-              Long Range Switching Time Series Prediction via State Space Model
+          <td><a href="https://www.semanticscholar.org/paper/39a9e812343d7550486a8b525adf2fcc87cd162e" target='_blank'>
+              Lifelong Graph Summarization with Neural Networks: 2012, 2022, and a Time Warp
               </a>
             </td>
           <td>
-            Jiaming Zhang, Yang Ding, Yunfeng Gao
+            Jonatan Frank, Marcel Hoffmann, N. Lell, David Richerby, A. Scherp
           </td>
-          <td>2024-07-27</td>
+          <td>2024-07-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>28</td>
         </tr>
 
-        <tr id="Interpretable graph neural networks (XGNNs ) are widely adopted in various scientific applications involving graph-structured data. Existing XGNNs predominantly adopt the attention-based mechanism to learn edge or node importance for extracting and making predictions with the interpretable subgraph. However, the representational properties and limitations of these methods remain inadequately explored. In this work, we present a theoretical framework that formulates interpretable subgraph learning with the multilinear extension of the subgraph distribution, coined as subgraph multilinear extension (SubMT). Extracting the desired interpretable subgraph requires an accurate approximation of SubMT, yet we find that the existing XGNNs can have a huge gap in fitting SubMT. Consequently, the SubMT approximation failure will lead to the degenerated interpretability of the extracted subgraphs. To mitigate the issue, we design a new XGNN architecture called Graph Multilinear neT (GMT), which is provably more powerful in approximating SubMT. We empirically validate our theoretical findings on a number of graph classification benchmarks. The results demonstrate that GMT outperforms the state-of-the-art up to 10% in terms of both interpretability and generalizability across 12 regular and geometric graph benchmarks.">
+        <tr id="We explore various neural network architectures for modeling the dynamics of the cryptocurrency market. Traditional linear models often fall short in accurately capturing the unique and complex dynamics of this market. In contrast, Deep Neural Networks (DNNs) have demonstrated considerable proficiency in time series forecasting. This papers introduces novel neural network framework that blend the principles of econometric state space models with the dynamic capabilities of Recurrent Neural Networks (RNNs). We propose state space models using Long Short Term Memory (LSTM), Gated Residual Units (GRU) and Temporal Kolmogorov-Arnold Networks (TKANs). According to the results, TKANs, inspired by Kolmogorov-Arnold Networks (KANs) and LSTM, demonstrate promising outcomes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/854342cf063eef4428a5441c8d317dfbabb8117f" target='_blank'>
-              How Interpretable Are Interpretable Graph Neural Networks?
+          <td><a href="https://www.semanticscholar.org/paper/f2be9285dd976d1dd4c063f13369b73af652e881" target='_blank'>
+              Deep State Space Recurrent Neural Networks for Time Series Forecasting
               </a>
             </td>
           <td>
-            Yongqiang Chen, Yatao Bian, Bo Han, James Cheng
+            Hugo Inzirillo
           </td>
-          <td>2024-06-12</td>
+          <td>2024-07-21</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>9</td>
+          <td>1</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Tabular datasets play a crucial role in various applications. Thus, developing efficient, effective, and widely compatible prediction algorithms for tabular data is important. Currently, two prominent model types, Gradient Boosted Decision Trees (GBDTs) and Deep Neural Networks (DNNs), have demonstrated performance advantages on distinct tabular prediction tasks. However, selecting an effective model for a specific tabular dataset is challenging, often demanding time-consuming hyperparameter tuning. To address this model selection dilemma, this paper proposes a new framework that amalgamates the advantages of both GBDTs and DNNs, resulting in a DNN algorithm that is as efficient as GBDTs and is competitively effective regardless of dataset preferences for GBDTs or DNNs. Our idea is rooted in an observation that deep learning (DL) offers a larger parameter space that can represent a well-performing GBDT model, yet the current back-propagation optimizer struggles to efficiently discover such optimal functionality. On the other hand, during GBDT development, hard tree pruning, entropy-driven feature gate, and model ensemble have proved to be more adaptable to tabular data. By combining these key components, we present a Tree-hybrid simple MLP (T-MLP). In our framework, a tensorized, rapidly trained GBDT feature gate, a DNN architecture pruning approach, as well as a vanilla back-propagation optimizer collaboratively train a randomly initialized MLP model. Comprehensive experiments show that T-MLP is competitive with extensively tuned DNNs and GBDTs in their dominating tabular benchmarks (88 datasets) respectively, all achieved with compact model storage and significantly reduced training duration.">
+        <tr id="Despite the massive attention given to time-series explanations due to their extensive applications, a notable limitation in existing approaches is their primary reliance on the time-domain. This overlooks the inherent characteristic of time-series data containing both time and frequency features. In this work, we present Spectral eXplanation (SpectralX), an XAI framework that provides time-frequency explanations for time-series black-box classifiers. This easily adaptable framework enables users to"plug-in"various perturbation-based XAI methods for any pre-trained time-series classification models to assess their impact on the explanation quality without having to modify the framework architecture. Additionally, we introduce Feature Importance Approximations (FIA), a new perturbation-based XAI method. These methods consist of feature insertion, deletion, and combination techniques to enhance computational efficiency and class-specific explanations in time-series classification tasks. We conduct extensive experiments in the generated synthetic dataset and various UCR Time-Series datasets to first compare the explanation performance of FIA and other existing perturbation-based XAI methods in both time-domain and time-frequency domain, and then show the superiority of our FIA in the time-frequency domain with the SpectralX framework. Finally, we conduct a user study to confirm the practicality of our FIA in SpectralX framework for class-specific time-frequency based time-series explanations. The source code is available in https://github.com/gustmd0121/Time_is_not_Enough">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c5f1d024ab3cc368985e609fc2cebead734ba141" target='_blank'>
-              Team up GBDTs and DNNs: Advancing Efficient and Effective Tabular Prediction with Tree-hybrid MLPs
+          <td><a href="https://www.semanticscholar.org/paper/a9a442393d869ce8529cda8dfa179e2d54425503" target='_blank'>
+              Time is Not Enough: Time-Frequency based Explanation for Time-Series Black-Box Models
               </a>
             </td>
           <td>
-            Jiahuan Yan, Jintai Chen, Qianxing Wang, D. Chen, Jian Wu
+            Hyunseung Chung, Sumin Jo, Yeonsu Kwon, Edward Choi
           </td>
-          <td>2024-07-13</td>
+          <td>2024-08-07</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>14</td>
+          <td>4</td>
         </tr>
 
-        <tr id="The prediction of time series is a challenging task relevant in such diverse applications as analyzing financial data, forecasting flow dynamics or understanding biological processes. Especially chaotic time series that depend on a long history pose an exceptionally difficult problem. While machine learning has shown to be a promising approach for predicting such time series, it either demands long training time and much training data when using deep recurrent neural networks. Alternative, when using a reservoir computing approach it comes with high uncertainty and typically a high number of random initializations and extensive hyper-parameter tuning when using a reservoir computing approach. In this paper, we focus on the reservoir computing approach and propose a new mapping of input data into the reservoir's state space. Furthermore, we incorporate this method in two novel network architectures increasing parallelizability, depth and predictive capabilities of the neural network while reducing the dependence on randomness. For the evaluation, we approximate a set of time series from the Mackey-Glass equation, inhabiting non-chaotic as well as chaotic behavior and compare our approaches in regard to their predictive capabilities to echo state networks and gated recurrent units. For the chaotic time series, we observe an error reduction of up to $85.45\%$ and up to $87.90\%$ in contrast to echo state networks and gated recurrent units respectively. Furthermore, we also observe tremendous improvements for non-chaotic time series of up to $99.99\%$ in contrast to existing approaches.">
+        <tr id="Dynamic graphs (DG) are often used to describe evolving interactions between nodes in real-world applications. Temporal patterns are a natural feature of DGs and are also key to representation learning. However, existing dynamic GCN models are mostly composed of static GCNs and sequence modules, which results in the separation of spatiotemporal information and cannot effectively capture complex temporal patterns in DGs. To address this problem, this study proposes a spatial-temporal graph convolutional networks with diversified transformation (STGCNDT), which includes three aspects: a) constructing a unified graph tensor convolutional network (GTCN) using tensor M-products without the need to represent spatiotemporal information separately; b) introducing three transformation schemes in GTCN to model complex temporal patterns to aggregate temporal information; and c) constructing an ensemble of diversified transformation schemes to obtain higher representation capabilities. Empirical studies on four DGs that appear in communication networks show that the proposed STGCNDT significantly outperforms state-of-the-art models in solving link weight estimation tasks due to the diversified transformations.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d488897997df288927a73befa218f42726e3f36d" target='_blank'>
-              Temporal Convolution Derived Multi-Layered Reservoir Computing
+          <td><a href="https://www.semanticscholar.org/paper/645c7ccb4c62510922512fdba7088d9493b9fd62" target='_blank'>
+              Spatial-temporal Graph Convolutional Networks with Diversified Transformation for Dynamic Graph Representation Learning
               </a>
             </td>
           <td>
-            Johannes Viehweg, Dominik Walther, Prof. Dr.-Ing. Patrick Mader
+            Ling Wang, Yixiang Huang, Hao Wu
           </td>
-          <td>2024-07-09</td>
+          <td>2024-08-05</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Temporal networks are effective in capturing the evolving interactions of networks over time, such as social networks and e-commerce networks. In recent years, researchers have primarily concentrated on developing specific model architectures for Temporal Graph Neural Networks (TGNNs) in order to improve the representation quality of temporal nodes and edges. However, limited attention has been given to the quality of negative samples during the training of TGNNs. When compared with static networks, temporal networks present two specific challenges for negative sampling: positive sparsity and positive shift. Positive sparsity refers to the presence of a single positive sample amidst numerous negative samples at each timestamp, while positive shift relates to the variations in positive samples across different timestamps. To robustly address these challenges in training TGNNs, we introduce Curriculum Negative Mining (CurNM), a model-aware curriculum learning framework that adaptively adjusts the difficulty of negative samples. Within this framework, we first establish a dynamically updated negative pool that balances random, historical, and hard negatives to address the challenges posed by positive sparsity. Secondly, we implement a temporal-aware negative selection module that focuses on learning from the disentangled factors of recently active edges, thus accurately capturing shifting preferences. Extensive experiments on 12 datasets and 3 TGNNs demonstrate that our method outperforms baseline methods by a significant margin. Additionally, thorough ablation studies and parameter sensitivity experiments verify the usefulness and robustness of our approach. Our code is available at https://github.com/zziyue83/CurNM.">
+        <tr id="Recently, the incorporation of both temporal features and the correlation across time series has become an effective approach in time series prediction. Spatio-Temporal Graph Neural Networks (STGNNs) demonstrate good performance on many Temporal-correlation Forecasting Problem. However, when applied to tasks lacking periodicity, such as stock data prediction, the effectiveness and robustness of STGNNs are found to be unsatisfactory. And STGNNs are limited by memory savings so that cannot handle problems with a large number of nodes. In this paper, we propose a novel approach called the Temporal-Correlation Graph Pre-trained Network (TCGPN) to address these limitations. TCGPN utilize Temporal-correlation fusion encoder to get a mixed representation and pre-training method with carefully designed temporal and correlation pre-training tasks. Entire structure is independent of the number and order of nodes, so better results can be obtained through various data enhancements. And memory consumption during training can be significantly reduced through multiple sampling. Experiments are conducted on real stock market data sets CSI300 and CSI500 that exhibit minimal periodicity. We fine-tune a simple MLP in downstream tasks and achieve state-of-the-art results, validating the capability to capture more robust temporal correlation patterns.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/56efc5b54a9beda670261028d60fe6056619863a" target='_blank'>
-              Curriculum Negative Mining For Temporal Networks
+          <td><a href="https://www.semanticscholar.org/paper/1184b61fe584f056e3f7156ed3fe740a346b75a1" target='_blank'>
+              TCGPN: Temporal-Correlation Graph Pre-trained Network for Stock Forecasting
               </a>
             </td>
           <td>
-            Ziyue Chen, Tongya Zheng, Mingli Song
+            Wenbo Yan, Ying Tan
           </td>
-          <td>2024-07-24</td>
+          <td>2024-07-26</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>5</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Time series self-supervised learning (SSL) aims to exploit unlabeled data for pre-training to mitigate the reliance on labels. Despite the great success in recent years, there is limited discussion on the potential noise in the time series, which can severely impair the performance of existing SSL methods. To mitigate the noise, the de facto strategy is to apply conventional denoising methods before model training. However, this pre-processing approach may not fully eliminate the effect of noise in SSL for two reasons: (i) the diverse types of noise in time series make it difficult to automatically determine suitable denoising methods; (ii) noise can be amplified after mapping raw data into latent space. In this paper, we propose denoising-aware contrastive learning (DECL), which uses contrastive learning objectives to mitigate the noise in the representation and automatically selects suitable denoising methods for every sample. Extensive experiments on various datasets verify the effectiveness of our method. The code is open-sourced.">
+        <tr id="Weather forecasting refers to learning evolutionary patterns of some key upper-air and surface variables which is of great significance. Recently, deep learning-based methods have been increasingly applied in the field of weather forecasting due to their powerful feature learning capabilities. However, prediction methods based on the original space iteration struggle to effectively and efficiently utilize large number of weather variables. Therefore, we propose an 'encoding-prediction-decoding' prediction network. This network can efficiently benefit to more related input variables with key variables, that is, it can adaptively extract key variable-related low-dimensional latent feature from much more input atmospheric variables for iterative prediction. And we construct a loss function to guide the iteration of latent feature by utilizing multiple atmospheric variables in corresponding lead times. The obtained latent features through iterative prediction are then decoded to obtain the predicted values of key variables in multiple lead times. In addition, we improve the HTA algorithm in \cite{bi2023accurate} by inputting more time steps to enhance the temporal correlation between the prediction results and input variables. Both qualitative and quantitative prediction results on ERA5 dataset validate the superiority of our method over other methods. (The code will be available at https://github.com/rs-lsl/Kvp-lsi)">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8ec9f1e385bacc765c58313b546ce21b8fd9bdcd" target='_blank'>
-              Denoising-Aware Contrastive Learning for Noisy Time Series
+          <td><a href="https://www.semanticscholar.org/paper/11cc8cb84dcb1157d6fac95012b48b1ab2b7d05d" target='_blank'>
+              Efficiently improving key weather variables forecasting by performing the guided iterative prediction in latent space
               </a>
             </td>
           <td>
-            Shuang Zhou, D. Zha, Xiao Shen, Xiao Huang, Rui Zhang, K. F. Chung
+            Shuangliang Li, Siwei Li
           </td>
-          <td>2024-06-07</td>
+          <td>2024-07-27</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>43</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Transformers can under some circumstances generalize to novel problem instances whose constituent parts might have been encountered during training but whose compositions have not. What mechanisms underlie this ability for compositional generalization? By reformulating multi-head attention as a hypernetwork, we reveal that a low-dimensional latent code specifies key-query specific operations. We find empirically that this latent code is highly structured, capturing information about the subtasks performed by the network. Using the framework of attention as a hypernetwork we further propose a simple modification of multi-head linear attention that strengthens the ability for compositional generalization on a range of abstract reasoning tasks. In particular, we introduce a symbolic version of the Raven Progressive Matrices human intelligence test on which we demonstrate how scaling model size and data enables compositional generalization and gives rise to a functionally structured latent code in the transformer.">
+        <tr id="This paper presents Diffusion Forcing, a new training paradigm where a diffusion model is trained to denoise a set of tokens with independent per-token noise levels. We apply Diffusion Forcing to sequence generative modeling by training a causal next-token prediction model to generate one or several future tokens without fully diffusing past ones. Our approach is shown to combine the strengths of next-token prediction models, such as variable-length generation, with the strengths of full-sequence diffusion models, such as the ability to guide sampling to desirable trajectories. Our method offers a range of additional capabilities, such as (1) rolling-out sequences of continuous tokens, such as video, with lengths past the training horizon, where baselines diverge and (2) new sampling and guiding schemes that uniquely profit from Diffusion Forcing's variable-horizon and causal architecture, and which lead to marked performance gains in decision-making and planning tasks. In addition to its empirical success, our method is proven to optimize a variational lower bound on the likelihoods of all subsequences of tokens drawn from the true joint distribution. Project website: https://boyuan.space/diffusion-forcing">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4946c625ee064bc83e7ec169662f8be115e9aabc" target='_blank'>
-              Attention as a Hypernetwork
+          <td><a href="https://www.semanticscholar.org/paper/40d63dc2b465c9081e4efc5a19514da151e97fe7" target='_blank'>
+              Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion
               </a>
             </td>
           <td>
-            Simon Schug, Seijin Kobayashi, Yassir Akram, Joao Sacramento, Razvan Pascanu
+            Boyuan Chen, Diego Marti Monso, Yilun Du, Max Simchowitz, Russ Tedrake, Vincent Sitzmann
           </td>
-          <td>2024-06-09</td>
+          <td>2024-07-01</td>
           <td>ArXiv</td>
           <td>1</td>
-          <td>67</td>
+          <td>3</td>
         </tr>
 
-        <tr id="With the remarkable success of generative models like ChatGPT, Artificial Intelligence Generated Content (AIGC) is undergoing explosive development. Not limited to text and images, generative models can generate industrial time series data, addressing challenges such as the difficulty of data collection and data annotation. Due to their outstanding generation ability, they have been widely used in Internet of Things, metaverse, and cyber-physical-social systems to enhance the efficiency of industrial production. In this paper, we present a comprehensive overview of generative models for industrial time series from deep generative models (DGMs) to large generative models (LGMs). First, a DGM-based AIGC framework is proposed for industrial time series generation. Within this framework, we survey advanced industrial DGMs and present a multi-perspective categorization. Furthermore, we systematically analyze the critical technologies required to construct industrial LGMs from four aspects: large-scale industrial dataset, LGMs architecture for complex industrial characteristics, self-supervised training for industrial time series, and fine-tuning of industrial downstream tasks. Finally, we conclude the challenges and future directions to enable the development of generative models in industry.">
+        <tr id="We present a knowledge-guided machine learning (KGML) framework for modeling multi-scale processes, and study its performance in the context of streamflow forecasting in hydrology. Specifically, we propose a novel hierarchical recurrent neural architecture that factorizes the system dynamics at multiple temporal scales and captures their interactions. This framework consists of an inverse and a forward model. The inverse model is used to empirically resolve the system's temporal modes from data (physical model simulations, observed data, or a combination of them from the past), and these states are then used in the forward model to predict streamflow. In a hydrological system, these modes can represent different processes, evolving at different temporal scales (e.g., slow: groundwater recharge and baseflow vs. fast: surface runoff due to extreme rainfall). A key advantage of our framework is that once trained, it can incorporate new observations into the model's context (internal state) without expensive optimization approaches (e.g., EnKF) that are traditionally used in physical sciences for data assimilation. Experiments with several river catchments from the NWS NCRFC region show the efficacy of this ML-based data assimilation framework compared to standard baselines, especially for basins that have a long history of observations. Even for basins that have a shorter observation history, we present two orthogonal strategies of training our FHNN framework: (a) using simulation data from imperfect simulations and (b) using observation data from multiple basins to build a global model. We show that both of these strategies (that can be used individually or together) are highly effective in mitigating the lack of training data. The improvement in forecast accuracy is particularly noteworthy for basins where local models perform poorly because of data sparsity.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/dc1ce4a6d24e82a1c9c05d41f69b1e606efa4115" target='_blank'>
-              AIGC for Industrial Time Series: From Deep Generative Models to Large Generative Models
+          <td><a href="https://www.semanticscholar.org/paper/520332f72d1a6deaabdd7dd965c0cf76e89053b5" target='_blank'>
+              Hierarchically Disentangled Recurrent Network for Factorizing System Dynamics of Multi-scale Systems
               </a>
             </td>
           <td>
-            Lei Ren, Haiteng Wang, Yang Tang, Chunhua Yang
+            Rahul Ghosh, Zac McEachran, Arvind Renganathan, Kelly Lindsay, Somya Sharma, M. Steinbach, John L. Nieber, Christopher J. Duffy, Vipin Kumar
           </td>
-          <td>2024-07-16</td>
+          <td>2024-07-29</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>44</td>
         </tr>
 
-        <tr id="Graph pooling has gained attention for its ability to obtain effective node and graph representations for various downstream tasks. Despite the recent surge in graph pooling approaches, there is a lack of standardized experimental settings and fair benchmarks to evaluate their performance. To address this issue, we have constructed a comprehensive benchmark that includes 15 graph pooling methods and 21 different graph datasets. This benchmark systematically assesses the performance of graph pooling methods in three dimensions, i.e., effectiveness, robustness, and generalizability. We first evaluate the performance of these graph pooling approaches across different tasks including graph classification, graph regression and node classification. Then, we investigate their performance under potential noise attacks and out-of-distribution shifts in real-world scenarios. We also involve detailed efficiency analysis and parameter analysis. Extensive experiments validate the strong capability and applicability of graph pooling approaches in various scenarios, which can provide valuable insights and guidance for deep geometric learning research. The source code of our benchmark is available at https://github.com/goose315/Graph_Pooling_Benchmark.">
+        <tr id="Concept Bottleneck Models (CBMs) have emerged as a promising interpretable method whose final prediction is based on intermediate, human-understandable concepts rather than the raw input. Through time-consuming manual interventions, a user can correct wrongly predicted concept values to enhance the model's downstream performance. We propose Stochastic Concept Bottleneck Models (SCBMs), a novel approach that models concept dependencies. In SCBMs, a single-concept intervention affects all correlated concepts, thereby improving intervention effectiveness. Unlike previous approaches that model the concept relations via an autoregressive structure, we introduce an explicit, distributional parameterization that allows SCBMs to retain the CBMs' efficient training and inference procedure. Additionally, we leverage the parameterization to derive an effective intervention strategy based on the confidence region. We show empirically on synthetic tabular and natural image datasets that our approach improves intervention effectiveness significantly. Notably, we showcase the versatility and usability of SCBMs by examining a setting with CLIP-inferred concepts, alleviating the need for manual concept annotations.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/324fc9d67de19b37af460db4ac03c0d5f9dbacb1" target='_blank'>
-              A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizability
+          <td><a href="https://www.semanticscholar.org/paper/aeef1c8046f93d178a091e733fe0d2c8c8c0ca3a" target='_blank'>
+              Stochastic Concept Bottleneck Models
               </a>
             </td>
           <td>
-            Pengyun Wang, Junyu Luo, Yanxin Shen, Siyu Heng, Xiao Luo
+            Moritz Vandenhirtz, Sonia Laguna, Ricards Marcinkevics, Julia E. Vogt
           </td>
-          <td>2024-06-13</td>
+          <td>2024-06-27</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>8</td>
         </tr>
 
-        <tr id="Graph machine learning (GML) is effective in many business applications. However, making GML easy to use and applicable to industry applications with massive datasets remain challenging. We developed GraphStorm, which provides an end-to-end solution for scalable graph construction, graph model training and inference. GraphStorm has the following desirable properties: (a) Easy to use: it can perform graph construction and model training and inference with just a single command; (b) Expert-friendly: GraphStorm contains many advanced GML modeling techniques to handle complex graph data and improve model performance; (c) Scalable: every component in GraphStorm can operate on graphs with billions of nodes and can scale model training and inference to different hardware without changing any code. GraphStorm has been used and deployed for over a dozen billion-scale industry applications after its release in May 2023. It is open-sourced in Github: https://github.com/awslabs/graphstorm.">
+        <tr id="Accurate short-term forecasting of power load is essential for the reliable operation of the comprehensive energy systems of ports and for effectively reducing energy consumption. Owing to the complexity of port systems, traditional load forecasting methods often struggle to capture the non-linearity and multifactorial interactions within the factors creating power load. To address these challenges, this study combines variational mode decomposition (VMD), temporal convolutional network (TCN), and long short-term memory (LSTM) network to develop a multi-feature-based VMD-TCN-LSTM model for the short-term forecasting of the power load of ports. VMD is first used to decompose the power load series of ports into multiple, relatively stable components to mitigate volatility. Furthermore, meteorological and temporal features are introduced into the TCN-LSTM model, which combines the temporal feature extraction capability of the TCN and the long term-dependent learning capability of the LSTM. Comparative analyses with other common forecasting models using the observed power load data from a coastal port in China demonstrate that the proposed forecasting model achieves a higher prediction accuracy, with an R-squared value of 0.94, mean squared error of 3.59 MW, and a mean absolute percentage error of 2.36%.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0130f2fab75c30c26635be32fdafa6a03c35af6a" target='_blank'>
-              GraphStorm: all-in-one graph machine learning framework for industry applications
+          <td><a href="https://www.semanticscholar.org/paper/0ede2faa5546cfbefa083cdef9bfe4e7663ea5a1" target='_blank'>
+              Multifeature-Based Variational Mode Decomposition–Temporal Convolutional Network–Long Short-Term Memory for Short-Term Forecasting of the Load of Port Power Systems
               </a>
             </td>
           <td>
-            Da Zheng, Xiang Song, Qi Zhu, Jian Zhang, Theodore Vasiloudis, Runjie Ma, Houyu Zhang, Zichen Wang, Soji Adeshina, Israt Nisa, Alejandro Mottini, Qingjun Cui, H. Rangwala, Belinda Zeng, Christos Faloutsos, G. Karypis
+            Guang Chen, Xiaofeng Ma, Lin Wei
           </td>
-          <td>2024-06-10</td>
-          <td>ArXiv</td>
+          <td>2024-06-22</td>
+          <td>Sustainability</td>
+          <td>0</td>
           <td>0</td>
-          <td>95</td>
         </tr>
 
-        <tr id="Large Language Models (LLMs) encounter significant challenges in continual learning due to catastrophic forgetting, where new information overwrites previously acquired knowledge. This limitation leads to substantial environmental and economic waste. In this study, we introduce the PMoE, Progressive Mixture of Experts with Asymmetric Transformer, which aims to minimize forgetting by utilizing an asymmetric design with shallow layers dedicated to general knowledge and deep layers for new knowledge. PMoE incorporates progressively added experts in deep layers and a router that allocates new knowledge to the appropriate experts efficiently. The router, positioned adjacent to the deep layers, utilizes deep features aggregating consolidated information. This enables the router to perform efficiently, allocating new knowledge to the appropriate experts, which progressively increase in the deep layers. Extensive experiments on TRACE datasets and general language understanding datasets demonstrate that the proposed PMoE outperforms previous state-of-the-art approaches.">
+        <tr id="Graph Neural Networks (GNNs)-based recommendation algorithms typically assume that training and testing data are drawn from independent and identically distributed (IID) spaces. However, this assumption often fails in the presence of out-of-distribution (OOD) data, resulting in significant performance degradation. In this study, we construct a Structural Causal Model (SCM) to analyze interaction data, revealing that environmental confounders (e.g., the COVID-19 pandemic) lead to unstable correlations in GNN-based models, thus impairing their generalization to OOD data. To address this issue, we propose a novel approach, graph representation learning via causal diffusion (CausalDiffRec) for OOD recommendation. This method enhances the model's generalization on OOD data by eliminating environmental confounding factors and learning invariant graph representations. Specifically, we use backdoor adjustment and variational inference to infer the real environmental distribution, thereby eliminating the impact of environmental confounders. This inferred distribution is then used as prior knowledge to guide the representation learning in the reverse phase of the diffusion process to learn the invariant representation. In addition, we provide a theoretical derivation that proves optimizing the objective function of CausalDiffRec can encourage the model to learn environment-invariant graph representations, thereby achieving excellent generalization performance in recommendations under distribution shifts. Our extensive experiments validate the effectiveness of CausalDiffRec in improving the generalization of OOD data, and the average improvement is up to 10.69% on Food, 18.83% on KuaiRec, 22.41% on Yelp2018, and 11.65% on Douban datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/35964703237d3a9799780075ab0cd795a89d7960" target='_blank'>
-              PMoE: Progressive Mixture of Experts with Asymmetric Transformer for Continual Learning
+          <td><a href="https://www.semanticscholar.org/paper/ce6c02c791a420b29ba47ebbf6ece6010fd1a289" target='_blank'>
+              Graph Representation Learning via Causal Diffusion for Out-of-Distribution Recommendation
               </a>
             </td>
           <td>
-            Min Jae Jung, JooHee Kim
+            Chu Zhao, Enneng Yang, Yuliang Liang, Pengxiang Lan, Yuting Liu, Jianzhe Zhao, Guibing Guo, Xingwei Wang
           </td>
-          <td>2024-07-31</td>
+          <td>2024-08-01</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Graph Neural Network (GNN) achieves great success for node-level and graph-level tasks via encoding meaningful topological structures of networks in various domains, ranging from social to biological networks. However, repeated aggregation operations lead to excessive mixing of node representations, particularly in dense regions with multiple GNN layers, resulting in nearly indistinguishable embeddings. This phenomenon leads to the oversmoothing problem that hampers downstream graph analytics tasks. To overcome this issue, we propose a novel and flexible truss-based graph sparsification model that prunes edges from dense regions of the graph. Pruning redundant edges in dense regions helps to prevent the aggregation of excessive neighborhood information during hierarchical message passing and pooling in GNN models. We then utilize our sparsification model in the state-of-the-art baseline GNNs and pooling models, such as GIN, SAGPool, GMT, DiffPool, MinCutPool, HGP-SL, DMonPool, and AdamGNN. Extensive experiments on different real-world datasets show that our model significantly improves the performance of the baseline GNN models in the graph classification task.">
+        <tr id="Accurate traffic forecasting is more necessary than ever for transportation departments, especially given its significant role in traffic planning, management, and control. However, most existing methods struggle to address complex spatial correlations on road networks, nonlinear temporal dynamics, and difficult long‐term prediction. This article proposes a novel spatial temporal graph gated transformer (STGGT) to overcome these challenges. The suggested model differs from Google's transformer because it uses a hybrid architecture that integrates graph convolutional networks (GCNs), attention, and gated recurrent units (GRUs) instead of solely relying on attention. Specifically, STGGT uses GCNs to extract spatial dependencies, utilizes attention and GRUs to extract temporal dependencies, and handle long‐term prediction. Experiments indicate that STGGT outperforms the state‐of‐the‐art baseline models on two real‐world traffic datasets of 9%–40%. The proposed model offers a promising solution for accurate traffic forecasting, simultaneously addressing the challenges of complex spatial correlations, nonlinear temporal dynamics, and long‐term prediction.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3c6b535bf90c88c1001770c3872f3caf3e8e11bb" target='_blank'>
-              Tackling Oversmoothing in GNN via Graph Sparsification: A Truss-based Approach
+          <td><a href="https://www.semanticscholar.org/paper/64e802ce9b30e768f218018adb39b56cd14ee339" target='_blank'>
+              A spatial-temporal graph gated transformer for traffic forecasting
               </a>
             </td>
           <td>
-            Tanvir Hossain, Khaled Mohammed Saifuddin, Muhammad Ifte Khairul Islam, Farhan Tanvir, Esra Akbas
+            Haroun Bouchemoukha, M. Zennir, Ahmed Alioua
           </td>
-          <td>2024-07-16</td>
-          <td>ArXiv</td>
+          <td>2024-06-26</td>
+          <td>Trans. Emerg. Telecommun. Technol.</td>
           <td>0</td>
-          <td>10</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Diffusion models have demonstrated effectiveness in generating natural images and have been extended to generate diverse data types, including graphs. This new generation of diffusion-based graph generative models has demonstrated significant performance improvements over methods that rely on variational autoencoders or generative adversarial networks. It's important to recognize, however, that most of these models employ Gaussian or categorical diffusion processes, which can struggle with sparse and long-tailed data distributions. In our work, we introduce Graph Beta Diffusion (GBD), a diffusion-based generative model particularly adept at capturing diverse graph structures. GBD utilizes a beta diffusion process, tailored for the sparse and range-bounded characteristics of graph adjacency matrices. Furthermore, we have developed a modulation technique that enhances the realism of the generated graphs by stabilizing the generation of critical graph structures, while preserving flexibility elsewhere. The outstanding performance of GBD across three general graph benchmarks and two biochemical graph benchmarks highlights its capability to effectively capture the complexities of real-world graph data. The code will be made available at https://github.com/YH-UtMSB/Graph_Beta_Diffusion">
+        <tr id="Dynamic Quality-of-Service (QoS) data capturing temporal variations in user-service interactions, are essential source for service selection and user behavior understanding. Approaches based on Latent Feature Analysis (LFA) have shown to be beneficial for discovering effective temporal patterns in QoS data. However, existing methods cannot well model the spatiality and temporality implied in dynamic interactions in a unified form, causing abundant accuracy loss for missing QoS estimation. To address the problem, this paper presents a novel Graph Convolutional Networks (GCNs)-based dynamic QoS estimator namely Spatiotemporal Coupling GCN (SCG) model with the three-fold ideas as below. First, SCG builds its dynamic graph convolution rules by incorporating generalized tensor product framework, for unified modeling of spatial and temporal patterns. Second, SCG combines the heterogeneous GCN layer with tensor factorization, for effective representation learning on bipartite user-service graphs. Third, it further simplifies the dynamic GCN structure to lower the training difficulties. Extensive experiments have been conducted on two large-scale widely-adopted QoS datasets describing throughput and response time. The results demonstrate that SCG realizes higher QoS estimation accuracy compared with the state-of-the-arts, illustrating it can learn powerful representations to users and cloud services.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/95ac1eb4b2fb3826c34ea1154e5bd561e1a18bbf" target='_blank'>
-              Advancing Graph Generation through Beta Diffusion
+          <td><a href="https://www.semanticscholar.org/paper/53de573b22bccc67f4c62494a24ad6245cd7246a" target='_blank'>
+              A Novel Spatiotemporal Coupling Graph Convolutional Network
               </a>
             </td>
           <td>
-            Yilin He, Xinyang Liu, Bo Chen, Mingyuan Zhou
+            Fanghui Bi
           </td>
-          <td>2024-06-13</td>
+          <td>2024-08-09</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Multi-relational temporal graphs are powerful tools for modeling real-world data, capturing the evolving and interconnected nature of entities over time. Recently, many novel models are proposed for ML on such graphs intensifying the need for robust evaluation and standardized benchmark datasets. However, the availability of such resources remains scarce and evaluation faces added complexity due to reproducibility issues in experimental protocols. To address these challenges, we introduce Temporal Graph Benchmark 2.0 (TGB 2.0), a novel benchmarking framework tailored for evaluating methods for predicting future links on Temporal Knowledge Graphs and Temporal Heterogeneous Graphs with a focus on large-scale datasets, extending the Temporal Graph Benchmark. TGB 2.0 facilitates comprehensive evaluations by presenting eight novel datasets spanning five domains with up to 53 million edges. TGB 2.0 datasets are significantly larger than existing datasets in terms of number of nodes, edges, or timestamps. In addition, TGB 2.0 provides a reproducible and realistic evaluation pipeline for multi-relational temporal graphs. Through extensive experimentation, we observe that 1) leveraging edge-type information is crucial to obtain high performance, 2) simple heuristic baselines are often competitive with more complex methods, 3) most methods fail to run on our largest datasets, highlighting the need for research on more scalable methods.">
+        <tr id="Industrial time-series, as a structural data responds to production process information, can be utilized to perform data-driven decision-making for effective monitoring of industrial production process. However, there are some challenges for time-series forecasting in industry, e.g., predicting few-shot caused by data shortage, and decision-confusing caused by unknown treatment policy. To cope with the problems, we propose a novel causal domain adaptation framework, Causal Domain Adaptation (CDA) forecaster to improve the performance on the interested domain with limited data (target). Firstly, we analyze the causality existing along with treatments, and thus ensure the shared causality over time. Subsequently, we propose an answer-based attention mechanism to achieve domain-invariant representation by the shared causality in both domains. Then, a novel domain-adaptation is built to model treatments and outcomes jointly training on source and target domain. The main insights are that our designed answer-based attention mechanism allows the target domain to leverage the existed causality in source time-series even with different treatments, and our forecaster can predict the counterfactual outcome of industrial time-series, meaning a guidance in production process. Compared with commonly baselines, our method on real-world and synthetic oilfield datasets demonstrates the effectiveness in across-domain prediction and the practicality in guiding production process">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/008283c83ba7061538062f9e56890f98e405f978" target='_blank'>
-              TGB 2.0: A Benchmark for Learning on Temporal Knowledge Graphs and Heterogeneous Graphs
+          <td><a href="https://www.semanticscholar.org/paper/156edecae87bbcc79ee4253c37525b426f87a42a" target='_blank'>
+              Domain Adaptation for Industrial Time-series Forecasting via Counterfactual Inference
               </a>
             </td>
           <td>
-            J. Gastinger, Shenyang Huang, Mikhail Galkin, Erfan Loghmani, Alipanah Parviz, Farimah Poursafaei, Jacob Danovitch, Emanuele Rossi, Ioannis Koutis, Heiner Stuckenschmidt, Reihaneh Rabbany, Guillaume Rabusseau
+            Chao Min, Guo-quan Wen, Jiangru Yuan, Jun Yi, Xing Guo
           </td>
-          <td>2024-06-14</td>
+          <td>2024-07-19</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>19</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Training models on spatio-temporal (ST) data poses an open problem due to the complicated and diverse nature of the data itself, and it is challenging to ensure the model's performance directly trained on the original ST data. While limiting the variety of training data can make training easier, it can also lead to a lack of knowledge and information for the model, resulting in a decrease in performance. To address this challenge, we presented an innovative paradigm that incorporates three separate forms of curriculum learning specifically targeting from spatial, temporal, and quantile perspectives. Furthermore, our framework incorporates a stacking fusion module to combine diverse information from three types of curriculum learning, resulting in a strong and thorough learning process. We demonstrated the effectiveness of this framework with extensive empirical evaluations, highlighting its better performance in addressing complex ST challenges. We provided thorough ablation studies to investigate the effectiveness of our curriculum and to explain how it contributes to the improvement of learning efficiency on ST data.">
+        <tr id="Graph Neural Networks (GNNs) have emerged as powerful tools for supervised machine learning over graph-structured data, while sampling-based node representation learning is widely utilized in unsupervised learning. However, scalability remains a major challenge in both supervised and unsupervised learning for large graphs (e.g., those with over 1 billion nodes). The scalability bottleneck largely stems from the mini-batch sampling phase in GNNs and the random walk sampling phase in unsupervised methods. These processes often require storing features or embeddings in memory. In the context of distributed training, they require frequent, inefficient random access to data stored across different workers. Such repeated inter-worker communication for each mini-batch leads to high communication overhead and computational inefficiency. We propose GraphScale, a unified framework for both supervised and unsupervised learning to store and process large graph data distributedly. The key insight in our design is the separation of workers who store data and those who perform the training. This separation allows us to decouple computing and storage in graph training, thus effectively building a pipeline where data fetching and data computation can overlap asynchronously. Our experiments show that GraphScale outperforms state-of-the-art methods for distributed training of both GNNs and node embeddings. We evaluate GraphScale both on public and proprietary graph datasets and observe a reduction of at least 40% in end-to-end training times compared to popular distributed frameworks, without any loss in performance. While most existing methods don't support billion-node graphs for training node embeddings, GraphScale is currently deployed in production at TikTok enabling efficient learning over such large graphs.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6785d8ecb5eb658efde7e06f9afec1ed69bfadb7" target='_blank'>
-              Enhancing Spatio-temporal Quantile Forecasting with Curriculum Learning: Lessons Learned
+          <td><a href="https://www.semanticscholar.org/paper/e5115bc6bf426026833b4f7fb72ae6282f678143" target='_blank'>
+              GraphScale: A Framework to Enable Machine Learning over Billion-node Graphs
               </a>
             </td>
           <td>
-            Du Yin, Jinliang Deng, Shuang Ao, Zechen Li, Hao Xue, Arian Prabowo, Renhe Jiang, Xuan Song, Flora D. Salim
+            Vipul Gupta, Xin Chen, Ruoyun Huang, Fanlong Meng, Jianjun Chen, Yujun Yan
           </td>
-          <td>2024-06-18</td>
+          <td>2024-07-22</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>18</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Understanding user interests is crucial for Click-Through Rate (CTR) prediction tasks. In sequential recommendation, pre-training from user historical behaviors through self-supervised learning can better comprehend user dynamic preferences, presenting the potential for direct integration with CTR tasks. Previous methods have integrated pre-trained models into downstream tasks with the sole purpose of extracting semantic information or well-represented user features, which are then incorporated as new features. However, these approaches tend to ignore the additional inference costs to the downstream tasks, and they do not consider how to transfer the effective information from the pre-trained models for specific estimated items in CTR prediction. In this paper, we propose a Sequential Recommendation Pre-training framework for CTR prediction (SRP4CTR) to tackle the above problems. Initially, we discuss the impact of introducing pre-trained models on inference costs. Subsequently, we introduced a pre-trained method to encode sequence side information concurrently.During the fine-tuning process, we incorporate a cross-attention block to establish a bridge between estimated items and the pre-trained model at a low cost. Moreover, we develop a querying transformer technique to facilitate the knowledge transfer from the pre-trained model to industrial CTR models. Offline and online experiments show that our method outperforms previous baseline models.">
+        <tr id="Deep learning models are widely used in multivariate time series forecasting, yet, they have high computational costs. One way to reduce this cost is by reducing data dimensionality, which involves removing unimportant or low importance information with the proper method. This work presents a study on an explainability feature selection framework composed of four methods (IMV‐LSTM Tensor, LIME‐LSTM, Average SHAP‐LSTM, and Instance SHAP‐LSTM) aimed at using the LSTM black‐box model complexity to its favour, with the end goal of improving the error metrics and reducing the computational cost on a forecast task. To test the framework, three datasets with a total of 101 multivariate time series were used, with the explainability methods outperforming the baseline methods in most of the data, be it in error metrics or computation time for the LSTM model training.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4a178e263ed1b774c6780e977b5a338b58cc1860" target='_blank'>
-              Enhancing CTR Prediction through Sequential Recommendation Pre-training: Introducing the SRP4CTR Framework
+          <td><a href="https://www.semanticscholar.org/paper/c38a287f4c56c37be6a1916bb90ba43b4504c73a" target='_blank'>
+              KDBI special issue: Explainability feature selection framework application for LSTM multivariate time‐series forecast self optimization
               </a>
             </td>
           <td>
-            Ruidong Han, Qianzhong Li, He Jiang, Rui Li, Yurou Zhao, Xiang Li, Wei Lin
+            Eduardo M. Rodrigues, Yassine Baghoussi, João Mendes‐Moreira
           </td>
-          <td>2024-07-29</td>
-          <td>ArXiv</td>
+          <td>2024-07-04</td>
+          <td>Expert Systems</td>
           <td>0</td>
-          <td>5</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Despite the rapid expansion of smart grids and large volumes of data at the individual consumer level, there are still various cases where adequate data collection to train accurate load forecasting models is challenging or even impossible. This paper proposes adapting an established model-agnostic meta-learning algorithm for short-term load forecasting in the context of few-shot learning. Specifically, the proposed method can rapidly adapt and generalize within any unknown load time series of arbitrary length using only minimal training samples. In this context, the meta-learning model learns an optimal set of initial parameters for a base-level learner recurrent neural network. The proposed model is evaluated using a dataset of historical load consumption data from real-world consumers. Despite the examined load series' short length, it produces accurate forecasts outperforming transfer learning and task-specific machine learning methods by $12.5\%$. To enhance robustness and fairness during model evaluation, a novel metric, mean average log percentage error, is proposed that alleviates the bias introduced by the commonly used MAPE metric. Finally, a series of studies to evaluate the model's robustness under different hyperparameters and time series lengths is also conducted, demonstrating that the proposed approach consistently outperforms all other models.">
+        <tr id="Time series forecasting (TSF) is immensely important in extensive applications, such as electricity transformation, financial trade, medical monitoring, and smart agriculture. Although Transformer-based methods can handle time series data, their ability to predict long-term time series is limited due to the ``anti-order"nature of the self-attention mechanism. To address this problem, we focus on frequency domain to weaken the impact of order in TSF and propose the FreqBlock, where we first obtain frequency representations through the Frequency Transform Module. Subsequently, a newly designed Frequency Cross Attention is used to obtian enhanced frequency representations between the real and imaginary parts, thus establishing a link between the attention mechanism and the inherent Kramer-Kronig relations (KKRs). Our backbone network, FreqTSF, adopts a residual structure by concatenating multiple FreqBlocks to simulate KKRs in the frequency domain and avoid degradation problems. On a theoretical level, we demonstrate that the proposed two modules can significantly reduce the time and memory complexity from $\mathcal{O}(L^2)$ to $\mathcal{O}(L)$ for each FreqBlock computation. Empirical studies on four benchmark datasets show that FreqTSF achieves an overall relative MSE reduction of 15\% and an overall relative MAE reduction of 11\% compared to the state-of-the-art methods. The code will be available soon.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/771acb3c029af38bd961bb2859d65ba1a145fc68" target='_blank'>
-              Few-Shot Load Forecasting Under Data Scarcity in Smart Grids: A Meta-Learning Approach
+          <td><a href="https://www.semanticscholar.org/paper/c7a597bc1188e94cf4e9583a7acbceb292b7f71f" target='_blank'>
+              FreqTSF: Time Series Forecasting Via Simulating Frequency Kramer-Kronig Relations
               </a>
             </td>
           <td>
-            Georgios Tsoumplekas, C. Athanasiadis, D.I. Doukas, Antonios C. Chrysopoulos, P. Mitkas
+            Rujia Shen, Liangliang Liu, Boran Wang, Yi Guan, Yang Yang, Jingchi Jiang
           </td>
-          <td>2024-06-09</td>
+          <td>2024-07-31</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>29</td>
+          <td>11</td>
         </tr>
 
-        <tr id="Time series forecasting has essential applications across various domains. For instance, forecasting power time series can optimize energy usage and bolster grid stability and reliability. Existing models based on transformer architecture are limited to classical design, ignoring the impact of spatial information and noise on model architecture design. Therefore, we propose an atypical design of Transformer-based models for multivariate time series forecasting. This design consists of two critical components: (i) spectral clustering center of time series employed as the focal point for attention computation; (ii) alternating attention mechanism wherein each query transformer is compatible with spectral clustering centers, executing attention at the sequence level instead of the token level. The alternating design has a two-fold benefit: firstly, it eliminates the uncertainty noise present in the dependent variable sequence of the channel input, and secondly, it incorporates the Euclidean distance to mitigate the impact of extreme values on the attention matrix, thereby aligning predictions more closely to the sequence's natural progression. Experiments on ten real-world datasets, encompassing Wind, Electricity, Weather, and others, demonstrate that our Spectral Central Alternating Transformer (SCAT) outperforms state-of-the-art methods (SOTA) by an average of 42.8% in prediction performance in power time series forecasting.">
+        <tr id="Track reconstruction is a crucial task in particle experiments and is traditionally very computationally expensive due to its combinatorial nature. Recently, graph neural networks (GNNs) have emerged as a promising approach that can improve scalability. Most of these GNN-based methods, including the edge classification (EC) and the object condensation (OC) approach, require an input graph that needs to be constructed beforehand. In this work, we consider a one-shot OC approach that reconstructs particle tracks directly from a set of hits (point cloud) by recursively applying graph attention networks with an evolving graph structure. This approach iteratively updates the graphs and can better facilitate the message passing across each graph. Preliminary studies on the TrackML dataset show better track performance compared to the methods that require a fixed input graph.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f0478468dc09d88ac952d50786c548b2bee25e6a" target='_blank'>
-              SCAT: A Time Series Forecasting with Spectral Central Alternating Transformers
+          <td><a href="https://www.semanticscholar.org/paper/398108b585c483e0611513c7746467f7cd38df17" target='_blank'>
+              EggNet: An Evolving Graph-based Graph Attention Network for Particle Track Reconstruction
               </a>
             </td>
           <td>
-            Chengjie Zhou, Chao Che, Pengfei Wang, Qiang Zhang
+            P. Calafiura, Jay Chan, Loic Delabrouille, Brandon Wang
           </td>
-          <td>2024-08-01</td>
-          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
+          <td>2024-07-18</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>48</td>
         </tr>
 
-        <tr id="Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (Joint Adaptive predictioN-region Estimation for Time-series), a novel framework for constructing conformal prediction regions that are valid for both univariate and multivariate time series. JANET generalises the inductive conformal framework and efficiently produces joint prediction regions with controlled K-familywise error rates, enabling flexible adaptation to specific application needs. Our empirical evaluation demonstrates JANET's superior performance in multi-step prediction tasks across diverse time series datasets, highlighting its potential for reliable and interpretable uncertainty quantification in sequential data.">
+        <tr id="The effectiveness of univariate forecasting models is often hampered by conditions that cause them stress. A model is considered to be under stress if it shows a negative behaviour, such as higher-than-usual errors or increased uncertainty. Understanding the factors that cause stress to forecasting models is important to improve their reliability, transparency, and utility. This paper addresses this problem by contributing with a novel framework called MAST (Meta-learning and data Augmentation for Stress Testing). The proposed approach aims to model and characterize stress in univariate time series forecasting models, focusing on conditions where they exhibit large errors. In particular, MAST is a meta-learning approach that predicts the probability that a given model will perform poorly on a given time series based on a set of statistical time series features. MAST also encompasses a novel data augmentation technique based on oversampling to improve the metadata concerning stress. We conducted experiments using three benchmark datasets that contain a total of 49.794 time series to validate the performance of MAST. The results suggest that the proposed approach is able to identify conditions that lead to large errors. The method and experiments are publicly available in a repository.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b21605b67376e0377590d3cdfb99e3c43495b865" target='_blank'>
-              JANET: Joint Adaptive predictioN-region Estimation for Time-series
+          <td><a href="https://www.semanticscholar.org/paper/21df316c9190406997a7ddcf7668a9d6a38d85cf" target='_blank'>
+              Meta-learning and Data Augmentation for Stress Testing Forecasting Models
               </a>
             </td>
           <td>
-            Eshant English, Eliot Wong-Toi, Matteo Fontana, Stephan Mandt, P. Smyth, Christoph Lippert
+            Ricardo In'acio, Vítor Cerqueira, Mar'ilia Barandas, Carlos Soares
           </td>
-          <td>2024-07-08</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>14</td>
         </tr>
 
-        <tr id="Transformer-based methods have recently demonstrated their potential in time series forecasting problems. However, the mainstream approach, primarily utilizing attention to model inter-step correlation in the time domain, is constrained by two significant issues that lead to ineffective and inefficient multivariate forecasting. The first is that key representations in the time domain are scattered and sparse, resulting in parameter bloat and increased difficulty in capturing time dependencies. The second is that treating time step points as uniformly embedded tokens leads to the erasure of inter-variate correlations. To address these challenges, we propose a frequency-wise and variables-oriented transformer-based method. This method leverages the intrinsic conjugate symmetry in the frequency domain, enabling compact frequency domain representations that naturally mix information across time points while reducing spatio-temporal costs. Multivariate inter-correlations can also be captured from similar frequency domain components, which enhances the variables-oriented attention mechanism modeling capability. Further, we employ both polar and complex domain perspectives to enrich the frequency domain representations and decode complicated temporal patterns. We propose frequency-enhanced independent representation multi-head attention (FIR-Attention) to leverage these advantages for improved multivariate interaction. Techniques such as cutting-off frequency and equivalent mapping are used to ensure the model’s lightweight nature. Extensive experiments on eight mainstream datasets show that our approach achieves first-rate satisfactory results and, importantly, requires only one percent of the spatio-temporal cost of mainstream methods.">
+        <tr id="Multivariate time series anomaly detection is a crucial data mining technique with a wide range of applications in areas such as IT applications. Currently, the majority of anomaly detection methods for time series data rely on unsupervised approaches due to the rarity of anomaly labels. However, in real-world scenarios, obtaining a limited number of anomaly labels is feasible and affordable. Effective usage of these labels can offer valuable insights into the temporal characteristics of anomalies and play a pivotal role in guiding anomaly detection efforts. To improve the performance of multivariate time series anomaly detection, we proposed a novel deep learning model named EDD (Encoder-Decoder-Discriminator) that leverages limited anomaly samples. The EDD model innovatively integrates a graph attention network with long short term memory (LSTM) to extract spatial and temporal features from multivariate time series data. This integrated approach enables the model to capture complex patterns and dependencies within the data. Additionally, the model skillfully maps series data into a latent space, utilizing a carefully crafted loss function to cluster normal data tightly in the latent space while dispersing abnormal data randomly. This innovative design results in distinct probability distributions for normal and abnormal data in the latent space, enabling precise identification of anomalous data. To evaluate the performance of our EDD model, we conducted extensive experimental validation across three diverse datasets. The results demonstrate the significant superiority of our model in multivariate time series anomaly detection. Specifically, the average F1-Score of our model outperformed the second-best method by 2.7% and 73.4% in both evaluation approaches, respectively, highlighting its superior detection capabilities. These findings validate the effectiveness of our proposed EDD model in leveraging limited anomaly samples for accurate and robust anomaly detection in multivariate time series data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/36f87cbd5187e521184ddb319b132292cb8ae608" target='_blank'>
-              Frequency-Enhanced Transformer with Symmetry-Based Lightweight Multi-Representation for Multivariate Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/6a0b2af4fae72e31c61e9b23f7aa121732e8dfa5" target='_blank'>
+              An anomaly detection model for multivariate time series with anomaly perception
               </a>
             </td>
           <td>
-            Chenyue Wang, Zhouyuan Zhang, Xin Wang, Mingyang Liu, Lin Chen, Jiatian Pi
+            Dong Wei, Wu Sun, Xiaofeng Zou, Dan Ma, Huarong Xu, Panfeng Chen, Chaoshu Yang, Mei Chen, Hui Li
           </td>
-          <td>2024-06-25</td>
-          <td>Symmetry</td>
+          <td>2024-07-31</td>
+          <td>PeerJ Comput. Sci.</td>
+          <td>0</td>
           <td>0</td>
-          <td>1</td>
         </tr>
 
-        <tr id="Graph neural networks (GNNs) have demonstrated remarkable success in numerous graph analytical tasks. Yet, their effectiveness is often compromised in real-world scenarios due to distribution shifts, limiting their capacity for knowledge transfer across changing environments or domains. Recently, Unsupervised Graph Domain Adaptation (UGDA) has been introduced to resolve this issue. UGDA aims to facilitate knowledge transfer from a labeled source graph to an unlabeled target graph. Current UGDA efforts primarily focus on model-centric methods, such as employing domain invariant learning strategies and designing model architectures. However, our critical examination reveals the limitations inherent to these model-centric methods, while a data-centric method allowed to modify the source graph provably demonstrates considerable potential. This insight motivates us to explore UGDA from a data-centric perspective. By revisiting the theoretical generalization bound for UGDA, we identify two data-centric principles for UGDA: alignment principle and rescaling principle. Guided by these principles, we propose GraphAlign, a novel UGDA method that generates a small yet transferable graph. By exclusively training a GNN on this new graph with classic Empirical Risk Minimization (ERM), GraphAlign attains exceptional performance on the target graph. Extensive experiments under various transfer scenarios demonstrate the GraphAlign outperforms the best baselines by an average of 2.16%, training on the generated graph as small as 0.25~1% of the original training graph.">
+        <tr id="The increasing adoption of rooftop photovoltaic (PV) power generation systems in residential areas necessitates accurate monitoring and disaggregation of behind-the-meter (BTM) load and PV power. Despite recent advancements, existing BTM disaggregation approaches suffer from three major drawbacks: neglecting task-relevant spatiotemporal features, overfitting, and lack of a sparse neural architecture which leads to high sample complexity. This paper addresses them by introducing a deep sparse attention graph recurrent framework. This framework conceptualizes a set of neighboring residential units as a graph where the nodes are the net load values of the units and the edges show the mutual information (MI) of these measurements. We develop an Attention Gated Recurrent Unit (AGRU) to capture enhanced temporal characteristics of the net load. We employ a novel low-rank Dictionary Learning (DL) method to discern spatiotemporal features of these measurements and further utilize a Rectified Linear Unit (ReLU) neural network that incorporates an MI-based dropout to provide a sparse model for the estimation of the BTM load and PV. Experimental results validate the effectiveness of our proposed model, exhibiting superior performance on the Ausgrid dataset in BTM load and PV power estimation compared to state-of-the-art methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d45d893d9da6312b1b82291e125fbfd9cc515c57" target='_blank'>
-              Can Modifying Data Address Graph Domain Adaptation?
+          <td><a href="https://www.semanticscholar.org/paper/ba52197a4d7f5071efd214b6546a45314b15bb13" target='_blank'>
+              Sparse Attention Graph Gated Recurrent Unit for Spatiotemporal Behind-The-Meter Load and PV Disaggregation
               </a>
             </td>
           <td>
-            Renhong Huang, Jiarong Xu, Xin Jiang, Ruichuan An, Yang Yang
+            Mahdi Khodayar, Ali Farajzadeh Bavil, M. Saffari
           </td>
-          <td>2024-07-27</td>
-          <td>ArXiv</td>
+          <td>2024-06-27</td>
+          <td>2024 16th International Conference on Electronics, Computers and Artificial Intelligence (ECAI)</td>
           <td>0</td>
-          <td>2</td>
+          <td>14</td>
         </tr>
 
-        <tr id="Probabilistic forecasting models for joint distributions of targets in irregular time series are a heavily under-researched area in machine learning with, to the best of our knowledge, only three models researched so far: GPR, the Gaussian Process Regression model~\citep{Durichen2015.Multitask}, TACTiS, the Transformer-Attentional Copulas for Time Series~\cite{Drouin2022.Tactis, ashok2024tactis} and ProFITi \citep{Yalavarthi2024.Probabilistica}, a multivariate normalizing flow model based on invertible attention layers. While ProFITi, thanks to using multivariate normalizing flows, is the more expressive model with better predictive performance, we will show that it suffers from marginalization inconsistency: it does not guarantee that the marginal distributions of a subset of variables in its predictive distributions coincide with the directly predicted distributions of these variables. Also, TACTiS does not provide any guarantees for marginalization consistency. We develop a novel probabilistic irregular time series forecasting model, Marginalization Consistent Mixtures of Separable Flows (moses), that mixes several normalizing flows with (i) Gaussian Processes with full covariance matrix as source distributions and (ii) a separable invertible transformation, aiming to combine the expressivity of normalizing flows with the marginalization consistency of Gaussians. In experiments on four different datasets we show that moses outperforms other state-of-the-art marginalization consistent models, performs on par with ProFITi, but different from ProFITi, guarantee marginalization consistency.">
+        <tr id="In the era of rapid globalization and digitalization, accurate identification of similar stocks has become increasingly challenging due to the non-stationary nature of financial markets and the ambiguity in conventional regional and sector classifications. To address these challenges, we examine SimStock, a novel temporal self-supervised learning framework that combines techniques from self-supervised learning (SSL) and temporal domain generalization to learn robust and informative representations of financial time series data. The primary focus of our study is to understand the similarities between stocks from a broader perspective, considering the complex dynamics of the global financial landscape. We conduct extensive experiments on four real-world datasets with thousands of stocks and demonstrate the effectiveness of SimStock in finding similar stocks, outperforming existing methods. The practical utility of SimStock is showcased through its application to various investment strategies, such as pairs trading, index tracking, and portfolio optimization, where it leads to superior performance compared to conventional methods. Our findings empirically examine the potential of data-driven approach to enhance investment decision-making and risk management practices by leveraging the power of temporal self-supervised learning in the face of the ever-changing global financial landscape.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cae76678907266cc922fd43d348b16dedc1d8a1d" target='_blank'>
-              Marginalization Consistent Mixture of Separable Flows for Probabilistic Irregular Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/c259bc9adf3019870613cbb7888ea4fac4e1929f" target='_blank'>
+              Temporal Representation Learning for Stock Similarities and Its Applications in Investment Management
               </a>
             </td>
           <td>
-            Vijaya Krishna Yalavarthi, Randolf Scholz, Kiran Madhusudhanan, Stefan Born, Lars Schmidt-Thieme
+            Yoon-Jeong Hwang, Stefan Zohren, Yongjae Lee
           </td>
-          <td>2024-06-11</td>
+          <td>2024-07-18</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>1</td>
         </tr>
 
-        <tr id="This paper addresses the challenge of incremental learning in growing graphs with increasingly complex tasks. The goal is to continually train a graph model to handle new tasks while retaining its inference ability on previous tasks. Existing methods usually neglect the importance of memory diversity, limiting in effectively selecting high-quality memory from previous tasks and remembering broad previous knowledge within the scarce memory on graphs. To address that, we introduce a novel holistic Diversified Memory Selection and Generation (DMSG) framework for incremental learning in graphs, which first introduces a buffer selection strategy that considers both intra-class and inter-class diversities, employing an efficient greedy algorithm for sampling representative training nodes from graphs into memory buffers after learning each new task. Then, to adequately rememorize the knowledge preserved in the memory buffer when learning new tasks, we propose a diversified memory generation replay method. This method first utilizes a variational layer to generate the distribution of buffer node embeddings and sample synthesized ones for replaying. Furthermore, an adversarial variational embedding learning method and a reconstruction-based decoder are proposed to maintain the integrity and consolidate the generalization of the synthesized node embeddings, respectively. Finally, we evaluate our model on node classification tasks involving increasing class numbers. Extensive experimental results on publicly accessible datasets demonstrate the superiority of DMSG over state-of-the-art methods.">
+        <tr id="This article describes the methods that achieved 4th and 6th place in the forecasting and investment challenges, respectively, of the M6 competition, ultimately securing the 1st place in the overall duathlon ranking. In the forecasting challenge, we tested a novel meta-learning model that utilizes hypernetworks to design a parametric model tailored to a specific family of forecasting tasks. This approach allowed us to leverage similarities observed across individual forecasting tasks while also acknowledging potential heterogeneity in their data generating processes. The model's training can be directly performed with backpropagation, eliminating the need for reliance on higher-order derivatives and is equivalent to a simultaneous search over the space of parametric functions and their optimal parameter values. The proposed model's capabilities extend beyond M6, demonstrating superiority over state-of-the-art meta-learning methods in the sinusoidal regression task and outperforming conventional parametric models on time-series from the M4 competition. In the investment challenge, we adjusted portfolio weights to induce greater or smaller correlation between our submission and that of other participants, depending on the current ranking, aiming to maximize the probability of achieving a good rank.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/b374bc85f787b8f51712f6e8836dd7ab039df455" target='_blank'>
-              Holistic Memory Diversification for Incremental Learning in Growing Graphs
+          <td><a href="https://www.semanticscholar.org/paper/79c059ff368b1797f8ebcd428512691d3f6bcd34" target='_blank'>
+              Designing Time-Series Models With Hypernetworks&Adversarial Portfolios
               </a>
             </td>
           <td>
-            Ziyue Qiao, Junren Xiao, Qingqiang Sun, Meng Xiao, Hui Xiong
+            Filip Stanvek
           </td>
-          <td>2024-06-11</td>
+          <td>2024-07-29</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>9</td>
+          <td>0</td>
         </tr>
 
-        <tr id="We introduce Graph Kolmogorov-Arnold Networks (GKAN), an innovative neural network architecture that extends the principles of the recently proposed Kolmogorov-Arnold Networks (KAN) to graph-structured data. By adopting the unique characteristics of KANs, notably the use of learnable univariate functions instead of fixed linear weights, we develop a powerful model for graph-based learning tasks. Unlike traditional Graph Convolutional Networks (GCNs) that rely on a fixed convolutional architecture, GKANs implement learnable spline-based functions between layers, transforming the way information is processed across the graph structure. We present two different ways to incorporate KAN layers into GKAN: architecture 1 -- where the learnable functions are applied to input features after aggregation and architecture 2 -- where the learnable functions are applied to input features before aggregation. We evaluate GKAN empirically using a semi-supervised graph learning task on a real-world dataset (Cora). We find that architecture generally performs better. We find that GKANs achieve higher accuracy in semi-supervised learning tasks on graphs compared to the traditional GCN model. For example, when considering 100 features, GCN provides an accuracy of 53.5 while a GKAN with a comparable number of parameters gives an accuracy of 61.76; with 200 features, GCN provides an accuracy of 61.24 while a GKAN with a comparable number of parameters gives an accuracy of 67.66. We also present results on the impact of various parameters such as the number of hidden nodes, grid-size, and the polynomial-degree of the spline on the performance of GKAN.">
+        <tr id="This study introduces an innovative deep learning approach for predicting the remaining useful life (RUL) of industrial machinery. Accurate RUL forecasts play a crucial role in enabling proactive maintenance and enhancing operational efficiency within the contexts of Industry 4.0 and 5.0. However, current data-driven models face challenges when dealing with complex, high-dimensional time-series sensor data. To address these obstacles, we present a framework for predicting RUL of industrial equipment, employing variational recurrent neural networks (VRNNs). By harnessing the expressive power of recurrent neural networks and variational inference, VRNNs demonstrate proficiency in modeling temporal relationships and managing intricate, high-dimensional time-series sensor data. This deep learning model represents a significant advancement in data-driven prognostics, providing more robust and interpretable RUL forecasts derived from intricate time-series sensor data. Potential applications encompass predictive maintenance and asset management in industries embracing Industry 4.0 and 5.0 paradigms.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/258641a687096d204cb1e0a0eae5b47f059afa44" target='_blank'>
-              GKAN: Graph Kolmogorov-Arnold Networks
+          <td><a href="https://www.semanticscholar.org/paper/4411fb5e68889eaebadb3fe36a16107e207404ff" target='_blank'>
+              Variational Recurrent Neural Networks (VRNN) for RUL Estimation
               </a>
             </td>
           <td>
-            Mehrdad Kiamari, Mohammad Kiamari, Bhaskar Krishnamachari
+            Amal Ayadi, M. Benatia, Ramzi Chaieb, Anne Louis
           </td>
-          <td>2024-06-10</td>
-          <td>ArXiv</td>
-          <td>8</td>
-          <td>5</td>
+          <td>2024-07-08</td>
+          <td>2024 16th International Conference on Human System Interaction (HSI)</td>
+          <td>0</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Forecasting multivariate time series is a computationally intensive task challenged by extreme or redundant samples. Recent resampling methods aim to increase training efficiency by reweighting samples based on their running losses. However, these methods do not solve the problems caused by heavy-tailed distribution losses, such as overfitting to outliers. To tackle these issues, we introduce a novel approach: a Gaussian loss-weighted sampler that multiplies their running losses with a Gaussian distribution weight. It reduces the probability of selecting samples with very low or very high losses while favoring those close to average losses. As it creates a weighted loss distribution that is not heavy-tailed theoretically, there are several advantages to highlight compared to existing methods: 1) it relieves the inefficiency in learning redundant easy samples and overfitting to outliers, 2) It improves training efficiency by preferentially learning samples close to the average loss. Application on real-world time series forecasting datasets demonstrate improvements in prediction quality for 1%-4% using mean square error measurements in channel-independent settings. The code will be available online after 1 the review.">
+        <tr id="Identification of critical nodes is a prominent topic in the study of complex networks. Numerous methods have been proposed, yet most exhibit inherent limitations. Traditional approaches primarily analyze specific structural features of the network; however, node influence is typically the result of a combination of multiple factors. Machine learning-based methods struggle to effectively represent the complex characteristics of network structures through suitable embedding techniques and require substantial data for training, rendering them prohibitively costly for large-scale networks. To address these challenges, this paper presents an active learning model based on GraphSAGE and Transformer, named GNNTAL. This model is initially pre-trained on random or synthetic networks and subsequently fine-tuned on real-world networks by selecting a few representative nodes using K-Means clustering and uncertainty sampling. This approach offers two main advantages: (1) it significantly reduces training costs; (2) it simultaneously incorporates both local and global features. A series of comparative experiments conducted on twelve real-world networks demonstrate that GNNTAL achieves superior performance. Additionally, this paper proposes an influence maximization method based on the predictions of the GNNTAL model, which achieves optimal performance without the need for complex computations. Finally, the paper analyses certain limitations of the GNNTAL model and suggests potential solutions.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ad56f787b7bab71041c092d434e98cae941c807c" target='_blank'>
-              Robust Time Series Forecasting with Non-Heavy-Tailed Gaussian Loss-Weighted Sampler
+          <td><a href="https://www.semanticscholar.org/paper/f2c2569fd1bd2320230e824c982a501344641e9c" target='_blank'>
+              GNNTAL:A Novel Model for Identifying Critical Nodes in Complex Networks
               </a>
             </td>
           <td>
-            Jiang You, A. Çela, Ren'e Natowicz, Jacob Ouanounou, Patrick Siarry
+            Hao Wang, Ting Luo, Shuang-ping Yang, Ming Jing, Jian Wang, Na Zhao
           </td>
-          <td>2024-06-19</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>20</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Modeling time series data has become a very at tractive research topic due to its wide application, such as human activity recognition, financial forecasting and sensor-based automatic system monitoring. Recently deep learning models have shown great advances in modeling the time series data but they heavily depend on a large amount of labeled data. To avoid costly labeling, this paper explores domain adaptation from a labeled source domain to the unlabeled target domain on time series data. To achieve the goal, we propose a disentangled representation learning framework named CADT to disentangle the domain-invariant features from the domain-specific ones. Particularly, CADT is injected with a novel class-wise hypersphere loss to improve the generalization of the classifier from the source domain to the target domain. Intuitively, it restricts the source data of the same class within the same hypersphere and minimizes the radius of it, which in turn enlarges the margin between different classes and makes the decision boundary of both domains easier. We further devise several kinds of domain-preserving data augmentation methods to better capture the domain-specific patterns. Extensive experiments on two public datasets and two real-world applications demonstrate the effectiveness of the proposed model against several state-of-the-art baselines.">
+        <tr id="Time series analysis is pivotal for business and financial decision making, especially with the increasing integration of the Internet of Things (IoT). However, leveraging time series data for forecasting requires extensive preprocessing to address challenges such as missing values, heteroscedasticity, seasonality, outliers, and noise. Different approaches are necessary for univariate and multivariate time series, Gaussian and non-Gaussian time series, and stationary versus non-stationary time series. Handling missing data alone is complex, demanding unique solutions for each type. Extracting statistical features, identifying data quality issues, and selecting appropriate cleaning and forecasting techniques require significant effort, time, and expertise. To streamline this process, we propose an automated strategy called Preptimize, which integrates statistical and machine learning techniques and recommends prediction model blueprints, suggesting the most suitable approaches for a given dataset as an initial step towards further analysis. Preptimize reads a sample from a large dataset and recommends the blueprint model based on optimization, making it easy to use even for non-experts. The results of various experiments indicated that Preptimize either outperformed or had comparable performance to benchmark models across multiple sectors, including stock prices, cryptocurrency, and power consumption prediction. This demonstrates the framework’s effectiveness in recommending suitable prediction models for various time series datasets, highlighting its broad applicability across different domains in time series forecasting.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a21870156817614d3af47fda7b03e99e6181a852" target='_blank'>
-              Disentangling Domain and General Representations for Time Series Classification
+          <td><a href="https://www.semanticscholar.org/paper/228a2e2a0f2984f0be41b8a4718860d9d8b020d5" target='_blank'>
+              Preptimize: Automation of Time Series Data Preprocessing and Forecasting
               </a>
             </td>
           <td>
-            Youmin Chen, Xinyu Yan, Yang Yang, Jianfeng Zhang, Jing Zhang, Lujia Pan, Juren Li
+            Mehak Usmani, Z. Memon, Adil Zulfiqar, Rizwan Qureshi
           </td>
           <td>2024-08-01</td>
-          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
+          <td>Algorithms</td>
           <td>0</td>
-          <td>6</td>
+          <td>18</td>
         </tr>
 
-        <tr id="In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a multi-task optimization problem as a regularization technique to enable single-task models to leverage multi-task learning information. We derive a closed-form solution for multi-task optimization in the context of linear models. Our analysis provides valuable insights by linking the multi-task learning performance to various model statistics such as raw data covariances, signal-generating hyperplanes, noise levels, as well as the size and number of datasets. We finally propose a consistent estimation of training and testing errors, thereby offering a robust foundation for hyperparameter optimization in multi-task regression scenarios. Experimental validations on both synthetic and real-world datasets in regression and multivariate time series forecasting demonstrate improvements on univariate models, incorporating our method into the training loss and thus leveraging multivariate information.">
+        <tr id="We conducted extensive experiments on domain adaptation of the Meta-Llama-3-70B-Instruct model on SEC data, exploring its performance on both general and domain-specific benchmarks. Our focus included continual pre-training (CPT) and model merging, aiming to enhance the model's domain-specific capabilities while mitigating catastrophic forgetting. Through this study, we evaluated the impact of integrating financial regulatory data into a robust language model and examined the effectiveness of our model merging techniques in preserving and improving the model's instructive abilities. The model is accessible at hugging face: https://huggingface.co/arcee-ai/Llama-3-SEC-Base, arcee-ai/Llama-3-SEC-Base. This is an intermediate checkpoint of our final model, which has seen 20B tokens so far. The full model is still in the process of training. This is a preprint technical report with thorough evaluations to understand the entire process.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/83734272d78baa3517416ebc962bcbb5accc3346" target='_blank'>
-              Analysing Multi-Task Regression via Random Matrix Theory with Application to Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/c6cc3ff91538d584ddfd0c07506ebaf195e5f5ca" target='_blank'>
+              Domain Adaptation of Llama3-70B-Instruct through Continual Pre-Training and Model Merging: A Comprehensive Evaluation
               </a>
             </td>
           <td>
-            Romain Ilbert, Malik Tiomoko, Cosme Louart, Ambroise Odonnat, Vasilii Feofanov, Themis Palpanas, I. Redko
+            Shamane Siriwardhana, Mark McQuade, Thomas Gauthier, Lucas Atkins, Fernando Fernandes Neto, Luke Meyers, Anneketh Vij, Tyler Odenthal, Charles Goddard, Mary MacCarthy, Jacob Solawetz
           </td>
-          <td>2024-06-14</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>49</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Time series forecasting has been an essential field in many different application areas, including economic analysis, meteorology, and so forth. The majority of time series forecasting models are trained using the mean squared error (MSE). However, this training based on MSE causes a limitation known as prediction delay. The prediction delay, which implies the ground-truth precedes the prediction, can cause serious problems in a variety of fields, e.g., finance and weather forecasting -- as a matter of fact, predictions succeeding ground-truth observations are not practically meaningful although their MSEs can be low. This paper proposes a new perspective on traditional time series forecasting tasks and introduces a new solution to mitigate the prediction delay. We introduce a continuous-time gated recurrent unit (GRU) based on the neural ordinary differential equation (NODE) which can supervise explicit time-derivatives. We generalize the GRU architecture in a continuous-time manner and minimize the prediction delay through our time-derivative regularization. Our method outperforms in metrics such as MSE, Dynamic Time Warping (DTW) and Time Distortion Index (TDI). In addition, we demonstrate the low prediction delay of our method in a variety of datasets.">
+        <tr id="With the advancement of deep learning techniques, the performance of Automatic Program Repair(APR) techniques has reached a new level. Previous deep learning-based APR techniques essentially modified program sentences in the Autoregressive(AR) manner, which predicts future values based on past values. Due to the manner of word-by-word generation, the AR-based APR technique has a huge time delay. This negative consequence overshadows the widespread adoption of APR techniques in real-life software development. To address the issue, we aim to apply the Non-Autoregressive(NAR) method to the APR task, which can output target code in a parallel manner to avoid huge inference delays. To effectively adapt the NAR manner for the APR task, we in this paper propose NARRepair, the first customized NAR code generation model for the APR task. The NARRepair features three major novelties, including 1) using repair actions to alleviate the over-correction issue, 2) extracting dependency information from AST to alleviate the issue of lacking inter-word dependency information, 3) employing two-stage decoding to alleviate the issue of lacking contextual information. We evaluated NARRepair on three widely used datasets in the APR community, and the results show that our technique can significantly improve the inference speed while maintaining high repair accuracy.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cb1274dd33e80fab3c983829e9b94abcebe9e2a8" target='_blank'>
-              Addressing Prediction Delays in Time Series Forecasting: A Continuous GRU Approach with Derivative Regularization
+          <td><a href="https://www.semanticscholar.org/paper/385934bd633b36326faa9d91a3be7c7bdd4ef956" target='_blank'>
+              NARRepair: Non-Autoregressive Code Generation Model for Automatic Program Repair
               </a>
             </td>
           <td>
-            Sheo Yon Jhin, Seojin Kim, Noseong Park
+            Zhen Yang, Zhen Yang, Zhongxing Yu
           </td>
-          <td>2024-06-29</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="Generative retrieval has recently emerged as a promising approach to sequential recommendation, framing candidate item retrieval as an autoregressive sequence generation problem. However, existing generative methods typically focus solely on either behavioral or semantic aspects of item information, neglecting their complementary nature and thus resulting in limited effectiveness. To address this limitation, we introduce EAGER, a novel generative recommendation framework that seamlessly integrates both behavioral and semantic information. Specifically, we identify three key challenges in combining these two types of information: a unified generative architecture capable of handling two feature types, ensuring sufficient and independent learning for each type, and fostering subtle interactions that enhance collaborative information utilization. To achieve these goals, we propose (1) a two-stream generation architecture leveraging a shared encoder and two separate decoders to decode behavior tokens and semantic tokens with a confidence-based ranking strategy; (2) a global contrastive task with summary tokens to achieve discriminative decoding for each type of information; and (3) a semantic-guided transfer task designed to implicitly promote cross-interactions through reconstruction and estimation objectives. We validate the effectiveness of EAGER on four public benchmarks, demonstrating its superior performance compared to existing methods.">
+        <tr id="The growing demand for air travel requires technological advancements in air traffic management as well as mechanisms for monitoring and ensuring safe and efficient operations. In terminal airspaces, predictive models of future movements and traffic flows can help with proactive planning and efficient coordination; however, varying airport topologies, and interactions with other agents, among other factors, make accurate predictions challenging. Data-driven predictive models have shown promise for handling numerous variables to enable various downstream tasks, including collision risk assessment, taxi-out time prediction, departure metering, and emission estimations. While data-driven methods have shown improvements in these tasks, prior works lack large-scale curated surface movement datasets within the public domain and the development of generalizable trajectory forecasting models. In response to this, we propose two contributions: (1) Amelia-48, a large surface movement dataset collected using the System Wide Information Management (SWIM) Surface Movement Event Service (SMES). With data collection beginning in Dec 2022, the dataset provides more than a year's worth of SMES data (~30TB) and covers 48 airports within the US National Airspace System. In addition to releasing this data in the public domain, we also provide post-processing scripts and associated airport maps to enable research in the forecasting domain and beyond. (2) Amelia-TF model, a transformer-based next-token-prediction large multi-agent multi-airport trajectory forecasting model trained on 292 days or 9.4 billion tokens of position data encompassing 10 different airports with varying topology. The open-sourced model is validated on unseen airports with experiments showcasing the different prediction horizon lengths, ego-agent selection strategies, and training recipes to demonstrate the generalization capabilities.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/aaa5d85787ce317c83d194f1b4d2ac66fda97b65" target='_blank'>
-              EAGER: Two-Stream Generative Recommender with Behavior-Semantic Collaboration
+          <td><a href="https://www.semanticscholar.org/paper/fe29091a5f28ae9c53d07479551f034ed3c2e387" target='_blank'>
+              Amelia: A Large Model and Dataset for Airport Surface Movement Forecasting
               </a>
             </td>
           <td>
-            Yejin Wang, Jiahao Xun, Mingjie Hong, Jieming Zhu, Tao Jin, Wang Lin, Haoyuan Li, Linjun Li, Yan Xia, Zhou Zhao, Zhenhua Dong
+            Ingrid Navarro, Pablo Ortega-Kral, Jay Patrikar, Haichuan Wang, Zelin Ye, Jong Hoon Park, Jean Oh, Sebastian Scherer
           </td>
-          <td>2024-06-20</td>
+          <td>2024-07-30</td>
           <td>ArXiv</td>
-          <td>1</td>
-          <td>6</td>
+          <td>0</td>
+          <td>8</td>
         </tr>
 
-        <tr id="A common problem of classical neural network architectures is that additional information or expert knowledge cannot be naturally integrated into the learning process. To overcome this limitation, we propose a two-step approach consisting of (1) generating rule functions from knowledge and (2) using these rules to define rule based layers -- a new type of dynamic neural network layer. The focus of this work is on the second step, i.e., rule based layers that are designed to dynamically arrange learnable parameters in the weight matrices and bias vectors depending on the input samples. Indeed, we prove that our approach generalizes classical feed-forward layers such as fully connected and convolutional layers by choosing appropriate rules. As a concrete application we present rule based graph neural networks (RuleGNNs) that overcome some limitations of ordinary graph neural networks. Our experiments show that the predictive performance of RuleGNNs is comparable to state-of-the-art graph classifiers using simple rules based on Weisfeiler-Leman labeling and pattern counting. Moreover, we introduce new synthetic benchmark graph datasets to show how to integrate expert knowledge into RuleGNNs making them more powerful than ordinary graph neural networks.">
+        <tr id="Dynamic graph learning aims to uncover evolutionary laws in real-world systems, enabling accurate social recommendation (link prediction) or early detection of cancer cells (classification). Inspired by the success of state space models, e.g., Mamba, for efficiently capturing long-term dependencies in language modeling, we propose DyG-Mamba, a new continuous state space model (SSM) for dynamic graph learning. Specifically, we first found that using inputs as control signals for SSM is not suitable for continuous-time dynamic network data with irregular sampling intervals, resulting in models being insensitive to time information and lacking generalization properties. Drawing inspiration from the Ebbinghaus forgetting curve, which suggests that memory of past events is strongly correlated with time intervals rather than specific details of the events themselves, we directly utilize irregular time spans as control signals for SSM to achieve significant robustness and generalization. Through exhaustive experiments on 12 datasets for dynamic link prediction and dynamic node classification tasks, we found that DyG-Mamba achieves state-of-the-art performance on most of the datasets, while also demonstrating significantly improved computation and memory efficiency.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/323f07171520382a593da0b618df114653ea4452" target='_blank'>
-              Rule Based Learning with Dynamic (Graph) Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/3cc84a5a1e02661fc3681d8be4134205b0b09954" target='_blank'>
+              DyG-Mamba: Continuous State Space Modeling on Dynamic Graphs
               </a>
             </td>
           <td>
-            Florian Seiffarth
+            Dongyuan Li, Shiyin Tan, Ying Zhang, Ming Jin, Shirui Pan, Manabu Okumura, Renhe Jiang
           </td>
-          <td>2024-06-14</td>
+          <td>2024-08-13</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Representation learning in sequential recommendation is critical for accurately modeling user interaction patterns and improving recommendation precision. However, existing approaches predominantly emphasize item-to-item transitions, often neglecting the time intervals between interactions, which are closely related to behavior pattern changes. Additionally, broader interaction attributes, such as item frequency, are frequently overlooked. We found that both sequences with more uniform time intervals and items with higher frequency yield better prediction performance. Conversely, non-uniform sequences exacerbate user interest drift and less-frequent items are difficult to model due to sparse sampling, presenting unique challenges inadequately addressed by current methods. In this paper, we propose UniRec, a novel bidirectional enhancement sequential recommendation method. UniRec leverages sequence uniformity and item frequency to enhance performance, particularly improving the representation of non-uniform sequences and less-frequent items. These two branches mutually reinforce each other, driving comprehensive performance optimization in complex sequential recommendation scenarios. Additionally, we present a multidimensional time module to further enhance adaptability. To the best of our knowledge, UniRec is the first method to utilize the characteristics of uniformity and frequency for feature augmentation. Comparing with eleven advanced models across four datasets, we demonstrate that UniRec outperforms SOTA models significantly. The code is available at https://github.com/Linxi000/UniRec.">
+        <tr id="Reliable gas price forecasts are an essential information for gas and energy traders, for risk managers and also economists. However, ahead of the war in Ukraine Europe began to suffer from substantially increased and volatile gas prices which culminated in the aftermath of the North Stream 1 explosion. This shock changed both trend and volatility structure of the prices and has considerable effects on forecasting models. In this study we investigate whether modern machine learning methods such as neural networks are more resilient against such changes than statistical models such as autoregressive moving average (ARMA) models with conditional heteroskedasticity, or copula-based time series models. Thereby the focus lies on interval forecasting and applying respective evaluation measures. As data, the Front Month prices from the Dutch Title Transfer Facility, currently the predominant European exchange, are used. We see that, during the shock period, most models underestimate the variance while overestimating the variance in the after-shock period. Furthermore, we recognize that, during the shock, the simpler models, i.e. an ARMA model with conditional heteroskedasticity and the multilayer perceptron (a neural network), perform best with regards to prediction interval coverage. Interestingly, the widely-used long-short term neural network is outperformed by its competitors.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e2fa9684b2eaa24786c3c445f8933d6f75f7921d" target='_blank'>
-              UniRec: A Dual Enhancement of Uniformity and Frequency in Sequential Recommendations
+          <td><a href="https://www.semanticscholar.org/paper/85754bf41e34f87a3356a090d97ccc44867749ef" target='_blank'>
+              Interval Forecasts for Gas Prices in the Face of Structural Breaks -- Statistical Models vs. Neural Networks
               </a>
             </td>
           <td>
-            Yang Liu, Yitong Wang, Chenyue Feng
+            Stephan Schluter, Sven Pappert, Martin Neumann
           </td>
-          <td>2024-06-26</td>
+          <td>2024-07-23</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Self-supervised contrastive learning has become a key technique in deep learning, particularly in time series analysis, due to its ability to learn meaningful representations without explicit supervision. Augmentation is a critical component in contrastive learning, where different augmentations can dramatically impact performance, sometimes influencing accuracy by over 30%. However, the selection of augmentations is predominantly empirical which can be suboptimal, or grid searching that is time-consuming. In this paper, we establish a principled framework for selecting augmentations based on dataset characteristics such as trend and seasonality. Specifically, we construct 12 synthetic datasets incorporating trend, seasonality, and integration weights. We then evaluate the effectiveness of 8 different augmentations across these synthetic datasets, thereby inducing generalizable associations between time series characteristics and augmentation efficiency. Additionally, we evaluated the induced associations across 6 real-world datasets encompassing domains such as activity recognition, disease diagnosis, traffic monitoring, electricity usage, mechanical fault prognosis, and finance. These real-world datasets are diverse, covering a range from 1 to 12 channels, 2 to 10 classes, sequence lengths of 14 to 1280, and data frequencies from 250 Hz to daily intervals. The experimental results show that our proposed trend-seasonality-based augmentation recommendation algorithm can accurately identify the effective augmentations for a given time series dataset, achieving an average Recall@3 of 0.667, outperforming baselines. Our work provides guidance for studies employing contrastive learning in time series analysis, with wide-ranging applications. All the code, datasets, and analysis results will be released at https://github.com/DL4mHealth/TS-Contrastive-Augmentation-Recommendation.">
+        <tr id="In this paper, we apply a supervised machine-learning approach to solve a fundamental problem in queueing theory: estimating the transient distribution of the number in the system for a G(t)/GI/1. We develop a neural network mechanism that provides a fast and accurate predictor of these distributions for moderate horizon lengths and practical settings. It is based on using a Recurrent Neural Network (RNN) architecture based on the first several moments of the time-dependant inter-arrival and the stationary service time distributions; we call it the Moment-Based Recurrent Neural Network (RNN) method (MBRNN ). Our empirical study suggests MBRNN requires only the first four inter-arrival and service time moments. We use simulation to generate a substantial training dataset and present a thorough performance evaluation to examine the accuracy of our method using two different test sets. We show that even under the configuration with the worst performance errors, the mean number of customers over the entire timeline has an error of less than 3%. While simulation modeling can achieve high accuracy, the advantage of the MBRNN over simulation is runtime, while the MBRNN analyzes hundreds of systems within a fraction of a second. This paper focuses on a G(t)/GI/1; however, the MBRNN approach demonstrated here can be extended to other queueing systems, as the training data labeling is based on simulations (which can be applied to more complex systems) and the training is based on deep learning, which can capture very complex time sequence tasks. In summary, the MBRNN can potentially revolutionize our ability to perform transient analyses of queueing systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8f81988b1b5f7abf716ef2eabd113a123b5df9c7" target='_blank'>
-              Guidelines for Augmentation Selection in Contrastive Learning for Time Series Classification
+          <td><a href="https://www.semanticscholar.org/paper/f691dfd4dff3b3fb9b91bf5e89d6572368165f58" target='_blank'>
+              Approximating G(t)/GI/1 queues with deep learning
               </a>
             </td>
           <td>
-            Ziyu Liu, Azadeh Alavi, Minyi Li, Xiang Zhang
+            Eliran Sherzer, Opher Baron, Dmitry Krass, Yehezkel S. Resheff
           </td>
-          <td>2024-07-12</td>
+          <td>2024-07-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>14</td>
         </tr>
 
-        <tr id="Attention-based models such as Transformers and recurrent models like state space models (SSMs) have emerged as successful methods for autoregressive sequence modeling. Although both enable parallel training, none enable parallel generation due to their autoregressiveness. We propose the variational SSM (VSSM), a variational autoencoder (VAE) where both the encoder and decoder are SSMs. Since sampling the latent variables and decoding them with the SSM can be parallelized, both training and generation can be conducted in parallel. Moreover, the decoder recurrence allows generation to be resumed without reprocessing the whole sequence. Finally, we propose the autoregressive VSSM that can be conditioned on a partial realization of the sequence, as is common in language generation tasks. Interestingly, the autoregressive VSSM still enables parallel generation. We highlight on toy problems (MNIST, CIFAR) the empirical gains in speed-up and show that it competes with traditional models in terms of generation quality (Transformer, Mamba SSM).">
+        <tr id="Generating synthetic financial time series data that accurately reflects real-world market dynamics holds tremendous potential for various applications, including portfolio optimization, risk management, and large scale machine learning. We present an approach for training generative models for financial time series using the maximum mean discrepancy (MMD) with a signature kernel. Our method leverages the expressive power of the signature transform to capture the complex dependencies and temporal structures inherent in financial data. We employ a moving average model to model the variance of the noise input, enhancing the model's ability to reproduce stylized facts such as volatility clustering. Through empirical experiments on S&P 500 index data, we demonstrate that our model effectively captures key characteristics of financial time series and outperforms a comparable GAN-based approach. In addition, we explore the application of the synthetic data generated to train a reinforcement learning agent for portfolio management, achieving promising results. Finally, we propose a method to add robustness to the generative model by tweaking the noise input so that the generated sequences can be adjusted to different market environments with minimal data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c788a35c2dcda370161d8beda4525409126416c4" target='_blank'>
-              Parallelizing Autoregressive Generation with Variational State Space Models
+          <td><a href="https://www.semanticscholar.org/paper/492d244da8647554a7439883786cfe931ec4c342" target='_blank'>
+              Generative model for financial time series trained with MMD using a signature kernel
               </a>
             </td>
           <td>
-            Gaspard Lambrechts, Yann Claes, Pierre Geurts, Damien Ernst
+            Chung I Lu, Julian Sester
           </td>
-          <td>2024-07-11</td>
+          <td>2024-07-29</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>0</td>
         </tr>
 
-        <tr id="In sequential event prediction, which finds applications in finance, retail, social networks, and healthcare, a crucial task is forecasting multiple future events within a specified time horizon. Traditionally, this has been addressed through autoregressive generation using next-event prediction models, such as Marked Temporal Point Processes. However, autoregressive methods use their own output for future predictions, potentially reducing quality as the prediction horizon extends. In this paper, we challenge traditional approaches by introducing a novel benchmark, HoTPP, specifically designed to evaluate a model's ability to predict event sequences over a horizon. This benchmark features a new metric inspired by object detection in computer vision, addressing the limitations of existing metrics in assessing models with imprecise time-step predictions. Our evaluations on established datasets employing various models demonstrate that high accuracy in next-event prediction does not necessarily translate to superior horizon prediction, and vice versa. HoTPP aims to serve as a valuable tool for developing more robust event sequence prediction methods, ultimately paving the way for further advancements in the field.">
+        <tr id="Continual Test-Time Adaptation (CTTA) involves adapting a pre-trained source model to continually changing unsupervised target domains. In this paper, we systematically analyze the challenges of this task: online environment, unsupervised nature, and the risks of error accumulation and catastrophic forgetting under continual domain shifts. To address these challenges, we reshape the online data buffering and organizing mechanism for CTTA. We propose an uncertainty-aware buffering approach to identify and aggregate significant samples with high certainty from the unsupervised, single-pass data stream. Based on this, we propose a graph-based class relation preservation constraint to overcome catastrophic forgetting. Furthermore, a pseudo-target replay objective is used to mitigate error accumulation. Extensive experiments demonstrate the superiority of our method in both segmentation and classification CTTA tasks. Code is available at https://github.com/z1358/OBAO.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5c0701f646c8eaac8073e437a46b0dddf2f8bc4f" target='_blank'>
-              HoTPP Benchmark: Are We Good at the Long Horizon Events Forecasting?
+          <td><a href="https://www.semanticscholar.org/paper/255e2aee4d754b98a3c9ead9618e48e3d9906ffe" target='_blank'>
+              Reshaping the Online Data Buffering and Organizing Mechanism for Continual Test-Time Adaptation
               </a>
             </td>
           <td>
-            Ivan Karpukhin, F. Shipilov, Andrey Savchenko
+            Zhilin Zhu, Xiaopeng Hong, Zhiheng Ma, Weijun Zhuang, Yaohui Ma, Yong Dai, Yaowei Wang
           </td>
-          <td>2024-06-20</td>
+          <td>2024-07-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>20</td>
         </tr>
 
-        <tr id="Multitude of deep learning models have been proposed for node classification in graphs. However, they tend to perform poorly under labeled-data scarcity. Although Few-shot learning for graphs has been introduced to overcome this problem, the existing models are not easily adaptable for generic graph learning frameworks like Graph Neural Networks (GNNs). Our work proposes an Uncertainty Estimator framework that can be applied on top of any generic GNN backbone network (which are typically designed for supervised/semi-supervised node classification) to improve the node classification performance. A neural network is used to model the Uncertainty Estimator as a probability distribution rather than probabilistic discrete scalar values. We train these models under the classic episodic learning paradigm in the $n$-way, $k$-shot fashion, in an end-to-end setting. Our work demonstrates that implementation of the uncertainty estimator on a GNN backbone network improves the classification accuracy under Few-shot setting without any meta-learning specific architecture. We conduct experiments on multiple datasets under different Few-shot settings and different GNN-based backbone networks. Our method outperforms the baselines, which demonstrates the efficacy of the Uncertainty Estimator for Few-shot node classification on graphs with a GNN.">
+        <tr id="Clinical trials need to recruit a sufficient number of volunteer patients to demonstrate the statistical power of the treatment (e.g., a new drug) in curing a certain disease. Clinical trial recruitment has a significant impact on trial success. Forecasting whether the recruitment process would be successful before we run the trial would save many resources and time. This paper develops a novel deep&cross network with large language model (LLM)-augmented text feature that learns semantic information from trial eligibility criteria and predicts enrollment success. The proposed method enables interpretability by understanding which sentence/word in eligibility criteria contributes heavily to prediction. We also demonstrate the empirical superiority of the proposed method (0.7002 PR-AUC) over a bunch of well-established machine learning methods. The code and curated dataset are publicly available at https://anonymous.4open.science/r/TrialEnroll-7E12.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8f1d410b4425cdef16d471b94e04bcfb4af0ef26" target='_blank'>
-              Graph Mining under Data scarcity
+          <td><a href="https://www.semanticscholar.org/paper/8b0084ee93fc8c700058b3d5d2d7c58de05f753a" target='_blank'>
+              TrialEnroll: Predicting Clinical Trial Enrollment Success with Deep&Cross Network and Large Language Models
               </a>
             </td>
           <td>
-            Appan Rakaraddi, Lam Siew-Kei, Mahardhika Pratama, Marcus Vinícius de Carvalho
+            Ling Yue, Sixue Xing, Jintai Chen, Tianfan Fu
           </td>
-          <td>2024-06-07</td>
+          <td>2024-07-18</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>4</td>
+          <td>1</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Performance prediction is a method to estimate the performance of Language Models (LMs) on various Natural Language Processing (NLP) tasks, mitigating computational costs associated with model capacity and data for fine-tuning. Our paper introduces ProxyLM, a scalable framework for predicting LM performance using proxy models in multilingual tasks. These proxy models act as surrogates, approximating the performance of the LM of interest. By leveraging proxy models, ProxyLM significantly reduces computational overhead on task evaluations, achieving up to a 37.08x speedup compared to traditional methods, even with our smallest proxy models. Additionally, our methodology showcases adaptability to previously unseen languages in pre-trained LMs, outperforming the state-of-the-art performance by 1.89x as measured by root-mean-square error (RMSE). This framework streamlines model selection, enabling efficient deployment and iterative LM enhancements without extensive computational resources.">
+        <tr id="Modern vehicles rely on a myriad of electronic control units (ECUs) interconnected via controller area networks (CANs) for critical operations. Despite their ubiquitous use and reliability, CANs are susceptible to sophisticated cyberattacks, particularly masquerade attacks, which inject false data that mimic legitimate messages at the expected frequency. These attacks pose severe risks such as unintended acceleration, brake deactivation, and rogue steering. Traditional intrusion detection systems (IDS) often struggle to detect these subtle intrusions due to their seamless integration into normal traffic. This paper introduces a novel framework for detecting masquerade attacks in the CAN bus using graph machine learning (ML). We hypothesize that the integration of shallow graph embeddings with time series features derived from CAN frames enhances the detection of masquerade attacks. We show that by representing CAN bus frames as message sequence graphs (MSGs) and enriching each node with contextual statistical attributes from time series, we can enhance detection capabilities across various attack patterns compared to using only graph-based features. Our method ensures a comprehensive and dynamic analysis of CAN frame interactions, improving robustness and efficiency. Extensive experiments on the ROAD dataset validate the effectiveness of our approach, demonstrating statistically significant improvements in the detection rates of masquerade attacks compared to a baseline that uses only graph-based features, as confirmed by Mann-Whitney U and Kolmogorov-Smirnov tests (p<0.05).">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2b0ce68cae4203c9f2785b4ce83d0b3aff0017a5" target='_blank'>
-              ProxyLM: Predicting Language Model Performance on Multilingual Tasks via Proxy Models
+          <td><a href="https://www.semanticscholar.org/paper/31a90fb5c4f3760898c538549095797acfa7f429" target='_blank'>
+              Detecting Masquerade Attacks in Controller Area Networks Using Graph Machine Learning
               </a>
             </td>
           <td>
-            David Anugraha, Genta Indra Winata, Chenyue Li, Patrick Amadeus Irawan, En-Shiun Annie Lee
+            William Marfo, P. Moriano, Deepak K. Tosh, Shirley V. Moore
           </td>
-          <td>2024-06-13</td>
+          <td>2024-08-10</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>33</td>
+          <td>8</td>
         </tr>
 
-        <tr id="We introduce Mini-Sequence Transformer (MsT), a simple and effective methodology for highly efficient and accurate LLM training with extremely long sequences. MsT partitions input sequences and iteratively processes mini-sequences to reduce intermediate memory usage. Integrated with activation recomputation, it enables significant memory savings in both forward and backward passes. In experiments with the Llama3-8B model, with MsT, we measure no degradation in throughput or convergence even with 12x longer sequences than standard implementations due to our careful memory optimizations. MsT is fully general, implementation-agnostic, and requires minimal code changes to integrate with existing LLM training frameworks.">
+        <tr id="Accurate modeling of car-following behaviors is essential for various applications in traffic management and autonomous driving systems. However, current approaches often suffer from limitations like high sensitivity to data quality and lack of interpretability. In this study, we propose GenFollower, a novel zero-shot prompting approach that leverages large language models (LLMs) to address these challenges. We reframe car-following behavior as a language modeling problem and integrate heterogeneous inputs into structured prompts for LLMs. This approach achieves improved prediction performance and interpretability compared to traditional baseline models. Experiments on the Waymo Open datasets demonstrate GenFollower's superior performance and ability to provide interpretable insights into factors influencing car-following behavior. This work contributes to advancing the understanding and prediction of car-following behaviors, paving the way for enhanced traffic management and autonomous driving systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6aca00d4d0c8e86a908a15659855ada4ed65eddb" target='_blank'>
-              MINI-SEQUENCE TRANSFORMER: Optimizing Intermediate Memory for Long Sequences Training
+          <td><a href="https://www.semanticscholar.org/paper/3c2dc1a2b947f863938dfbf2e05352e7bff43498" target='_blank'>
+              GenFollower: Enhancing Car-Following Prediction with Large Language Models
               </a>
             </td>
           <td>
-            Cheng Luo, Jiawei Zhao, Zhuoming Chen, Beidi Chen, A. Anandkumar
+            Xianda Chen, Mingxing Peng, PakHin Tiu, Yuanfei Wu, Junjie Chen, Meixin Zhu, Xinhu Zheng
           </td>
-          <td>2024-07-22</td>
+          <td>2024-07-08</td>
           <td>ArXiv</td>
+          <td>2</td>
+          <td>5</td>
+        </tr>
+
+        <tr id="None">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/24a196d9ee7fda6754365bee42a89aa1d9add80b" target='_blank'>
+              Generalized spatial–temporal regression graph convolutional transformer for traffic forecasting
+              </a>
+            </td>
+          <td>
+            Lang Xiong, Liyun Su, Shiyi Zeng, Xiangjing Li, Tong Wang, Feng Zhao
+          </td>
+          <td>2024-08-10</td>
+          <td>Complex &amp; Intelligent Systems</td>
+          <td>0</td>
           <td>0</td>
-          <td>6</td>
         </tr>
 
-        <tr id="Long sequences occur in abundance within real-world scenarios, hence properly modelling them opens numerous down-stream use-cases. Deep neural networks, however, have often struggled with these for a variety of reasons. Recent advances, both in system engineering as well as model design, have enabled the scaling up of model that are purported to support extended context length. In particular, the state-space and linear recurrent neural network families of models hypothetically can entend to infinite sequence lenth. However, is this too good to be true? We conduct an evaluation to show that while such claims may be sound theoretically, there remain large practical gaps that are empirically observed. In particular, recurrent models still suffer in the same settings as long-context LLMs with attention. We further show that different inductive biases have inconsistent extrapolation capabilities, highlighting the need to further study such paradigms and investigate why long-context models seemingly fail to behave as one might expect.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fa2f8963df88d8684b38c33aa59cc3ae0927561b" target='_blank'>
-              How Well Can a Long Sequence Model Model Long Sequences? Comparing Architechtural Inductive Biases on Long-Context Abilities
+          <td><a href="https://www.semanticscholar.org/paper/4ccc940a891f74aa82e4a858d918d21d59774433" target='_blank'>
+              A binary-domain recurrent-like architecture-based dynamic graph neural network
               </a>
             </td>
           <td>
-            Jerry Huang
+            Zi-chao Chen, Sui Lin
           </td>
-          <td>2024-07-11</td>
-          <td>ArXiv</td>
+          <td>2024-06-25</td>
+          <td>Auton. Intell. Syst.</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Time series prediction is a basic regression task in data mining, and the research of traditional methods, machine learning and deep learning has made great progress in this area. In this paper, starting from the concept of long time series, feature extraction and other related techniques and data series prediction methods, we introduce the current research status of deep learning networks in time series data and analyze the application of deep learning networks in time series prediction.">
+        <tr id="The dynamic characteristics of multiphase industrial processes present significant challenges in the field of industrial big data modeling. Traditional soft sensing models frequently neglect the process dynamics and have difficulty in capturing transient phenomena like phase transitions. To address this issue, this article introduces a causality-driven sequence segmentation (CDSS) model. This model first identifies the local dynamic properties of the causal relationships between variables, which are also referred to as causal mechanisms. It then segments the sequence into different phases based on the sudden shifts in causal mechanisms that occur during phase transitions. Additionally, a novel metric, similarity distance, is designed to evaluate the temporal consistency of causal mechanisms, which includes both causal similarity distance and stable similarity distance. The discovered causal relationships in each phase are represented as a temporal causal graph (TCG). Furthermore, a soft sensing model called temporal-causal graph convolutional network (TC-GCN) is trained for each phase, by using the time-extended data and the adjacency matrix of TCG. The numerical examples are utilized to validate the proposed CDSS model, and the segmentation results demonstrate that CDSS has excellent performance on segmenting both stable and unstable multiphase series. Especially, it has higher accuracy in separating non-stationary time series compared to other methods. The effectiveness of the proposed CDSS model and the TC-GCN model is also verified through a penicillin fermentation process. Experimental results indicate that the breakpoints discovered by CDSS align well with the reaction mechanisms and TC-GCN significantly has excellent predictive accuracy.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8527d89e646358076fca533139f3e8b5af466134" target='_blank'>
-              Bi-directional LSTM-GRU Based Time Series Forecasting Approach
+          <td><a href="https://www.semanticscholar.org/paper/f4b2b1a8bce30a394b4fb8eac0b13365c9a406b2" target='_blank'>
+              Causality-driven Sequence Segmentation for Enhancing Multiphase Industrial Process Data Analysis and Soft Sensing
               </a>
             </td>
           <td>
-            Bo He, Longbing Li, Yunya Bo, Jingxuan Zhou
+            Yimeng He, Le Yao, Xinmin Zhang, Xiangyin Kong, Zhihuan Song
           </td>
-          <td>2024-07-19</td>
-          <td>International Journal of Computer Science and Information Technology</td>
+          <td>2024-06-30</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>7</td>
         </tr>
 
-        <tr id="AI systems are notorious for their fragility; minor input changes can potentially cause major output swings. When such systems are deployed in critical areas like finance, the consequences of their uncertain behavior could be severe. In this paper, we focus on multi-modal time-series forecasting, where imprecision due to noisy or incorrect data can lead to erroneous predictions, impacting stakeholders such as analysts, investors, and traders. Recently, it has been shown that beyond numeric data, graphical transformations can be used with advanced visual models to achieve better performance. In this context, we introduce a rating methodology to assess the robustness of Multi-Modal Time-Series Forecasting Models (MM-TSFM) through causal analysis, which helps us understand and quantify the isolated impact of various attributes on the forecasting accuracy of MM-TSFM. We apply our novel rating method on a variety of numeric and multi-modal forecasting models in a large experimental setup (six input settings of control and perturbations, ten data distributions, time series from six leading stocks in three industries over a year of data, and five time-series forecasters) to draw insights on robust forecasting models and the context of their strengths. Within the scope of our study, our main result is that multi-modal (numeric + visual) forecasting, which was found to be more accurate than numeric forecasting in previous studies, can also be more robust in diverse settings. Our work will help different stakeholders of time-series forecasting understand the models` behaviors along trust (robustness) and accuracy dimensions to select an appropriate model for forecasting using our rating method, leading to improved decision-making.">
+        <tr id="
+ One of the core assumptions of most deep-learning-based data-driven models is that samples are independent. However, this assumption poses a key challenge in production forecasting—performance is influenced by well interference and reservoir connectivity. Most shale gas wells are hydraulically fractured and exist in complex fracture systems, and the neighboring well characteristics should also be considered when constructing data-driven forecast models. Researchers have explored using the graph convolutional network (GCN) to address this issue by incorporating neighboring well characteristics into production forecasting models. However, applying GCN to field-scale studies is problematic, as it requires training on a full batch, leading to gigantic cache allocation. In addition, the transductive nature of GCN poses challenges for direct generalization to unseen nodes. To overcome these limitations, we adopt the graph sampling and aggregation (GraphSAGE) network architecture, which allows training large graphs with batches and generalizing predictions for previously unseen nodes. By utilizing the gated recurrent unit (GRU) network, the proposed spatial-temporal (ST)-GraphSAGE model can capture cross-time relationships between the target and the neighboring wells and generate promising prediction time series for the target wells, even if they are newly drilled wells.
+ The proposed approach is validated and tested using the field data from 2,240 Montney shale gas wells, including formation properties, hydraulic fracture parameters, production history, and operational data. The algorithm aggregates the first-hop information to the target node for each timestep. The encoder-decoder (ED) architecture is used to generate forecasts for the subsequent 3-year production rate by using the 1-year production history of the wells. The trained model enables the evaluation of production predictions for newly developed wells at any location. We evaluate the model’s performance using P10, P50, and P90 of the test data set’s root mean square error (RMSE). Our method preserves the topological characteristics of wells and generalizes the prediction to unseen nodes while significantly reducing training complexity, making it applicable to larger data sets. By incorporating information from adjacent wells and integrating ST data, our ST-GraphSAGE model outperforms the traditional GRU-ED model and shows enhanced interpretability.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1d6d01816a36ea78b2c97fe4fbd6ed4dddec8d71" target='_blank'>
-              Rating Multi-Modal Time-Series Forecasting Models (MM-TSFM) for Robustness Through a Causal Lens
+          <td><a href="https://www.semanticscholar.org/paper/3acb14c12dea5fe005f993df58cb0487b23127f2" target='_blank'>
+              Shale Gas Production Forecasting with Well Interference Based on Spatial-Temporal Graph Convolutional Network
               </a>
             </td>
           <td>
-            Kausik Lakkaraju, Rachneet Kaur, Zhen Zeng, Parisa Zehtabi, Sunandita Patra, Biplav Srivastava, Marco Valtorta
+            Ziming Xu, Juliana Y. Leung
           </td>
-          <td>2024-06-12</td>
-          <td>ArXiv</td>
+          <td>2024-07-01</td>
+          <td>SPE Journal</td>
           <td>0</td>
-          <td>7</td>
+          <td>2</td>
         </tr>
 
-        <tr id="The goal of stock trend prediction is to forecast future market movements for informed investment decisions. Existing methods mostly focus on predicting stock trends with supervised models trained on extensive annotated data. However, human annotation can be resource-intensive and the annotated data are not readily available. Inspired by the impressive few-shot capability of Large Language Models (LLMs), we propose using LLMs in a few-shot setting to overcome the scarcity of labeled data and make prediction more feasible to investors. Previous works typically merge multiple financial news for predicting stock trends, causing two significant problems when using LLMs: (1) Merged news contains noise, and (2) it may exceed LLMs' input limits, leading to performance degradation. To overcome these issues, we propose a two-step method 'denoising-then-voting'. Specifically, we introduce an `Irrelevant' category, and predict stock trends for individual news instead of merged news. Then we aggregate these predictions using majority voting. The proposed method offers two advantages: (1) Classifying noisy news as irrelevant removes its impact on the final prediction. (2) Predicting for individual news mitigates LLMs' input length limits. Our method achieves 66.59% accuracy in S&P 500, 62.17% in CSI-100, and 61.17% in HK stock prediction, outperforming the standard few-shot counterparts by around 7%, 4%, and 4%. Furthermore, our proposed method performs on par with state-of-the-art supervised methods.">
+        <tr id="Understanding causal relationships between machines is crucial for fault diagnosis and optimization in manufacturing processes. Real-world datasets frequently exhibit up to 90% missing data and high dimensionality from hundreds of sensors. These datasets also include domain-specific expert knowledge and chronological order information, reflecting the recording order across different machines, which is pivotal for discerning causal relationships within the manufacturing data. However, previous methods for handling missing data in scenarios akin to real-world conditions have not been able to effectively utilize expert knowledge. Conversely, prior methods that can incorporate expert knowledge struggle with datasets that exhibit missing values. Therefore, we propose COKE to construct causal graphs in manufacturing datasets by leveraging expert knowledge and chronological order among sensors without imputing missing data. Utilizing the characteristics of the recipe, we maximize the use of samples with missing values, derive embeddings from intersections with an initial graph that incorporates expert knowledge and chronological order, and create a sensor ordering graph. The graph-generating process has been optimized by an actor-critic architecture to obtain a final graph that has a maximum reward. Experimental evaluations in diverse settings of sensor quantities and missing proportions demonstrate that our approach compared with the benchmark methods shows an average improvement of 39.9% in the F1-score. Moreover, the F1-score improvement can reach 62.6% when considering the configuration similar to real-world datasets, and 85.0% in real-world semiconductor datasets. The source code is available at https://github.com/OuTingYun/COKE.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/69ec9e81b1d4ced8ceb0214bdf33e38627aa5f5c" target='_blank'>
-              Enhancing Few-Shot Stock Trend Prediction with Large Language Models
+          <td><a href="https://www.semanticscholar.org/paper/01c7381bbb5f5ffdc2ffb14208944e6202b5a8e9" target='_blank'>
+              COKE: Causal Discovery with Chronological Order and Expert Knowledge in High Proportion of Missing Manufacturing Data
               </a>
             </td>
           <td>
-            Yiqi Deng, Xingwei He, Jiahao Hu, S.M. Yiu
+            Ting-Yun Ou, Ching Chang, Wen-Chih Peng
           </td>
-          <td>2024-07-12</td>
+          <td>2024-07-17</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>2</td>
         </tr>
 
-        <tr id="The modern autoregressive Large Language Models (LLMs) have achieved outstanding performance on NLP benchmarks, and they are deployed in the real world. However, they still suffer from limitations of the autoregressive training paradigm. For example, autoregressive token generation is notably slow and can be prone to \textit{exposure bias}. The diffusion-based language models were proposed as an alternative to autoregressive generation to address some of these limitations. We evaluate the recently proposed Score Entropy Discrete Diffusion (SEDD) approach and show it is a promising alternative to autoregressive generation but it has some short-comings too. We empirically demonstrate the advantages and challenges of SEDD, and observe that SEDD generally matches autoregressive models in perplexity and on benchmarks such as HellaSwag, Arc or WinoGrande. Additionally, we show that in terms of inference latency, SEDD can be up to 4.5$\times$ more efficient than GPT-2. While SEDD allows conditioning on tokens at abitrary positions, SEDD appears slightly weaker than GPT-2 for conditional generation given short prompts. Finally, we reproduced the main results from the original SEDD paper.">
+        <tr id="Long-term time series forecasting is a long-standing challenge in various applications. A central issue in time series forecasting is that methods should expressively capture long-term dependency. Furthermore, time series forecasting methods should be flexible when applied to different scenarios. Although Fourier analysis offers an alternative to effectively capture reusable and periodic patterns to achieve long-term forecasting in different scenarios, existing methods often assume high-frequency components represent noise and should be discarded in time series forecasting. However, we conduct a series of motivation experiments and discover that the role of certain frequencies varies depending on the scenarios. In some scenarios, removing high-frequency components from the original time series can improve the forecasting performance, while in others scenarios, removing them is harmful to forecasting performance. Therefore, it is necessary to treat the frequencies differently according to specific scenarios. To achieve this, we first reformulate the time series forecasting problem as learning a transfer function of each frequency in the Fourier domain. Further, we design Frequency Dynamic Fusion (FreDF), which individually predicts each Fourier component, and dynamically fuses the output of different frequencies. Moreover, we provide a novel insight into the generalization ability of time series forecasting and propose the generalization bound of time series forecasting. Then we prove FreDF has a lower bound, indicating that FreDF has better generalization ability. Extensive experiments conducted on multiple benchmark datasets and ablation studies demonstrate the effectiveness of FreDF.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c80e4529318d9cbfb6d8f8dd80b74cb69d3129b3" target='_blank'>
-              Promises, Outlooks and Challenges of Diffusion Language Modeling
+          <td><a href="https://www.semanticscholar.org/paper/180860f60e6655bebc9757b695b4fbc18a0c39ee" target='_blank'>
+              Not All Frequencies Are Created Equal:Towards a Dynamic Fusion of Frequencies in Time-Series Forecasting
               </a>
             </td>
           <td>
-            Justin Deschenaux, Caglar Gulcehre
+            Xingyu Zhang, Siyu Zhao, Zeen Song, Huijie Guo, Jianqi Zhang, Changwen Zheng, Wenwen Qiang
           </td>
-          <td>2024-06-17</td>
+          <td>2024-07-17</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
+          <td>8</td>
         </tr>
 
-        <tr id="Recently, multiple models proposed for link prediction (LP) demonstrate impressive results on benchmark datasets. However, many popular benchmark datasets often assume that dataset samples are drawn from the same distribution (i.e., IID samples). In real-world situations, this assumption is often incorrect; since uncontrolled factors may lead train and test samples to come from separate distributions. To tackle the distribution shift problem, recent work focuses on creating datasets that feature distribution shifts and designing generalization methods that perform well on the new data. However, those studies only consider distribution shifts that affect {\it node-} and {\it graph-level} tasks, thus ignoring link-level tasks. Furthermore, relatively few LP generalization methods exist. To bridge this gap, we introduce a set of LP-specific data splits which utilizes structural properties to induce a controlled distribution shift. We verify the shift's effect empirically through evaluation of different SOTA LP methods and subsequently couple these methods with generalization techniques. Interestingly, LP-specific methods frequently generalize poorly relative to heuristics or basic GNN methods. Finally, this work provides analysis to uncover insights for enhancing LP generalization. Our code is available at: \href{https://github.com/revolins/LPStructGen}{https://github.com/revolins/LPStructGen}">
+        <tr id="We present working notes for DS@GT team in the eRisk 2024 for Tasks 1 and 3. We propose a ranking system for Task 1 that predicts symptoms of depression based on the Beck Depression Inventory (BDI-II) questionnaire using binary classifiers trained on question relevancy as a proxy for ranking. We find that binary classifiers are not well calibrated for ranking, and perform poorly during evaluation. For Task 3, we use embeddings from BERT to predict the severity of eating disorder symptoms based on user post history. We find that classical machine learning models perform well on the task, and end up competitive with the baseline models. Representation of text data is crucial in both tasks, and we find that sentence transformers are a powerful tool for downstream modeling. Source code and models are available at \url{https://github.com/dsgt-kaggle-clef/erisk-2024}.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ab05a23225a9dda684892f106820bcee73d616f1" target='_blank'>
-              Understanding the Generalizability of Link Predictors Under Distribution Shifts on Graphs
+          <td><a href="https://www.semanticscholar.org/paper/ca43005a97c3f1e83533ca7844c05d8888da1f70" target='_blank'>
+              DS@GT eRisk 2024: Sentence Transformers for Social Media Risk Assessment
               </a>
             </td>
           <td>
-            Jay Revolinsky, Harry Shomer, Jiliang Tang
+            David Guecha, Aaryan Potdar, Anthony Miyaguchi
           </td>
-          <td>2024-06-13</td>
-          <td>ArXiv</td>
+          <td>2024-07-10</td>
+          <td>ArXiv, DBLP</td>
+          <td>0</td>
           <td>0</td>
-          <td>4</td>
         </tr>
 
-        <tr id="With the advent of large models based on the Transformer architecture, researchers have observed an anomalous phenomenon in the Attention mechanism--there is a very high attention on the first element, which is prevalent across Transformer-based models. It is crucial to understand it for the development of techniques focusing on attention distribution, such as Key-Value (KV) Cache compression and infinite extrapolation; however, the latent cause leaves to be unknown. In this paper, we analyze such a phenomenon from the perspective of waiver phenomenon, which involves reducing the internal values of certain elements in the sequence, allowing them to absorb excess attention without affecting their contribution to information. In specific models, due to differences in positional encoding and attention patterns, we have found that the selection of waiver elements by the model can be categorized into two methods: positional-encoding-based and feature-distribution-within-elements-based.">
+        <tr id="Visual analytics is essential for studying large time series due to its ability to reveal trends, anomalies, and insights. DeepVATS is a tool that merges Deep Learning (Deep) with Visual Analytics (VA) for the analysis of large time series data (TS). It has three interconnected modules. The Deep Learning module, developed in R, manages the load of datasets and Deep Learning models from and to the Storage module. This module also supports models training and the acquisition of the embeddings from the latent space of the trained model. The Storage module operates using the Weights and Biases system. Subsequently, these embeddings can be analyzed in the Visual Analytics module. This module, based on an R Shiny application, allows the adjustment of the parameters related to the projection and clustering of the embeddings space. Once these parameters are set, interactive plots representing both the embeddings, and the time series are shown. This paper introduces the tool and examines its scalability through log analytics. The execution time evolution is examined while the length of the time series is varied. This is achieved by resampling a large data series into smaller subsets and logging the main execution and rendering times for later analysis of scalability.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cb15472f8041a122fac2d0004d34596990719a33" target='_blank'>
-              Unveiling and Controlling Anomalous Attention Distribution in Transformers
+          <td><a href="https://www.semanticscholar.org/paper/4512438def79546a16c0581fc3e2b73339d52b93" target='_blank'>
+              Exploring Scalability in Large-Scale Time Series in DeepVATS framework
               </a>
             </td>
           <td>
-            Ruiqing Yan, Xingbo Du, Haoyu Deng, Linghan Zheng, Qiuzhuang Sun, Jifang Hu, Yuhang Shao, Penghao Jiang, Jinrong Jiang, Lian Zhao
+            Inmaculada Santamaria-Valenzuela, V. Rodríguez-Fernández, David Camacho
           </td>
-          <td>2024-06-26</td>
+          <td>2024-08-08</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>10</td>
         </tr>
 
-        <tr id="CPU performance prediction, which involves forecasting the performance scores of a CPU based on its hardware characteristics during its operation, is a critical technology for computational system design and resource management in the big data era. However, this research field currently faces two significant challenges. First, collecting real-world data is challenging due to the wide variety of CPU products on the market and the highly specialized nature of relevant hardware characteristics. In the research process, this field lacks a standard dataset with unified hardware characteristics, wide data coverage, and comprehensive benchmarks. Second, existing methods based on hardware simulation models or machine learning exhibit notable shortcomings, such as lengthy simulation test cycles and low prediction accuracy. To bridge these gaps, we first collect, preprocess, and standardize historical data from the 4th Generation Intel Xeon Scalable Processors across multiple benchmark suites to create a new dataset, named PerfCastDB. Subsequently, we design a deep learning based model called Nova CPU Performance Predictor (NCPP) as the baseline for this new dataset. The NCPP network is designed based on group attention mechanism. It effectively quantifies the implicit relationships between hardware characteristics within and across groups and comprehensively models the impact of various hardware characteristics on CPU performance prediction. We conduct comparative experiments using the proposed PerfCastDB dataset. Compared to existing approaches, NCPP achieves superior evaluation results, demonstrating its effectiveness. Furthermore, we have open-sourced part of the dataset and the NCPP network code to facilitate subsequent research. The resources can be accessed at https://github.com/xiaoman-liu/NCPP.">
+        <tr id="Macroeconomic data are crucial for monitoring countries' performance and driving policy. However, traditional data acquisition processes are slow, subject to delays, and performed at a low frequency. We address this 'ragged-edge' problem with a two-step framework. The first step is a supervised learning model predicting observed low-frequency figures. We propose a neural-network-based nowcasting model that exploits mixed-frequency, high-dimensional data. The second step uses the elasticities derived from the previous step to interpolate unobserved high-frequency figures. We apply our method to nowcast countries' yearly research and development (R&D) expenditure series. These series are collected through infrequent surveys, making them ideal candidates for this task. We exploit a range of predictors, chiefly Internet search volume data, and document the relevance of these data in improving out-of-sample predictions. Furthermore, we leverage the high frequency of our data to derive monthly estimates of R&D expenditures, which are currently unobserved. We compare our results with those obtained from the classical regression-based and the sparse temporal disaggregation methods. Finally, we validate our results by reporting a strong correlation with monthly R&D employment data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f6bd30a14faf2ececc0fbe53c82a92f9137f7f37" target='_blank'>
-              Towards CPU Performance Prediction: New Challenge Benchmark Dataset and Novel Approach
+          <td><a href="https://www.semanticscholar.org/paper/755d4e35574496bb86e54a9124bcf609f8663ce7" target='_blank'>
+              Nowcasting R&D Expenditures: A Machine Learning Approach
               </a>
             </td>
           <td>
-            Xiaoman Liu
+            Atin Aboutorabi, Gaétan de Rassenfosse
           </td>
-          <td>2024-07-03</td>
+          <td>2024-07-16</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>23</td>
         </tr>
 
-        <tr id="None">
+        <tr id="Modeling count-valued time sequences has been receiving growing interests because count time sequences naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture the expressive latent transition structure and bursty dynamics behind count sequences. In particular, PGDSs demonstrate superior performance in terms of data imputation and prediction, compared with canonical linear dynamical system (LDS) based methods. Despite these advantages, PGDS cannot capture the heterogeneous overdispersed behaviours of the underlying dynamic processes. To mitigate this defect, we propose a negative-binomial-randomized gamma Markov process, which not only significantly improves the predictive performance of the proposed dynamical system, but also facilitates the fast convergence of the inference algorithm. Moreover, we develop methods to estimate both factor-structured and graph-structured transition dynamics, which enable us to infer more explainable latent structure, compared with PGDSs. Finally, we demonstrate the explainable latent structure learned by the proposed method, and show its superior performance in imputing missing data and forecasting future observations, compared with the related models.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f5525624998a69eda4aa0ec2d507973f15dabde2" target='_blank'>
-              SeeMore: a spatiotemporal predictive model with bidirectional distillation and level-specific meta-adaptation
+          <td><a href="https://www.semanticscholar.org/paper/d6fa589fdaa2383d6e9edb62b53fd8d71ec793f5" target='_blank'>
+              Negative-Binomial Randomized Gamma Dynamical Systems for Heterogeneous Overdispersed Count Time Sequences
               </a>
             </td>
           <td>
-            Yuqing Ma, Wei Liu, Yajun Gao, Yang Yuan, Shihao Bai, Haotong Qin, Xianglong Liu
+            Rui Huang, Sikun Yang, Heinz Koeppl
           </td>
-          <td>2024-07-22</td>
-          <td>Science China Information Sciences</td>
+          <td>2024-08-01</td>
+          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>15</td>
+          <td>4</td>
         </tr>
 
-        <tr id="The prediction of ocean currents is crucial to the development and utilization of marine resources. However, traditional prediction methods often fail to accurately capture the irregular behavior of ocean currents, which results in low accuracy. To solve this problem, this paper introduces a novel network for ocean current prediction, termed ATL-Net, which integrates the self-attention mechanism, temporal convolutional network (TCN), and long short-term memory (LSTM) network. ATL-Net enhances feature extraction through the inflated convolutions of TCN, captures ocean current dynamics more effectively with the self-attention mechanism, and uses LSTM for its ability to memorize long sequences of current information. Experimental results on WaMoSII data demonstrate the effectiveness of ATL-Net, which achieves the current speed prediction accuracy of 92.9% and the current direction accuracy of 90.4%. The results outperform those of existing methods. The method proposed in this paper is not only vital for the development and utilization of marine resources but also presents an efficient method for accurate ocean current prediction.">
+        <tr id="An overview of various open-source Python libraries for time series analysis and forecasting is presented. It covers such tools as Prophet, Kats, Merlion, as well as ARIMA, LSTM algorithms, which allow to study seasonality, trends and anomalies in time series data. The capabilities of each library, their advantages and applications in time series data analysis are discussed in detail.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a59ac8f2cf409c0c7592ff030179254e218725ab" target='_blank'>
-              ATL-Net: Ocean Current Prediction Based on Self-Attention Mechanism and Feature Enhancement
+          <td><a href="https://www.semanticscholar.org/paper/7bdeb61d1e26117d5e63a3cb3e86b8b03e7303b1" target='_blank'>
+              Review of Open-Source Libraries for Solving Time Series Forecasting Problems
               </a>
             </td>
           <td>
-            Qingyu Sun, Yi An, Xiangjun Yu, Lin Wu, Shuang Wei
+            E.A. Svekolnikova, V.N. Panovskiy
           </td>
-          <td>2024-06-07</td>
-          <td>2024 39th Youth Academic Annual Conference of Chinese Association of Automation (YAC)</td>
+          <td>2024-07-01</td>
+          <td>Моделирование и анализ данных</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="
- Traffic forecasting problems involve jointly modeling the non-linear spatio-temporal dependencies at different scales. While Graph Neural Network models have been effectively used to capture the non-linear spatial dependencies, capturing the dynamic spatial dependencies between the locations remains a major challenge. The errors in capturing such dependencies propagate in modeling the temporal dependencies between the locations, thereby severely affecting the performance of long-term predictions. While transformer-based mechanisms have been recently proposed for capturing the dynamic spatial dependencies, these methods are susceptible to fluctuations in data brought on by unforeseen events like traffic congestion and accidents. To mitigate these issues we propose an improvised Spatio-temporal parallel transformer (STPT) based model for traffic prediction that uses multiple adjacency graphs passed through a pair of coupled graph transformer-convolution network units, operating in parallel, to generate more noise-resilient embeddings. We conduct extensive experiments on 4 real-world traffic datasets and compare the performance of STPT with several state-of-the-art baselines, in terms of measures like RMSE, MAE, and MAPE. We find that using STPT improves the performance by around
-
- \(10-34\%\)
-
- as compared to the baselines. We also investigate the applicability of the model on other spatio-temporal data in other domains. We use a covid-19 dataset to predict the number of future occurrences in different regions from a given set of historical occurrences. The results demonstrate the superiority of our model for such datasets.
-">
+        <tr id="Stock price forecasting has been an important area of interest for economists and computer scientists. In addition to traditional statistical methods, advanced artificial intelligence techniques such as machine learning can stand out with their ability to process complex data sets and adapt to historical data. In recent years, hybrid models combining deep learning and time series methods have demonstrated superior performance in stock selection and portfolio optimisation. This study comparatively analyses the performance of LSTM and ARIMA models in time series forecasting. In the study, the stock prices of Oracle company are predicted using two different models, LSTM and ARIMA. Model performance is evaluated using metrics like MSE, MAE, RMSE, and MAPE. Both models have been found to be successful in different metrics. The LSTM model has lower error values; meanwhile, the ARIMA model produced proportionally more accurate forecasts. The study concludes that given the potential offered by deep learning, models such as LSTM are essential for time series forecasting. The flexibility of deep learning allows the development of customized models for different data types and time series problems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d890dbf3502df2b73e7403abca6b1585a2a7bdd4" target='_blank'>
-              Spatio-Temporal Parallel Transformer based model for Traffic Prediction
+          <td><a href="https://www.semanticscholar.org/paper/7fa13189dabbbc094e6e28d8bc9e13d6f6bccac1" target='_blank'>
+              Comparative Analysis of LSTM and ARIMA Models in Stock Price Prediction: A Technology Company Example
               </a>
             </td>
           <td>
-            Rahul Kumar, João Mendes‐Moreira, Joydeep Chandra
+            Y. Kırelli
           </td>
-          <td>2024-07-19</td>
-          <td>ACM Transactions on Knowledge Discovery from Data</td>
+          <td>2024-07-30</td>
+          <td>Black Sea Journal of Engineering and Science</td>
           <td>0</td>
-          <td>5</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Although recent advances in higher-order Graph Neural Networks (GNNs) improve the theoretical expressiveness and molecular property predictive performance, they often fall short of the empirical performance of models that explicitly use fragment information as inductive bias. However, for these approaches, there exists no theoretic expressivity study. In this work, we propose the Fragment-WL test, an extension to the well-known Weisfeiler&Leman (WL) test, which enables the theoretic analysis of these fragment-biased GNNs. Building on the insights gained from the Fragment-WL test, we develop a new GNN architecture and a fragmentation with infinite vocabulary that significantly boosts expressiveness. We show the effectiveness of our model on synthetic and real-world data where we outperform all GNNs on Peptides and have 12% lower error than all GNNs on ZINC and 34% lower error than other fragment-biased models. Furthermore, we show that our model exhibits superior generalization capabilities compared to the latest transformer-based architectures, positioning it as a robust solution for a range of molecular modeling tasks.">
+        <tr id="Local natural gas distribution companies (LDCs) require accurate demand forecasts across various time periods, geographic regions, and customer class hierarchies. Achieving coherent forecasts across these hierarchies is challenging but crucial for optimal decision making, resource allocation, and operational efficiency. This work introduces a method that structures the gas distribution system into cross-temporal hierarchies to produce accurate and coherent forecasts. We apply our method to a case study involving three operational regions, forecasting at different geographical levels and analyzing both hourly and daily frequencies. Trained on five years of data and tested on one year, our model achieves a 10% reduction in hourly mean absolute scaled error and a 3% reduction in daily mean absolute scaled error.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2c8d8c23156f886865df2cf99f18f658cbdea826" target='_blank'>
-              Expressivity and Generalization: Fragment-Biases for Molecular GNNs
+          <td><a href="https://www.semanticscholar.org/paper/737511869f437a80c5594b5ce945f660699fd7a2" target='_blank'>
+              Cross-Temporal Hierarchical Forecast Reconciliation of Natural Gas Demand
               </a>
             </td>
           <td>
-            Tom Wollschläger, Niklas Kemper, Leon Hetzel, Johanna Sommer, Stephan Günnemann
+            Colin O. Quinn, G. Corliss, Richard J. Povinelli
           </td>
-          <td>2024-06-12</td>
-          <td>ArXiv</td>
+          <td>2024-06-21</td>
+          <td>Energies</td>
           <td>0</td>
-          <td>6</td>
+          <td>27</td>
         </tr>
 
-        <tr id="As a pivotal subfield within the domain of time series forecasting, runoff forecasting plays a crucial role in water resource management and scheduling. Recent advancements in the application of artificial neural networks (ANNs) and attention mechanisms have markedly enhanced the accuracy of runoff forecasting models. This article introduces an innovative hybrid model, ResTCN-DAM, which synergizes the strengths of deep residual network (ResNet), temporal convolutional networks (TCNs), and dual attention mechanisms (DAMs). The proposed ResTCN-DAM is designed to leverage the unique attributes of these three modules: TCN has outstanding capability to process time series data in parallel. By combining with modified ResNet, multiple TCN layers can be densely stacked to capture more hidden information in the temporal dimension. DAM module adeptly captures the interdependencies within both temporal and feature dimensions, adeptly accentuating relevant time steps/features while diminishing less significant ones with minimal computational cost. Furthermore, the snapshot ensemble method is able to obtain the effect of training multiple models through one single training process, which ensures the accuracy and robustness of the forecasts. The deep integration and collaborative cooperation of these modules comprehensively enhance the model's forecasting capability from various perspectives. Ablation studies conducted validate the efficacy of each module, and through multiple sets of comparative experiments, it is shown that the proposed ResTCN-DAM has exceptional and consistent performance across varying lead times. We also employ visualization techniques to display heatmaps of the model's weights, thereby enhancing the interpretability of the model. When compared with the prevailing neural network-based runoff forecasting models, ResTCN-DAM exhibits state-of-the-art accuracy, temporal robustness, and interpretability, positioning it at the forefront of contemporary research.">
+        <tr id="Accurate transfer time prediction and future transfer time information are important for both public transport operators and passengers. However, existing studies cannot effectively manage high-dimensional transfer time data, capture the complex nonlinearity of transfer time, or provide accurate transfer time information. This study provides a reliable prediction model called low-rank Bayesian temporal matrix factorization (LBTMF) to address these challenges. First, on the basis of a high-dimensional spatiotemporal matrix of transfer time data, we develop a low-rank temporal-regularized matrix factorization-based imputation module to capture spatial and temporal characteristics to replace missing transfer time data. Second, to further predict the transfer time with the imputation of missing data, we propose the spatiotemporal-based Bayesian temporal matrix factorization prediction module to recover hourly and daily regular characteristics to predict the transfer time at different metro stations during various periods. Finally, the comprehensive experimental findings suggest that the LBTMF model outperforms other excellent approaches in terms of imputation efficiency, prediction accuracy, and robustness.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/079c42245248c40b0b391ca3bab0fb7ff75c9d0f" target='_blank'>
-              Residual Temporal Convolutional Network With Dual Attention Mechanism for Multilead-Time Interpretable Runoff Forecasting.
+          <td><a href="https://www.semanticscholar.org/paper/3d330ce1319f0da72418d383026426b3a3674268" target='_blank'>
+              A Low-Rank Bayesian Temporal Matrix Factorization for the Transfer Time Prediction Between Metro and Bus Systems
               </a>
             </td>
           <td>
-            Ziyu Sheng, Yuting Cao, Yin Yang, Zhong-Kai Feng, Kaibo Shi, Tingwen Huang, Shiping Wen
+            Pan Wu, Mingyang Pei, Tao Wang, Yang Liu, Zhiyuan Liu, Lingshu Zhong
           </td>
-          <td>2024-06-13</td>
-          <td>IEEE transactions on neural networks and learning systems</td>
+          <td>2024-07-01</td>
+          <td>IEEE Transactions on Intelligent Transportation Systems</td>
           <td>0</td>
-          <td>17</td>
+          <td>8</td>
         </tr>
 
-        <tr id="Distribution shift over time occurs in many settings. Leveraging historical data is necessary to learn a model for the last time point when limited data is available in the final period, yet few methods have been developed specifically for this purpose. In this work, we construct a benchmark with different sequences of synthetic shifts to evaluate the effectiveness of 3 classes of methods that 1) learn from all data without adapting to the final period, 2) learn from historical data with no regard to the sequential nature and then adapt to the final period, and 3) leverage the sequential nature of historical data when tailoring a model to the final period. We call this benchmark Seq-to-Final to highlight the focus on using a sequence of time periods to learn a model for the final time point. Our synthetic benchmark allows users to construct sequences with different types of shift and compare different methods. We focus on image classification tasks using CIFAR-10 and CIFAR-100 as the base images for the synthetic sequences. We also evaluate the same methods on the Portraits dataset to explore the relevance to real-world shifts over time. Finally, we create a visualization to contrast the initializations and updates from different methods at the final time step. Our results suggest that, for the sequences in our benchmark, methods that disregard the sequential structure and adapt to the final time point tend to perform well. The approaches we evaluate that leverage the sequential nature do not offer any improvement. We hope that this benchmark will inspire the development of new algorithms that are better at leveraging sequential historical data or a deeper understanding of why methods that disregard the sequential nature are able to perform well.">
+        <tr id="The recurring neural network is a deep learning algorithm that is commonly used to develop prediction systems. There are many variants of RNN such as RNN itself, long-short-term memory (LSTM), and gated recurring unit, so it is frequently debatable which algorithm from the RNN family has the most optimal efficiency and computation time. When developing a prediction system, sequential or time series data is required so that an accurate prediction can be made. Sequential or time series data involve data arranged in a time sequence, such as weather data, financial data, carbon emission data, and traffic data recorded over time. This research will be carried out by predicting the three RNN models against historical Bitcoin value data. The research method used is Experimental Design by comparing the performance between the three models on bitcoin value time series data, testing is done by involving hyperparameters such as Tanh, Sigmoid, and ReLU activation functions, batch size, and epochs. The aim of this research is to find out which RNN model can produce the most optimal performance and find out what performance measures can be used to evaluate and compare the performance between the three models. The results of the study show that LSTM is the most effective model with RMSE 0.012441 and MSE 0.000155 but inefficient because it takes 3 minutes 24 seconds to run the computation; in the meantime, the Tanh activation function gives the most optimal prediction than Sigmoid and RelU and therefore should be the main candidate to be used with RNN models when predicting Bitcoin prices.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/dff5247f9c46cb7745eb5c8b20a4225f15cd7d8a" target='_blank'>
-              Seq-to-Final: A Benchmark for Tuning from Sequential Distributions to a Final Time Point
+          <td><a href="https://www.semanticscholar.org/paper/2db311833b4fea063c64e56f36d23366568c488b" target='_blank'>
+              Comparative Analysis of Recurrent Neural Network Models Performance in Predicting Bitcoin Prices
               </a>
             </td>
           <td>
-            Christina X. Ji, Ahmed M. Alaa, David Sontag
+            Zidane Ikkoy Ramadhan, H. Widiputra
           </td>
-          <td>2024-07-12</td>
-          <td>ArXiv</td>
+          <td>2024-06-21</td>
+          <td>Jurnal RESTI (Rekayasa Sistem dan Teknologi Informasi)</td>
           <td>0</td>
-          <td>3</td>
+          <td>9</td>
         </tr>
 
-        <tr id="Cross-Domain Sequential Recommendation (CDSR) improves recommendation performance by utilizing information from multiple domains, which contrasts with Single-Domain Sequential Recommendation (SDSR) that relies on a historical interaction within a specific domain. However, CDSR may underperform compared to the SDSR approach in certain domains due to negative transfer, which occurs when there is a lack of relation between domains or different levels of data sparsity. To address the issue of negative transfer, our proposed CDSR model estimates the degree of negative transfer of each domain and adaptively assigns it as a weight factor to the prediction loss, to control gradient flows through domains with significant negative transfer. To this end, our model compares the performance of a model trained on multiple domains (CDSR) with a model trained solely on the specific domain (SDSR) to evaluate the negative transfer of each domain using our asymmetric cooperative network. In addition, to facilitate the transfer of valuable cues between the SDSR and CDSR tasks, we developed an auxiliary loss that maximizes the mutual information between the representation pairs from both tasks on a per-domain basis. This cooperative learning between SDSR and CDSR tasks is similar to the collaborative dynamics between pacers and runners in a marathon. Our model outperformed numerous previous works in extensive experiments on two real-world industrial datasets across ten service domains. We also have deployed our model in the recommendation system of our personal assistant app service, resulting in 21.4% increase in click-through rate compared to existing models, which is valuable to real-world business.">
+        <tr id="Accurate traffic flow forecasting is vital for intelligent transportation systems, especially with urbanization worsening traffic congestion, which affects daily life, economic growth, and the environment. Precise forecasts aid in managing and optimizing transportation systems, reducing congestion, and improving air quality by cutting emissions. However, predicting outcomes is difficult due to intricate spatial relationships, nonlinear temporal patterns, and the challenges associated with long-term forecasting. Current research often uses static graph structures, overlooking dynamic and long-range dependencies. To tackle these issues, we introduce the spatiotemporal dynamic multi-hop network (ST-DMN), a Seq2Seq framework. This model incorporates spatiotemporal convolutional blocks (ST-Blocks) with residual connections in the encoder to condense historical traffic data into a fixed-dimensional vector. A dynamic graph represents time-varying inter-segment relationships, and multi-hop operation in the encoder’s spatial convolutional layer and the decoder’s diffusion multi-hop graph convolutional gated recurrent units (DMGCGRUs) capture long-range dependencies. Experiments on two real-world datasets METR-LA and PEMS-BAY show that ST-DMN surpasses existing models in three metrics.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/72d35cc6a6489d7ec661e3f9c73befa28fe91d68" target='_blank'>
-              Pacer and Runner: Cooperative Learning Framework between Single- and Cross-Domain Sequential Recommendation
+          <td><a href="https://www.semanticscholar.org/paper/a95e1e501ec2f4452c161c53c744ae576c08979c" target='_blank'>
+              Spatiotemporal Dynamic Multi-Hop Network for Traffic Flow Forecasting
               </a>
             </td>
           <td>
-            Chung Park, Taesan Kim, Hyungjun Yoon, Junui Hong, Yelim Yu, Mincheol Cho, Minsung Choi, Jaegul Choo
+            Wenguang Chai, Qingfeng Luo, Zhizhe Lin, Jingwen Yan, Jinglin Zhou, Teng Zhou
           </td>
-          <td>2024-07-10</td>
-          <td>DBLP, ArXiv</td>
+          <td>2024-07-09</td>
+          <td>Sustainability</td>
           <td>0</td>
-          <td>2</td>
+          <td>12</td>
         </tr>
 
-        <tr id="The growing number of connected vehicles offers an opportunity to leverage internet of vehicles (IoV) data for traffic state estimation (TSE) which plays a crucial role in intelligent transportation systems (ITS). By utilizing only a portion of IoV data instead of the entire dataset, the significant overheads associated with collecting and processing large amounts of data can be avoided. In this paper, we introduce a novel framework that utilizes sparse IoV data to achieve cost-effective TSE. Particularly, we propose a novel spatial-temporal attention model called the convolutional retentive network (CRNet) to improve the TSE accuracy by mining spatial-temporal traffic state correlations. The model employs the convolutional neural network (CNN) for spatial correlation aggregation and the retentive network (RetNet) based on the attention mechanism to extract temporal correlations. Extensive simulations on a real-world IoV dataset validate the advantage of the proposed TSE approach in achieving accurate TSE using sparse IoV data, demonstrating its cost effectiveness and practicality for real-world applications.">
+        <tr id="Objectives. To build neural network models of time series (LSTM, GRU, RNN) and compare the results of forecasting with their mutual help and the results of standard models (ARIMA, ETS), in order to ascertain in which cases a certain group of models should be used.Methods. The paper provides a review of neural network models and considers the structure of RNN, LSTM, and GRU models. They are used for modeling time series in Russian macroeconomic statistics. The quality of model adjustment to the data and the quality of forecasts are compared experimentally. Neural network and standard models can be used both for the entire series and for its parts (trend and seasonality). When building a forecast for several time intervals in the future, two approaches are considered: building a forecast for the entire interval at once, and step-by-step forecasting. In this way there are several combinations of models that can be used for forecasting. These approaches are analyzed in the computational experiment.Results. Several experiments have been conducted in which standard (ARIMA, ETS, LOESS) and neural network models (LSTM, GRU, RNN) are built and compared in terms of proximity of the forecast to the series data in the test period.Conclusions. In the case of seasonal time series, models based on neural networks surpassed the standard ARIMA and ETS models in terms of forecast accuracy for the test period. The single-step forecast is computationally less efficient than the integral forecast for the entire target period. However, it is not possible to accurately indicate which approach is the best in terms of quality for a given series. Combined models (neural networks for trend, ARIMA for seasonality) almost always give good results. When forecasting a non-seasonal heteroskedastic series of share price, the standard approaches (LOESS method and ETS model) showed the best results.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ab1f0647032a9954876f7bbb100dc801fe171bff" target='_blank'>
-              Spatial-Temporal Attention Model for Traffic State Estimation with Sparse Internet of Vehicles
+          <td><a href="https://www.semanticscholar.org/paper/18b38c6aa6bc97b32d3a4d813c85a98d07c92494" target='_blank'>
+              Neural network analysis in time series forecasting
               </a>
             </td>
           <td>
-            Jianzhe Xue, Dongcheng Yuan, Yu Sun, Tianqi Zhang, Wenchao Xu, Haibo Zhou, Xuemin Shen
+            B. Pashshoev, D. Petrusevich
           </td>
-          <td>2024-07-10</td>
-          <td>ArXiv</td>
+          <td>2024-08-05</td>
+          <td>Russian Technological Journal</td>
           <td>0</td>
-          <td>3</td>
+          <td>2</td>
         </tr>
 
-        <tr id="We present the history-aware transformer (HAT), a transformer-based model that uses shoppers' purchase history to personalise outfit predictions. The aim of this work is to recommend outfits that are internally coherent while matching an individual shopper's style and taste. To achieve this, we stack two transformer models, one that produces outfit representations and another one that processes the history of purchased outfits for a given shopper. We use these models to score an outfit's compatibility in the context of a shopper's preferences as inferred from their previous purchases. During training, the model learns to discriminate between purchased and random outfits using 3 losses: the focal loss for outfit compatibility typically used in the literature, a contrastive loss to bring closer learned outfit embeddings from a shopper's history, and an adaptive margin loss to facilitate learning from weak negatives. Together, these losses enable the model to make personalised recommendations based on a shopper's purchase history. Our experiments on the IQON3000 and Polyvore datasets show that HAT outperforms strong baselines on the outfit Compatibility Prediction (CP) and the Fill In The Blank (FITB) tasks. The model improves AUC for the CP hard task by 15.7% (IQON3000) and 19.4% (Polyvore) compared to previous SOTA results. It further improves accuracy on the FITB hard task by 6.5% and 9.7%, respectively. We provide ablation studies on the personalisation, constrastive loss, and adaptive margin loss that highlight the importance of these modelling choices.">
+        <tr id="A dynamic weighted directed graph (DWDG) is commonly encountered in various application scenarios. It involves extensive dynamic interactions among numerous nodes. Most existing approaches explore the intricate temporal patterns hidden in a DWDG from the purely data-driven perspective, which suffers from accuracy loss when a DWDG exhibits strong fluctuations over time. To address this issue, this study proposes a novel Extended-Kalman-Filter-Incorporated Latent Feature (EKLF) model to represent a DWDG from the model-driven perspective. Its main idea is divided into the following two-fold ideas: a) adopting a control model, i.e., the Extended Kalman Filter (EKF), to track the complex temporal patterns precisely with its nonlinear state-transition and observation functions; and b) introducing an alternating least squares (ALS) algorithm to train the latent features (LFs) alternatively for precisely representing a DWDG. Empirical studies on DWDG datasets demonstrate that the proposed EKLF model outperforms state-of-the-art models in prediction accuracy and computational efficiency for missing edge weights of a DWDG. It unveils the potential for precisely representing a DWDG by incorporating a control model.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/aec5922c6f689cea2ed911aea992c605accd90f5" target='_blank'>
-              Personalised Outfit Recommendation via History-aware Transformers
+          <td><a href="https://www.semanticscholar.org/paper/8a67cf8783fcc0ce6aba4d219506d923562461ab" target='_blank'>
+              An Extended Kalman Filter Integrated Latent Feature Model on Dynamic Weighted Directed Graphs
               </a>
             </td>
           <td>
-            David Jung, Julien Monteil, Philip Schulz, Volodymyr Vaskovych
+            Hongxun Zhou, Xiangyu Chen, Ye Yuan
           </td>
-          <td>2024-06-29</td>
+          <td>2024-07-31</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>2</td>
+          <td>0</td>
         </tr>
 
-        <tr id="In response to the insufficient consideration of spatio-temporal dependencies and traffic pattern similarity in traffic flow prediction methods based on federated learning, as well as the neglect of model heterogeneity and objective heterogeneity, a traffic flow prediction model based on federated learning and spatio-temporal graph neural networks is proposed. The model is divided into two stages. In the road network division stage, the traffic road network is divided into subnetworks by the dynamic time warping algorithm and the K-means algorithm, to ensure the same subnetwork has the similar traffic flow pattern. The federated learning stage is divided into two sub-stages. In the local training phase, the spatio-temporal graph neural network with an attention mechanism is utilized to create personalized models and meme models to capture the spatio-temporal dependencies of each subnetwork. At the same time, deep mutual learning is utilized to address model heterogeneity and objective heterogeneity through knowledge distillation. In the global aggregation phase, a multi-factor weighted aggregation strategy is designed to measure the contribution of each local model to the global model, to enhance the fairness of aggregation. Three sets of experiments were conducted on two real datasets, and the experimental results demonstrate that the proposed model outperforms the baseline models in three common evaluation metrics.">
+        <tr id="Time series forecasting plays a crucial role in various fields, including economics, finance, and weather prediction. This study explores the application of time series forecasting techniques to predict future values based on historical data patterns. Different models, such as ARIMA, SARIMA, and exponential smoothing, are commonly employed to capture the underlying trends, seasonality, and irregularities in time series data. The accuracy of the forecasts depends on selecting the appropriate model and fine-tuning its parameters. Regular validation and refinement of the forecasting models are essential to ensure their reliability and adaptability to changing conditions. Overall, time series forecasting serves as a valuable tool for decision-making, resource allocation, and planning in numerous domains. The Autoregressive Integrated Moving Average (ARIMA) model was used in this research to predict Albanian exports. The ARIMA models provided reliable forecasts for the near future and placed more importance on recent observations rather than distant past data. However, a limitation of this study is the lack of using multiple models on new data to improve future forecasts. Considering the significance of exports in Albania, it is crucial to periodically validate and refine the model-building exercises. Based on the findings, the study recommends using the ARIMA (3,2,3) model for forecasting. Furthermore, the forecast errors were statistically tested and validated, confirming the model's strong predictive ability. It is important to note that a forecasting technique that performs well in one situation may not be suitable for another. Therefore, the validation of a specific model should be regularly assessed as time progresses. For the purpose of forecasting the annual exports of Albania, researchers can employ these models.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2e28c42dd920b2051aed0b2541a2f1897a0594b3" target='_blank'>
-              Traffic Flow Prediction Based on Federated Learning and Spatio-Temporal Graph Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/0d8ae00de95edb0226fad574129969bcb6e56842" target='_blank'>
+              FORECASTING EXPORTS IN ALBANIA
               </a>
             </td>
           <td>
-            Jian Feng, Cailing Du, Qi Mu
+            Brikena Sulejmani
           </td>
-          <td>2024-06-18</td>
-          <td>ISPRS Int. J. Geo Inf.</td>
+          <td>2024-07-30</td>
+          <td>PEOPLE: International Journal of Social Sciences</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="As the usage of user-private-data is increasingly monitored by regulatory institutions for security purposes, its transfer becomes more constrained. Synthetic data has recently emerged as a viable alternative to prevent the disclosure of user-protected information that complies with data sharing regulations. Both public and private sectors commonly use a combination of tabular and time-series tables that often contains user-related sensitive information. They are usually intrinsically interlinked as they describe the users and their behaviors over different perimeters. Moreover, it contains both numerical and categorical features, adding complexity to the anonymization task. State of the art generative methods, specialized either in tabular or time-series data, are able to generate high quality synthetic data. However, if each table is generated independently, it becomes impossible to link them. As a result, the usability of such synthetic data is impacted. To address this issue, we not only propose a coherent multi-table generative model that uses Generative Adversarial Networks (GANs) to sample both tabular and time-series tables , but also a conditional time-series generative model that handles both numerical and categorical features. Additionally, many experiments are conducted to analyse the inner modules of our model and evaluate it on an in-house private dataset in order to prove the viability of the synthetic data generated for machine learning tasks.">
+        <tr id="Large Language Models (LLMs) excel in diverse tasks but often underperform in specialized fields due to limited domain-specific or proprietary corpus. Continual pre-training (CPT) enhances LLM capabilities by imbuing new domain-specific or proprietary knowledge while replaying general corpus to prevent catastrophic forgetting. The data mixture ratio of general corpus and domain-specific corpus, however, has been chosen heuristically, leading to sub-optimal training efficiency in practice. In this context, we attempt to re-visit the scaling behavior of LLMs under the hood of CPT, and discover a power-law relationship between loss, mixture ratio, and training tokens scale. We formalize the trade-off between general and domain-specific capabilities, leading to a well-defined Critical Mixture Ratio (CMR) of general and domain data. By striking the balance, CMR maintains the model's general ability and achieves the desired domain transfer, ensuring the highest utilization of available resources. Therefore, if we value the balance between efficiency and effectiveness, CMR can be consider as the optimal mixture ratio.Through extensive experiments, we ascertain the predictability of CMR, and propose CMR scaling law and have substantiated its generalization. These findings offer practical guidelines for optimizing LLM training in specialized domains, ensuring both general and domain-specific performance while efficiently managing training resources.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/abd28aa286d305de80cc5e681b63d89087603518" target='_blank'>
-              Coherent Multi-Table Data Synthesis for Tabular and Time-Series Data with GANs
+          <td><a href="https://www.semanticscholar.org/paper/fce434329773bdec3deb7e5985c1780492f8cd6f" target='_blank'>
+              CMR Scaling Law: Predicting Critical Mixture Ratios for Continual Pre-training of Language Models
               </a>
             </td>
           <td>
-            Clément Elliker, Emeric Tonnelier, A. Shabou
+            Jiawei Gu, Zacc Yang, Chuanghao Ding, Rui Zhao, Fei Tan
           </td>
-          <td>2024-06-19</td>
-          <td>Proceedings of the Fourteenth ACM Conference on Data and Application Security and Privacy</td>
+          <td>2024-07-24</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>9</td>
+          <td>5</td>
         </tr>
 
-        <tr id="We explore various neural network architectures for modeling the dynamics of the cryptocurrency market. Traditional linear models often fall short in accurately capturing the unique and complex dynamics of this market. In contrast, Deep Neural Networks (DNNs) have demonstrated considerable proficiency in time series forecasting. This papers introduces novel neural network framework that blend the principles of econometric state space models with the dynamic capabilities of Recurrent Neural Networks (RNNs). We propose state space models using Long Short Term Memory (LSTM), Gated Residual Units (GRU) and Temporal Kolmogorov-Arnold Networks (TKANs). According to the results, TKANs, inspired by Kolmogorov-Arnold Networks (KANs) and LSTM, demonstrate promising outcomes.">
+        <tr id="Learning spatio-temporal patterns of polar ice layers is crucial for monitoring the change in ice sheet balance and evaluating ice dynamic processes. While a few researchers focus on learning ice layer patterns from echogram images captured by airborne snow radar sensors via different convolutional neural networks, the noise in the echogram images proves to be a major obstacle. Instead, we focus on geometric deep learning based on graph neural networks to learn the spatio-temporal patterns from thickness information of shallow ice layers and make predictions for deep layers. In this paper, we propose a physics-informed hybrid graph neural network that combines the GraphSAGE framework for graph feature learning with the long short-term memory (LSTM) structure for learning temporal changes, and introduce measurements of physical ice properties from Model Atmospheric Regional (MAR) weather model as physical node features. We found that our proposed network can consistently outperform the current non-inductive or non-physical model in predicting deep ice layer thickness.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f2be9285dd976d1dd4c063f13369b73af652e881" target='_blank'>
-              Deep State Space Recurrent Neural Networks for Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/14283719423d1b3a94963bf3dac91b3889050624" target='_blank'>
+              Learning Spatio-Temporal Patterns of Polar Ice Layers With Physics-Informed Graph Neural Network
               </a>
             </td>
           <td>
-            Hugo Inzirillo
+            Zesheng Liu, Maryam Rahnemoonfar
           </td>
-          <td>2024-07-21</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Condition-Based Maintenance is pivotal in enabling the early detection of potential failures in engineering systems, where precise prediction of the Remaining Useful Life is essential for effective maintenance and operation. However, a predominant focus in the field centers on predicting the Remaining Useful Life using unprocessed or minimally processed data, frequently neglecting the intricate dynamics inherent in the dataset. In this work we introduce a novel methodology grounded in the analysis of statistical similarity within latent data from system components. Leveraging a specifically designed architecture based on a Vector Quantized Variational Autoencoder, we create a sequence of discrete vectors which is used to estimate system-specific priors. We infer the similarity between systems by evaluating the divergence of these priors, offering a nuanced understanding of individual system behaviors. The efficacy of our approach is demonstrated through experiments on the NASA commercial modular aero-propulsion system simulation (C-MAPSS) dataset. Our validation not only underscores the potential of our method in advancing the study of latent statistical divergence but also demonstrates its superiority over existing techniques.">
+        <tr id="Temporal data modelling techniques with neural networks are useful in many domain applications, including time-series forecasting and control engineering. This paper aims at developing a recurrent version of stochastic configuration networks (RSCNs) for problem solving, where we have no underlying assumption on the dynamic orders of the input variables. Given a collection of historical data, we first build an initial RSCN model in the light of a supervisory mechanism, followed by an online update of the output weights by using a projection algorithm. Some theoretical results are established, including the echo state property, the universal approximation property of RSCNs for both the offline and online learnings, and the convergence of the output weights. The proposed RSCN model is remarkably distinguished from the well-known echo state networks (ESNs) in terms of the way of assigning the input random weight matrix and a special structure of the random feedback matrix. A comprehensive comparison study among the long short-term memory (LSTM) network, the original ESN, and several state-of-the-art ESN methods such as the simple cycle reservoir (SCR), the polynomial ESN (PESN), the leaky-integrator ESN (LIESN) and RSCN is carried out. Numerical results clearly indicate that the proposed RSCN performs favourably over all of the datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f903b52dba21c112670ba5fbcb29005beb19bbff" target='_blank'>
-              The Significance of Latent Data Divergence in Predicting System Degradation
+          <td><a href="https://www.semanticscholar.org/paper/46e3c55f0b0e77192fb6cc422ecf599a47334d73" target='_blank'>
+              Recurrent Stochastic Configuration Networks for Temporal Data Analytics
               </a>
             </td>
           <td>
-            Miguel Fernandes, Catarina Silva, Alberto Cardoso, Bernardete Ribeiro
+            Dianhui Wang, Gang Dang
           </td>
-          <td>2024-06-13</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>3</td>
+          <td>1</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Multivariate time series modeling has been essential in sensor-based data mining tasks. However, capturing complex dynamics caused by intra-variable (temporal) and inter-variable (spatial) relationships while simultaneously taking into account evolving data distributions is a non-trivial task, which faces accumulated computational overhead and multiple temporal patterns or distribution modes. Most existing methods focus on the former direction without adaptive task-specific learning ability. To this end, we developed a holistic spatial-temporal meta-learning probabilistic inference framework, entitled ST-MeLaPI, for the efficient and versatile learning of complex dynamics. Specifically, first, a multivariate relationship recognition module is utilized to learn task-specific inter-variable dependencies. Then, a multiview meta-learning and probabilistic inference strategy was designed to learn shared parameters while enabling the fast and flexible learning of task-specific parameters for different batches. At the core are spatial dependency-oriented and temporal pattern-oriented meta-learning approximate probabilistic inference modules, which can quickly adapt to changing environments via stochastic neurons at each timestamp. Finally, a gated aggregation scheme is leveraged to realize appropriate information selection for the generative style prediction. We benchmarked our approach against state-of-the-art methods with real-world data. The experimental results demonstrate the superiority of our approach over the baselines.">
+        <tr id="Abstract Predicting the strength of promoters and guiding their directed evolution is a crucial task in synthetic biology. This approach significantly reduces the experimental costs in conventional promoter engineering. Previous studies employing machine learning or deep learning methods have shown some success in this task, but their outcomes were not satisfactory enough, primarily due to the neglect of evolutionary information. In this paper, we introduce the Chaos-Attention net for Promoter Evolution (CAPE) to address the limitations of existing methods. We comprehensively extract evolutionary information within promoters using merged chaos game representation and process the overall information with modified DenseNet and Transformer structures. Our model achieves state-of-the-art results on two kinds of distinct tasks related to prokaryotic promoter strength prediction. The incorporation of evolutionary information enhances the model’s accuracy, with transfer learning further extending its adaptability. Furthermore, experimental results confirm CAPE’s efficacy in simulating in silico directed evolution of promoters, marking a significant advancement in predictive modeling for prokaryotic promoter strength. Our paper also presents a user-friendly website for the practical implementation of in silico directed evolution on promoters. The source code implemented in this study and the instructions on accessing the website can be found in our GitHub repository https://github.com/BobYHY/CAPE.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4dea55e0f4c4c2f82b1128047a54ec3d4fccaa7f" target='_blank'>
-              Multiview Spatial-Temporal Meta-Learning for Multivariate Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/04f78ff241635d6b984404fb6a2df4fcea90938f" target='_blank'>
+              CAPE: a deep learning framework with Chaos-Attention net for Promoter Evolution
               </a>
             </td>
           <td>
-            Liang Zhang, Jianping Zhu, Bo Jin, Xiaopeng Wei
+            Ruohan Ren, Hongyu Yu, Jiahao Teng, Sihui Mao, Zixuan Bian, Yangtianze Tao, Stephen S.-T. Yau
           </td>
-          <td>2024-07-01</td>
-          <td>Sensors (Basel, Switzerland)</td>
+          <td>2024-07-25</td>
+          <td>Briefings in Bioinformatics</td>
           <td>0</td>
-          <td>8</td>
+          <td>4</td>
         </tr>
 
-        <tr id="In the context of medical decision making, counterfactual prediction enables clinicians to predict treatment outcomes of interest under alternative courses of therapeutic actions given observed patient history. Prior machine learning approaches for counterfactual predictions under time-varying treatments focus on static time-varying treatment regimes where treatments do not depend on previous covariate history. In this work, we present G-Transformer, a Transformer-based framework supporting g-computation for counterfactual prediction under dynamic and time-varying treatment strategies. G-Transfomer captures complex, long-range dependencies in time-varying covariates using a Transformer architecture. G-Transformer estimates the conditional distribution of relevant covariates given covariate and treatment history at each time point using an encoder architecture, then produces Monte Carlo estimates of counterfactual outcomes by simulating forward patient trajectories under treatment strategies of interest. We evaluate G-Transformer extensively using two simulated longitudinal datasets from mechanistic models, and a real-world sepsis ICU dataset from MIMIC-IV. G-Transformer outperforms both classical and state-of-the-art counterfactual prediction models in these settings. To the best of our knowledge, this is the first Transformer-based architecture for counterfactual outcome prediction under dynamic and time-varying treatment strategies.">
+        <tr id="
+ Time series data prediction holds a significant importance in various applications. In this study, we specifically concentrate on long-time series data prediction. Recurrent Neural Networks are widely recognized as a fundamental neural network architecture for processing effectively time-series data. Recurrent Neural Network models encounter the gradient disappearance or gradient explosion challenge in long series data. To resolve the gradient problem and improve accuracy, the Fractional Order Lipschitz Recurrent Neural Network (FOLRNN) model is proposed to predict long time series in this paper. The proposed method uses the Lipschitz continuity to alleviate the gradient problem. The fractional order integration is applied to compute the hidden states of the Recurrent Neural Network in the proposed method. The intricate dynamics of long-time series data can be captured by fractional order calculus. It has more accurate predictions compared with Lipschitz Recurrent Neural Networks models. Then self-attention is used to improve feature representation. It can describe the correlation of features and improve predict performance. Some experiments show that the FOLRNN model achieves better results than other methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/abfd52aef0b77c3c09982f13b6e164605186ffa6" target='_blank'>
-              G-Transformer: Counterfactual Outcome Prediction under Dynamic and Time-varying Treatment Regimes
+          <td><a href="https://www.semanticscholar.org/paper/50bdbfa75458c6d63dead6aa6573849b191fe2ec" target='_blank'>
+              Fractional order Lipschitz recurrent neural network with attention for long time series prediction
               </a>
             </td>
           <td>
-            Hong Xiong, Feng Wu, Leon Deng, Megan Su, Li-wei H. Lehman
+            Zelong Zhu, Chunna Zhao, Yaqun Huang
           </td>
-          <td>2024-06-08</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>Journal of Physics: Conference Series</td>
           <td>0</td>
-          <td>2</td>
+          <td>7</td>
         </tr>
 
-        <tr id="The telecommunications industry is becoming increasingly aware of potential subscriber churn as a result of the growing popularity of smartphones in the mobile Internet era, the quick development of telecommunications services, the implementation of the number portability policy, and the intensifying competition among operators. At the same time, users' consumption preferences and choices are evolving. Excellent churn prediction models must be created in order to accurately predict the churn tendency, since keeping existing customers is far less expensive than acquiring new ones. But conventional or learning-based algorithms can only go so far into a single subscriber's data; they cannot take into consideration changes in a subscriber's subscription and ignore the coupling and correlation between various features. Additionally, the current churn prediction models have a high computational burden, a fuzzy weight distribution, and significant resource economic costs. The prediction algorithms involving network models currently in use primarily take into account the private information shared between users with text and pictures, ignoring the reference value supplied by other users with the same package. This work suggests a user churn prediction model based on Graph Attention Convolutional Neural Network (GAT-CNN) to address the aforementioned issues. The main contributions of this paper are as follows: Firstly, we present a three-tiered hierarchical cloud-edge cooperative framework that increases the volume of user feature input by means of two aggregations at the device, edge, and cloud layers. Second, we extend the use of users' own data by introducing self-attention and graph convolution models to track the relative changes of both users and packages simultaneously. Lastly, we build an integrated offline-online system for churn prediction based on the strengths of the two models, and we experimentally validate the efficacy of cloud-side collaborative training and inference. In summary, the churn prediction model based on Graph Attention Convolutional Neural Network presented in this paper can effectively address the drawbacks of conventional algorithms and offer telecom operators crucial decision support in developing subscriber retention strategies and cutting operational expenses.">
+        <tr id="ABSTRACT The rebalancing of bikes and demand prediction at the station level plays a fundamental role in the regular operation and maintenance of bike-sharing systems (BSSs). In this paper, a novel model which incorporates discrete wavelet transform (DWT), autoregressive integrated moving average (ARIMA), and long-short term memory neural network (LSTM NN), is proposed for BSS station-level check-in/out demand prediction. This study adopts the wavelet analysis method to denoise the raw BSS demand series firstly. Then, DWT is developed to decompose the denoised sequence into three high-frequency components (i.e. details) and one low-frequency component (i.e. approximation). ARIMA and LSTM are employed to forecast the detailed components and one approximation component, respectively. The predicted results of each model are reconstructed into the final outputs by DWT. An experiment on a real-world trip dataset showed that the proposed approach consistently outperforms the standard ARIMA model and LSTM model.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/389c1f686431f303fa0095054fe8c8ecdb8f4c61" target='_blank'>
-              User churn prediction hierarchical model based on graph attention convolutional neural networks
+          <td><a href="https://www.semanticscholar.org/paper/d3df2f965dd2a9f63b2f94e55287bae82e6e6b12" target='_blank'>
+              Discrete wavelet transform application for bike sharing system check-in/out demand prediction
               </a>
             </td>
           <td>
-            Mei Miao, Tang Miao, Zhou Long
+            Yu Chen, Wei Wang, Xuedong Hua, Weijie Yu, Jialiang Xiao
           </td>
-          <td>2024-07-01</td>
-          <td>China Communications</td>
-          <td>0</td>
+          <td>2024-07-02</td>
+          <td>Transportation Letters</td>
           <td>0</td>
+          <td>10</td>
         </tr>
 
-        <tr id="Effective imputation is a crucial preprocessing step for time series analysis. Despite the development of numerous deep learning algorithms for time series imputation, the community lacks standardized and comprehensive benchmark platforms to effectively evaluate imputation performance across different settings. Moreover, although many deep learning forecasting algorithms have demonstrated excellent performance, whether their modeling achievements can be transferred to time series imputation tasks remains unexplored. To bridge these gaps, we develop TSI-Bench, the first (to our knowledge) comprehensive benchmark suite for time series imputation utilizing deep learning techniques. The TSI-Bench pipeline standardizes experimental settings to enable fair evaluation of imputation algorithms and identification of meaningful insights into the influence of domain-appropriate missingness ratios and patterns on model performance. Furthermore, TSI-Bench innovatively provides a systematic paradigm to tailor time series forecasting algorithms for imputation purposes. Our extensive study across 34,804 experiments, 28 algorithms, and 8 datasets with diverse missingness scenarios demonstrates TSI-Bench's effectiveness in diverse downstream tasks and potential to unlock future directions in time series imputation research and analysis. The source code and experiment logs are available at https://github.com/WenjieDu/AwesomeImputation.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/74049a723c1c52b4f2dc01b28bef137771cb1148" target='_blank'>
-              TSI-Bench: Benchmarking Time Series Imputation
+          <td><a href="https://www.semanticscholar.org/paper/ca70c38270fe1f47a4e82ae81496c70c0e541ccf" target='_blank'>
+              Multivariate Bayesian Time-Series Model with Multi-temporal Convolution Network for Forecasting Stock Market During COVID-19 Pandemic
               </a>
             </td>
           <td>
-            Wenjie Du, Jun Wang, Linglong Qian, Yiyuan Yang, Fanxing Liu, Zepu Wang, Zina Ibrahim, Haoxin Liu, Zhiyuan Zhao, Yingjie Zhou, Wenjia Wang, Kaize Ding, Yuxuan Liang, B. A. Prakash, Qingsong Wen
+            Paramita Ray, B. Ganguli, Amlan Chakrabarti
           </td>
-          <td>2024-06-18</td>
-          <td>ArXiv</td>
-          <td>2</td>
-          <td>4</td>
+          <td>2024-06-27</td>
+          <td>Int. J. Comput. Intell. Syst.</td>
+          <td>0</td>
+          <td>13</td>
         </tr>
 
-        <tr id="Recently, the incorporation of both temporal features and the correlation across time series has become an effective approach in time series prediction. Spatio-Temporal Graph Neural Networks (STGNNs) demonstrate good performance on many Temporal-correlation Forecasting Problem. However, when applied to tasks lacking periodicity, such as stock data prediction, the effectiveness and robustness of STGNNs are found to be unsatisfactory. And STGNNs are limited by memory savings so that cannot handle problems with a large number of nodes. In this paper, we propose a novel approach called the Temporal-Correlation Graph Pre-trained Network (TCGPN) to address these limitations. TCGPN utilize Temporal-correlation fusion encoder to get a mixed representation and pre-training method with carefully designed temporal and correlation pre-training tasks. Entire structure is independent of the number and order of nodes, so better results can be obtained through various data enhancements. And memory consumption during training can be significantly reduced through multiple sampling. Experiments are conducted on real stock market data sets CSI300 and CSI500 that exhibit minimal periodicity. We fine-tune a simple MLP in downstream tasks and achieve state-of-the-art results, validating the capability to capture more robust temporal correlation patterns.">
+        <tr id="Evaluating the performance of causal discovery algorithms that aim to find causal relationships between time-dependent processes remains a challenging topic. In this paper, we show that certain characteristics of datasets, such as varsortability (Reisach et al. 2021) and $R^2$-sortability (Reisach et al. 2023), also occur in datasets for autocorrelated stationary time series. We illustrate this empirically using four types of data: simulated data based on SVAR models and Erd\H{o}s-R\'enyi graphs, the data used in the 2019 causality-for-climate challenge (Runge et al. 2019), real-world river stream datasets, and real-world data generated by the Causal Chamber of (Gamella et al. 2024). To do this, we adapt var- and $R^2$-sortability to time series data. We also investigate the extent to which the performance of score-based causal discovery methods goes hand in hand with high sortability. Arguably, our most surprising finding is that the investigated real-world datasets exhibit high varsortability and low $R^2$-sortability indicating that scales may carry a significant amount of causal information.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1184b61fe584f056e3f7156ed3fe740a346b75a1" target='_blank'>
-              TCGPN: Temporal-Correlation Graph Pre-trained Network for Stock Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/e3d479da542a4353c2379183fe7b1a2c9e34e919" target='_blank'>
+              Sortability of Time Series Data
               </a>
             </td>
           <td>
-            Wenbo Yan, Ying Tan
+            Christopher Lohse, Jonas Wahl
           </td>
-          <td>2024-07-26</td>
+          <td>2024-07-18</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Mixed-type time series (MTTS) is a bimodal data type that is common in many domains, such as healthcare, finance, environmental monitoring, and social media. It consists of regularly sampled continuous time series and irregularly sampled categorical event sequences. The integration of both modalities through multimodal fusion is a promising approach for processing MTTS. However, the question of how to effectively fuse both modalities remains open. In this paper, we present a comprehensive evaluation of several deep multimodal fusion approaches for MTTS forecasting. Our comparison includes three fusion types (early, intermediate, and late) and five fusion methods (concatenation, weighted mean, weighted mean with correlation, gating, and feature sharing). We evaluate these fusion approaches on three distinct datasets, one of which was generated using a novel framework. This framework allows for the control of key data properties, such as the strength and direction of intermodal interactions, modality imbalance, and the degree of randomness in each modality, providing a more controlled environment for testing fusion approaches. Our findings show that the performance of different fusion approaches can be substantially influenced by the direction and strength of intermodal interactions. The study reveals that early and intermediate fusion approaches excel at capturing fine-grained and coarse-grained cross-modal features, respectively. These findings underscore the crucial role of intermodal interactions in determining the most effective fusion strategy for MTTS forecasting.">
+        <tr id="This paper proposes a new self-organizing interval type-2 fuzzy neural network with multiple outputs (SOIT2FNN-MO) for multi-step time series prediction. Differing from the traditional six-layer IT2FNN, a nine-layer network is developed to improve prediction accuracy, uncertainty handling and model interpretability. First, a new co-antecedent layer and a modified consequent layer are devised to improve the interpretability of the fuzzy model for multi-step predictions. Second, a new transformation layer is designed to address the potential issues in the vanished rule firing strength caused by highdimensional inputs. Third, a new link layer is proposed to build temporal connections between multi-step predictions. Furthermore, a two-stage self-organizing mechanism is developed to automatically generate the fuzzy rules, in which the first stage is used to create the rule base from empty and perform the initial optimization, while the second stage is to fine-tune all network parameters. Finally, various simulations are carried out on chaotic and microgrid time series prediction problems, demonstrating the superiority of our approach in terms of prediction accuracy, uncertainty handling and model interpretability.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/cd47b7d7471bfc7a0350e0368dc26ea8f28828a1" target='_blank'>
-              How Intermodal Interaction Affects the Performance of Deep Multimodal Fusion for Mixed-Type Time Series
+          <td><a href="https://www.semanticscholar.org/paper/966cd74254d10e689fc476d8fb5dfec5e7e234b6" target='_blank'>
+              A New Self-organizing Interval Type-2 Fuzzy Neural Network for Multi-Step Time Series Prediction
               </a>
             </td>
           <td>
-            S.J. Dietz, Thomas Altstidl, Dario Zanca, Björn Eskofier, An Nguyen
+            Fulong Yao, Wanqing Zhao, Matthew Forshaw, Yang Song
           </td>
-          <td>2024-06-21</td>
+          <td>2024-07-10</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>4</td>
+          <td>1</td>
         </tr>
 
-        <tr id="We present a knowledge-guided machine learning (KGML) framework for modeling multi-scale processes, and study its performance in the context of streamflow forecasting in hydrology. Specifically, we propose a novel hierarchical recurrent neural architecture that factorizes the system dynamics at multiple temporal scales and captures their interactions. This framework consists of an inverse and a forward model. The inverse model is used to empirically resolve the system's temporal modes from data (physical model simulations, observed data, or a combination of them from the past), and these states are then used in the forward model to predict streamflow. In a hydrological system, these modes can represent different processes, evolving at different temporal scales (e.g., slow: groundwater recharge and baseflow vs. fast: surface runoff due to extreme rainfall). A key advantage of our framework is that once trained, it can incorporate new observations into the model's context (internal state) without expensive optimization approaches (e.g., EnKF) that are traditionally used in physical sciences for data assimilation. Experiments with several river catchments from the NWS NCRFC region show the efficacy of this ML-based data assimilation framework compared to standard baselines, especially for basins that have a long history of observations. Even for basins that have a shorter observation history, we present two orthogonal strategies of training our FHNN framework: (a) using simulation data from imperfect simulations and (b) using observation data from multiple basins to build a global model. We show that both of these strategies (that can be used individually or together) are highly effective in mitigating the lack of training data. The improvement in forecast accuracy is particularly noteworthy for basins where local models perform poorly because of data sparsity.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/520332f72d1a6deaabdd7dd965c0cf76e89053b5" target='_blank'>
-              Hierarchically Disentangled Recurrent Network for Factorizing System Dynamics of Multi-scale Systems
+          <td><a href="https://www.semanticscholar.org/paper/c6f317b12417c129221d4d1696f5c5b193bef61a" target='_blank'>
+              Discrete-time graph neural networks for transaction prediction in Web3 social platforms
               </a>
             </td>
           <td>
-            Rahul Ghosh, Zac McEachran, Arvind Renganathan, Kelly Lindsay, Somya Sharma, M. Steinbach, John L. Nieber, Christopher J. Duffy, Vipin Kumar
+            Manuel Dileo, Matteo Zignani
           </td>
-          <td>2024-07-29</td>
-          <td>ArXiv</td>
+          <td>2024-06-25</td>
+          <td>Mach. Learn.</td>
           <td>0</td>
-          <td>44</td>
+          <td>15</td>
         </tr>
 
-        <tr id="
- Graph Neural Networks (GNNs) are deep learning models specifically designed for analyzing graph-structured data, capturing complex relationships and structures to improve analysis and prediction. A common task in GNNs is node classification, where each node in the graph is assigned a predefined category. The Graph Attention Network (GAT) is a popular variant of GNNs known for its ability to capture complex dependencies by assigning importance weights to nodes during information aggregation. However, the GAT’s reliance on local attention mechanisms limits its effectiveness in capturing global information and long-range dependencies. To address this limitation, we propose a new attention mechanism called Global-Local Graph Attention (GLGA). Our mechanism enables the GAT to capture long-range dependencies and global graph structures while maintaining its ability to focus on local interactions. We evaluate our algorithm on three citation datasets (Cora, Citeseer, and Pubmed) using multiple metrics, demonstrating its superiority over other baseline models. The proposed GLGA mechanism has been proven to be an effective solution for improving node classification tasks.">
+        <tr id="Generative pretrained models represent a significant advancement in natural language processing and computer vision, which can generate coherent and contextually relevant content based on the pre-training on large general datasets and fine-tune for specific tasks. Building foundation models using large scale omic data is promising to decode and understand the complex signaling language patterns within cells. Different from existing foundation models of omic data, we build a foundation model, mosGraphGPT, for multi-omic signaling (mos) graphs, in which the multi-omic data was integrated and interpreted using a multi-level signaling graph. The model was pretrained using multi-omic data of cancers in The Cancer Genome Atlas (TCGA), and fine-turned for multi-omic data of Alzheimer’s Disease (AD). The experimental evaluation results showed that the model can not only improve the disease classification accuracy, but also is interpretable by uncovering disease targets and signaling interactions. And the model code are uploaded via GitHub with link: https://github.com/mosGraph/mosGraphGPT">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c1f387e285df6163f69689ed5ed40e0e4c8fcc01" target='_blank'>
-              Global-local graph attention: unifying global and local attention for node classification
+          <td><a href="https://www.semanticscholar.org/paper/921061abb7058296f902de2f988608493d126a30" target='_blank'>
+              mosGraphGPT: a foundation model for multi-omic signaling graphs using generative AI
               </a>
             </td>
           <td>
-            Keao Lin, Xiao-Zhu Xie, Wei Weng, Xiaofeng Du
+            Heming Zhang, Di Huang, Emily Chen, Dekang Cao, Tim Xu, Ben Dizdar, Guangfu Li, Yixin Chen, Philip R. O. Payne, Michael Province, Fuhai Li
           </td>
-          <td>2024-07-11</td>
-          <td>The Computer Journal</td>
+          <td>2024-08-06</td>
+          <td>bioRxiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Advertising platforms have evolved in estimating Lifetime Value (LTV) to better align with advertisers' true performance metric. However, the sparsity of real-world LTV data presents a significant challenge to LTV predictive model(i.e., pLTV), severely limiting the their capabilities. Therefore, we propose to utilize external data, in addition to the internal data of advertising platform, to expand the size of purchase samples and enhance the LTV prediction model of the advertising platform. To tackle the issue of data distribution shift between internal and external platforms, we introduce an Adaptive Difference Siamese Network (ADSNet), which employs cross-domain transfer learning to prevent negative transfer. Specifically, ADSNet is designed to learn information that is beneficial to the target domain. We introduce a gain evaluation strategy to calculate information gain, aiding the model in learning helpful information for the target domain and providing the ability to reject noisy samples, thus avoiding negative transfer. Additionally, we also design a Domain Adaptation Module as a bridge to connect different domains, reduce the distribution distance between them, and enhance the consistency of representation space distribution. We conduct extensive offline experiments and online A/B tests on a real advertising platform. Our proposed ADSNet method outperforms other methods, improving GINI by 2$\%$. The ablation study highlights the importance of the gain evaluation strategy in negative gain sample rejection and improving model performance. Additionally, ADSNet significantly improves long-tail prediction. The online A/B tests confirm ADSNet's efficacy, increasing online LTV by 3.47$\%$ and GMV by 3.89$\%$.">
+        <tr id="The balance between model capacity and generalization has been a key focus of recent discussions in long-term time series forecasting. Two representative channel strategies are closely associated with model expressivity and robustness, including channel independence (CI) and channel dependence (CD). The former adopts individual channel treatment and has been shown to be more robust to distribution shifts, but lacks sufficient capacity to model meaningful channel interactions. The latter is more expressive for representing complex cross-channel dependencies, but is prone to overfitting. To balance the two strategies, we present a channel-aware low-rank adaptation method to condition CD models on identity-aware individual components. As a plug-in solution, it is adaptable for a wide range of backbone architectures. Extensive experiments show that it can consistently and significantly improve the performance of both CI and CD models with demonstrated efficiency and flexibility. The code is available at https://github.com/tongnie/C-LoRA.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/41ea7e90e94f637a06b34100fe0e7527df480572" target='_blank'>
-              ADSNet: Cross-Domain LTV Prediction with an Adaptive Siamese Network in Advertising
+          <td><a href="https://www.semanticscholar.org/paper/99eb0dde01b9d4215864beae7111853843550b8a" target='_blank'>
+              Channel-Aware Low-Rank Adaptation in Time Series Forecasting
               </a>
             </td>
           <td>
-            Ruize Wang, Hui Xu, Ying Cheng, Qi He, Xing Zhou, Rui Feng, Wei Xu, Lei Huang, Jie Jiang
+            Tong Nie, Yuewen Mei, Guoyang Qin, Jiangming Sun, Wei Ma
           </td>
-          <td>2024-06-15</td>
+          <td>2024-07-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>5</td>
-        </tr>
-
-        <tr id="This study introduces a novel approach that integrates dynamic Bayesian network with attention based spatio-temporal graph convolutional network to forecast railway train delays, capturing the intricate operation interactions between train events and the dynamic evolution of train delays. Initially, train delay patterns are identified using the K-means clustering algorithm and incorporated as additional variables into the prediction model. To capture dynamic causality in delay propagation, we utilize a dynamic Bayesian network-based dynamic causality graph, incorporating train delay data and domain knowledge to effectively model the train delay propagation. Leveraging these insights on delay dynamic propagation, we propose an attention based spatio-temporal graph convolutional network that effectively models the dynamic spatio-temporal dependency among train events and enhances the accuracy of delay predictions. The proposed method is assessed using operational data from the Wuhan-Guangzhou high-speed railway. Results show that the proposed model outperforms the baseline models, particularly with the expansion of the prediction horizon. The learned dynamic causality of the train delay propagation enhances interpretability and results in a 6.97% reduction in mean absolute error. Furthermore, train delay patterns and weather variables contribute to a respective 12.85% and 4.37% reduction in mean absolute error. The statistical tests further validate the efficacy of the proposed model.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/31fbcd9b82bde6579a24f9baa5171614e4509e9c" target='_blank'>
-              Bayesian Spatio-Temporal Graph Convolutional Network for Railway Train Delay Prediction
-              </a>
-            </td>
-          <td>
-            Jianmin Li, Xinyue Xu, Xin Ding, Jun Liu, Bin Ran
-          </td>
-          <td>2024-07-01</td>
-          <td>IEEE Transactions on Intelligent Transportation Systems</td>
-          <td>0</td>
-          <td>6</td>
+          <td>3</td>
         </tr>
 
-        <tr id="A Marked Temporal Point Process (MTPP) is a stochastic process whose realization is a set of event-time data. MTPP is often used to understand complex dynamics of asynchronous temporal events such as money transaction, social media, healthcare, etc. Recent studies have utilized deep neural networks to capture complex temporal dependencies of events and generate embedding that aptly represent the observed events. While most previous studies focus on the inter-event dependencies and their representations, how individual events influence the overall dynamics over time has been under-explored. In this regime, we propose a Decoupled MTPP framework that disentangles characterization of a stochastic process into a set of evolving influences from different events. Our approach employs Neural Ordinary Differential Equations (Neural ODEs) to learn flexible continuous dynamics of these influences while simultaneously addressing multiple inference problems, such as density estimation and survival rate computation. We emphasize the significance of disentangling the influences by comparing our framework with state-of-the-art methods on real-life datasets, and provide analysis on the model behavior for potential applications.">
+        <tr id="In many situations, the measurements of a studied phenomenon are provided sequentially, and the prediction of its class needs to be made as early as possible so as not to incur too high a time penalty, but not too early and risk paying the cost of misclassification. This problem has been particularly studied in the case of time series, and is known as Early Classification of Time Series (ECTS). Although it has been the subject of a growing body of literature, there is still a lack of a systematic, shared evaluation protocol to compare the relative merits of the various existing methods. This document begins by situating these methods within a principle-based taxonomy. It defines dimensions for organizing their evaluation, and then reports the results of a very extensive set of experiments along these dimensions involving nine state-of-the art ECTS algorithms. In addition, these and other experiments can be carried out using an open-source library in which most of the existing ECTS algorithms have been implemented (see \url{https://github.com/ML-EDM/ml_edm}).">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/01528db95c399e0822e827b108710fdf76fd5f21" target='_blank'>
-              Decoupled Marked Temporal Point Process using Neural Ordinary Differential Equations
+          <td><a href="https://www.semanticscholar.org/paper/b398a7a69b9500f231044e06baa20805f2eb5afd" target='_blank'>
+              Early Classification of Time Series: Taxonomy and Benchmark
               </a>
             </td>
           <td>
-            Yujee Song, Donghyun Lee, Rui Meng, Won Hwa Kim
+            Aurélien Renault, A. Bondu, Antoine Cornu'ejols, Vincent Lemaire
           </td>
-          <td>2024-06-10</td>
+          <td>2024-06-26</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>10</td>
         </tr>
 
-        <tr id="Foundation models (FMs) currently dominate news headlines. They employ advanced deep learning architectures to extract structural information autonomously from vast datasets through self-supervision. The resulting rich representations of complex systems and dynamics can be applied to many downstream applications. Therefore, FMs can find uses in electric power grids, challenged by the energy transition and climate change. In this paper, we call for the development of, and state why we believe in, the potential of FMs for electric grids. We highlight their strengths and weaknesses amidst the challenges of a changing grid. We argue that an FM learning from diverse grid data and topologies could unlock transformative capabilities, pioneering a new approach in leveraging AI to redefine how we manage complexity and uncertainty in the electric grid. Finally, we discuss a power grid FM concept, namely GridFM, based on graph neural networks and show how different downstream tasks benefit.">
+        <tr id="This paper presents a new method to determine the optimal batch size for applying deep learning models with time series data. A set of batch sizes is determined by considering the length of the repetition pattern of the data using the Fast Fourier Transform (FFT). A comparative analysis is conducted to identify the impact of varying batch sizes on prediction errors for the three deep learning models. The results show that the RNN model has the optimal batch size that produces the minimum prediction error. In the DNN and CNN models, the optimal batch size is not correlated with the repetition pattern of time series data. Therefore, it is not recommended to apply CNN and DNN models of time series data. However, if used, a small batch size can be selected to reduce training time. In addition, the range of prediction error according to batch size is significantly larger for RNN models compared to DNN and CNN models.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/ccdce57aa37af5fab8e15c5c8f5d8a9b8a8675a2" target='_blank'>
-              A Perspective on Foundation Models for the Electric Power Grid
+          <td><a href="https://www.semanticscholar.org/paper/d1d9bac2cd18ff1641bc3ec0c44bcff2270a3253" target='_blank'>
+              Determination of Optimal Batch Size of Deep Learning Models with Time Series Data
               </a>
             </td>
           <td>
-            Hendrik Hamann, Thomas Brunschwiler, B. Gjorgiev, Leonardo S. A. Martins, Alban Puech, Anna Varbella, Jonas Weiss, Juan Bernabé-Moreno, Alexandre Blondin Mass'e, Seong Choi, Ian Foster, B. Hodge, Rishabh Jain, Kibaek Kim, Vincent Mai, Franccois Miralles, M. D. Montigny, Octavio Ramos-Leaños, Hussein Suprême, Le Xie, El-Nasser S. Youssef, Arnaud Zinflou, Alexander J. Belvi, Ricardo J. Bessa, Bishnu Prasad Bhattari, J. Schmude, Stanislav Sobolevsky
+            J. Hwang, Sang-Soo Lee, Jeong-Won Gil, Choul-Ki Lee
           </td>
           <td>2024-07-12</td>
-          <td>ArXiv</td>
+          <td>Sustainability</td>
           <td>0</td>
-          <td>58</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Accurate short-term forecasting of power load is essential for the reliable operation of the comprehensive energy systems of ports and for effectively reducing energy consumption. Owing to the complexity of port systems, traditional load forecasting methods often struggle to capture the non-linearity and multifactorial interactions within the factors creating power load. To address these challenges, this study combines variational mode decomposition (VMD), temporal convolutional network (TCN), and long short-term memory (LSTM) network to develop a multi-feature-based VMD-TCN-LSTM model for the short-term forecasting of the power load of ports. VMD is first used to decompose the power load series of ports into multiple, relatively stable components to mitigate volatility. Furthermore, meteorological and temporal features are introduced into the TCN-LSTM model, which combines the temporal feature extraction capability of the TCN and the long term-dependent learning capability of the LSTM. Comparative analyses with other common forecasting models using the observed power load data from a coastal port in China demonstrate that the proposed forecasting model achieves a higher prediction accuracy, with an R-squared value of 0.94, mean squared error of 3.59 MW, and a mean absolute percentage error of 2.36%.">
+        <tr id="In the financial industry, the ability to predict financial metrics accurately and in a timely manner can significantly impact investment decisions, risk management, and strategic planning. In recent years, machine learning has emerged as a powerful tool for such predictions. This study aims to explore the heretofore underexplored predictive potential of ChatGPT by predicting positive or negative changes in quarterly financial metrics, such as revenue and sales numbers, using textual data from social media. The performance of ChatGPT is compared against Long Short-Term Memory (LSTM) neural network models developed as part of this research. The methodology involves preprocessing large datasets from Twitter concerning major companies such as Amazon, Google, and Tesla, training LSTM models, and prompt engineering for ChatGPT-based predictions. Initial findings indicate that LSTM models can predict quarterly financial metric changes with up to 87% accuracy, significantly outperforming ChatGPT, which achieves a maximum accuracy of 67%. Therefore, at the current time, ChatGPT cannot be considered a reliable predictive tool for changes in quarterly financial metrics.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/0ede2faa5546cfbefa083cdef9bfe4e7663ea5a1" target='_blank'>
-              Multifeature-Based Variational Mode Decomposition–Temporal Convolutional Network–Long Short-Term Memory for Short-Term Forecasting of the Load of Port Power Systems
+          <td><a href="https://www.semanticscholar.org/paper/8b4e2a6ac5ac0110e5991ee0a5cd2260ead16e09" target='_blank'>
+              Comparing ChatGPT And LSTM In Predicting Changes In Quarterly Financial Metrics
               </a>
             </td>
           <td>
-            Guang Chen, Xiaofeng Ma, Lin Wei
+            Vitali Chaiko
           </td>
-          <td>2024-06-22</td>
-          <td>Sustainability</td>
+          <td>2024-06-30</td>
+          <td>Business &amp; Management Compass</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Weather forecasting refers to learning evolutionary patterns of some key upper-air and surface variables which is of great significance. Recently, deep learning-based methods have been increasingly applied in the field of weather forecasting due to their powerful feature learning capabilities. However, prediction methods based on the original space iteration struggle to effectively and efficiently utilize large number of weather variables. Therefore, we propose an 'encoding-prediction-decoding' prediction network. This network can efficiently benefit to more related input variables with key variables, that is, it can adaptively extract key variable-related low-dimensional latent feature from much more input atmospheric variables for iterative prediction. And we construct a loss function to guide the iteration of latent feature by utilizing multiple atmospheric variables in corresponding lead times. The obtained latent features through iterative prediction are then decoded to obtain the predicted values of key variables in multiple lead times. In addition, we improve the HTA algorithm in \cite{bi2023accurate} by inputting more time steps to enhance the temporal correlation between the prediction results and input variables. Both qualitative and quantitative prediction results on ERA5 dataset validate the superiority of our method over other methods. (The code will be available at https://github.com/rs-lsl/Kvp-lsi)">
+        <tr id="Capturing long-term dependency from historical behaviors is the key to the success of sequential recommendation; however, existing methods focus on extracting global sequential information while neglecting to obtain deep representations from subsequences. Previous research has revealed that the restricted inter-item transfer is fundamental to sequential modeling, and some potential substructures of sequences can help models learn more effective long-term dependency compared to the whole sequence. To automatically find better subsequences and perform efficient learning, we propose a sequential recommendation model with a gated recurrent unit and Transformers, abbreviated as GAT4Rec, which employs Transformers with shared parameters across layers to model users’ historical interaction sequences. The representation learned by the gated recurrent unit is used as the gating signal to identify the optimal substructure in user sequences. The fused representation of the subsequence and edge information is extracted by the encoding layer to make the corresponding recommendations. Experimental results on four well-known publicly available datasets demonstrate that our GAT4Rec model outperforms other recommendation models, achieving performance improvements of 5.77%, 1.35%, 11.58%, and 1.79% in the normalized discounted cumulative gain metric (NDCG@10), respectively.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/11cc8cb84dcb1157d6fac95012b48b1ab2b7d05d" target='_blank'>
-              Efficiently improving key weather variables forecasting by performing the guided iterative prediction in latent space
+          <td><a href="https://www.semanticscholar.org/paper/79a52d00fb976862ea5711ed640577ec503068bd" target='_blank'>
+              GAT4Rec: Sequential Recommendation with a Gated Recurrent Unit and Transformers
               </a>
             </td>
           <td>
-            Shuangliang Li, Siwei Li
+            Huaiwen He, Xiangdong Yang, Feng Huang, Feng Yi, Shangsong Liang
           </td>
-          <td>2024-07-27</td>
-          <td>ArXiv</td>
+          <td>2024-07-12</td>
+          <td>Mathematics</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="This paper presents Diffusion Forcing, a new training paradigm where a diffusion model is trained to denoise a set of tokens with independent per-token noise levels. We apply Diffusion Forcing to sequence generative modeling by training a causal next-token prediction model to generate one or several future tokens without fully diffusing past ones. Our approach is shown to combine the strengths of next-token prediction models, such as variable-length generation, with the strengths of full-sequence diffusion models, such as the ability to guide sampling to desirable trajectories. Our method offers a range of additional capabilities, such as (1) rolling-out sequences of continuous tokens, such as video, with lengths past the training horizon, where baselines diverge and (2) new sampling and guiding schemes that uniquely profit from Diffusion Forcing's variable-horizon and causal architecture, and which lead to marked performance gains in decision-making and planning tasks. In addition to its empirical success, our method is proven to optimize a variational lower bound on the likelihoods of all subsequences of tokens drawn from the true joint distribution. Project website: https://boyuan.space/diffusion-forcing">
+        <tr id="The prediction of vacant parking spaces (VPSs) can reduce the time drivers spend searching for parking, thus alleviating traffic congestion. However, previous studies have mostly focused on modeling the temporal features of VPSs using historical data, neglecting the complex and extensive spatial characteristics of different parking lots within the transportation network. This is mainly due to the lack of direct physical connections between parking lots, making it challenging to quantify the spatio-temporal features among them. To address this issue, we propose a dynamic spatio-temporal adaptive graph convolutional recursive network (DSTAGCRN) for VPS prediction. Specifically, DSTAGCRN divides VPS data into seasonal and periodic trend components and combines daily and weekly information with node embeddings using the dynamic parameter-learning module (DPLM) to generate dynamic graphs. Then, by integrating gated recurrent units (GRUs) with the parameter-learning graph convolutional recursive module (PLGCRM) of DPLM, we infer the spatio-temporal dependencies for each time step. Furthermore, we introduce a multihead attention mechanism to effectively capture and fuse the spatio-temporal dependencies and dynamic changes in the VPS data, thereby enhancing the prediction performance. Finally, we evaluate the proposed DSTAGCRN on three real parking datasets. Extensive experiments and analyses demonstrate that the DSTAGCRN model proposed in this study not only improves the prediction accuracy but can also better extract the dynamic spatio-temporal characteristics of available parking space data in multiple parking lots.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/40d63dc2b465c9081e4efc5a19514da151e97fe7" target='_blank'>
-              Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion
+          <td><a href="https://www.semanticscholar.org/paper/eca0d5f95593149c00ab5b7ac8b7112a781351ba" target='_blank'>
+              Dynamic Spatio-Temporal Adaptive Graph Convolutional Recurrent Networks for Vacant Parking Space Prediction
               </a>
             </td>
           <td>
-            Boyuan Chen, Diego Marti Monso, Yilun Du, Max Simchowitz, Russ Tedrake, Vincent Sitzmann
+            Liangpeng Gao, Wenli Fan, Wenliang Jian
           </td>
-          <td>2024-07-01</td>
-          <td>ArXiv</td>
-          <td>1</td>
+          <td>2024-07-07</td>
+          <td>Applied Sciences</td>
+          <td>0</td>
           <td>3</td>
         </tr>
 
-        <tr id="Heterogeneous graphs have attracted a lot of research interests recently due to the success for representing complex real-world systems. However, existing methods have two pain points in embedding them into low-dimensional spaces: the mixing of structural and semantic information, and the distributional mismatch between data and embedding spaces. These two challenges require representation methods to consider the global and partial data distributions while unmixing the information. Therefore, in this paper, we propose $\text{Dis-H}^2\text{GCN}$, a Disentangled Hyperbolic Heterogeneous Graph Convolutional Network. On the one hand, we leverage the mutual information minimization and discrimination maximization constraints to disentangle the semantic features from comprehensively learned representations by independent message propagation for each edge type, away from the pure structural features. On the other hand, the entire model is constructed upon the hyperbolic geometry to narrow the gap between data distributions and representing spaces. We evaluate our proposed $\text{Dis-H}^2\text{GCN}$ on five real-world heterogeneous graph datasets across two downstream tasks: node classification and link prediction. The results demonstrate its superiority over state-of-the-art methods, showcasing the effectiveness of our method in disentangling and representing heterogeneous graph data in hyperbolic spaces.">
+        <tr id="In this paper, we explore advanced modifications to the Tweedie regression model in order to address its limitations in modeling aggregate claims for various types of insurance such as automobile, health, and liability. Traditional Tweedie models, while effective in capturing the probability and magnitude of claims, usually fall short in accurately representing the large incidence of zero claims. Our recommended approach involves a refined modeling of the zero-claim process, together with the integration of boosting methods in order to help leverage an iterative process to enhance predictive accuracy. Despite the inherent slowdown in learning algorithms due to this iteration, several efficient implementation techniques that also help precise tuning of parameter like XGBoost, LightGBM, and CatBoost have emerged. Nonetheless, we chose to utilize CatBoost, a efficient boosting approach that effectively handles categorical and other special types of data. The core contribution of our paper is the assembly of separate modeling for zero claims and the application of tree-based boosting ensemble methods within a CatBoost framework, assuming that the inflated probability of zero is a function of the mean parameter. The efficacy of our enhanced Tweedie model is demonstrated through the application of an insurance telematics dataset, which presents the additional complexity of compositional feature variables. Our modeling results reveal a marked improvement in model performance, showcasing its potential to deliver more accurate predictions suitable for insurance claim analytics.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6355ae279eec7cb2aaad055238e6210bd4c04683" target='_blank'>
-              Disentangled Hyperbolic Representation Learning for Heterogeneous Graphs
+          <td><a href="https://www.semanticscholar.org/paper/5af74d76d784bacfe974c20112cdcad54eedeb64" target='_blank'>
+              Zero-Inflated Tweedie Boosted Trees with CatBoost for Insurance Loss Analytics
               </a>
             </td>
           <td>
-            Qijie Bai, Changli Nie, Haiwei Zhang, Zhicheng Dou, Xiaojie Yuan
+            Banghee So, Emiliano A. Valdez
           </td>
-          <td>2024-06-14</td>
+          <td>2024-06-23</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>27</td>
         </tr>
 
-        <tr id="Distribution shifts between training and test data are all but inevitable over the lifecycle of a deployed model and lead to performance decay. Adapting the model can hopefully mitigate this drop in performance. Yet, adaptation is challenging since it must be unsupervised: we usually do not have access to any labeled data at test time. In this paper, we propose a probabilistic state-space model that can adapt a deployed model subjected to distribution drift. Our model learns the dynamics induced by distribution shifts on the last set of hidden features. Without requiring labels, we infer time-evolving class prototypes that serve as a dynamic classification head. Moreover, our approach is lightweight, modifying only the model's last linear layer. In experiments on real-world distribution shifts and synthetic corruptions, we demonstrate that our approach performs competitively with methods that require back-propagation and access to the model backbone. Our model especially excels in the case of small test batches - the most difficult setting.">
+        <tr id="Industrial processes generate vast amounts of time series data, yet extracting meaningful relationships and insights remains challenging. This paper introduces a framework for automated knowledge graph learning from time series data, specifically tailored for industrial applications. Our framework addresses the complexities inherent in industrial datasets, transforming them into knowledge graphs that improve decision-making, process optimization, and knowledge discovery. Additionally, it employs Granger causality to identify key attributes that can inform the design of predictive models. To illustrate the practical utility of our approach, we also present a motivating use case demonstrating the benefits of our framework in a real-world industrial scenario. Further, we demonstrate how the automated conversion of time series data into knowledge graphs can identify causal influences or dependencies between important process parameters.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2b1d8333834155ef8196c5d42306122cf3b18d7f" target='_blank'>
-              Test-Time Adaptation with State-Space Models
+          <td><a href="https://www.semanticscholar.org/paper/97316fa9b00e993db090c916509994ba4b2d0b70" target='_blank'>
+              Automated Knowledge Graph Learning in Industrial Processes
               </a>
             </td>
           <td>
-            Mona Schirmer, Dan Zhang, Eric Nalisnick
+            Lolitta Ammann, Jorge Martínez Gil, Michael Mayr, Georgios C. Chasparis
           </td>
-          <td>2024-07-17</td>
+          <td>2024-07-02</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>12</td>
         </tr>
 
-        <tr id="Sequential recommendation (SR) tasks enhance recommendation accuracy by capturing the connection between users' past interactions and their changing preferences. Conventional models often focus solely on capturing sequential patterns within the training data, neglecting the broader context and semantic information embedded in item titles from external sources. This limits their predictive power and adaptability. Recently, large language models (LLMs) have shown promise in SR tasks due to their advanced understanding capabilities and strong generalization abilities. Researchers have attempted to enhance LLMs' recommendation performance by incorporating information from SR models. However, previous approaches have encountered problems such as 1) only influencing LLMs at the result level; 2) increased complexity of LLMs recommendation methods leading to reduced interpretability; 3) incomplete understanding and utilization of SR models information by LLMs. To address these problems, we proposes a novel framework, DELRec, which aims to extract knowledge from SR models and enable LLMs to easily comprehend and utilize this supplementary information for more effective sequential recommendations. DELRec consists of two main stages: 1) SR Models Pattern Distilling, focusing on extracting behavioral patterns exhibited by SR models using soft prompts through two well-designed strategies; 2) LLMs-based Sequential Recommendation, aiming to fine-tune LLMs to effectively use the distilled auxiliary information to perform SR tasks. Extensive experimental results conducted on three real datasets validate the effectiveness of the DELRec framework.">
+        <tr id="Time series data is widely available in a variety of industries. By forecasting time series, decision-makers can better grasp future trends and make more effective decisions. Financial time series data exhibit non-stationarity and high volatility. High-frequency fluctuations in financial products such as exchange rates, bonds and equities may reflect external shocks and risks in global financial markets, which are potentially dangerous and may threaten national economic security or even trigger financial crises. For financial time series data, a deep recurrent neural network first progressively processes each data point in the time series through its recurrent unit. Each recurring unit can adjust its own weights to better predict or analyze future values. Over time, these recurrent units continuously update their internal state, resulting in a comprehensive understanding of the characteristics of the entire data sequence. In addition, we add a gating mechanism to further improve the network's ability to control the flow of information, so that the model is more effective when retaining long-term dependencies, so as to improve the accuracy of prediction and the stability of the model. Experimental results show that our recurrent neural network model shows higher prediction accuracy and stability than other baseline models on financial time series datasets.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a12502995c4fcfa87be04bf3cc72bdfe05fe9ea8" target='_blank'>
-              DELRec: Distilling Sequential Pattern to Enhance LLM-based Recommendation
+          <td><a href="https://www.semanticscholar.org/paper/6f5f866e6e62fae9396ebd199496590a68d45ac8" target='_blank'>
+              Research on time-series financial data prediction and analysis based on deep recurrent neural network
               </a>
             </td>
           <td>
-            Guohao Sun, Haoyi Zhang
+            Feng Yuan
           </td>
-          <td>2024-06-17</td>
-          <td>ArXiv</td>
+          <td>2024-07-25</td>
+          <td>Applied and Computational Engineering</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="The utilization of Transformer-based models prospers the growth of multi-document summarization (MDS). Given the huge impact and widespread adoption of Transformer-based models in various natural language processing tasks, investigating their performance and behaviors in the context of MDS becomes crucial for advancing the field and enhancing the quality of summary. To thoroughly examine the behaviours of Transformer-based MDS models, this paper presents five empirical studies on (1) measuring the impact of document boundary separators quantitatively; (2) exploring the effectiveness of different mainstream Transformer structures; (3) examining the sensitivity of the encoder and decoder; (4) discussing different training strategies; and (5) discovering the repetition in a summary generation. The experimental results on prevalent MDS datasets and eleven evaluation metrics show the influence of document boundary separators, the granularity of different level features and different model training strategies. The results also reveal that the decoder exhibits greater sensitivity to noises compared to the encoder. This underscores the important role played by the decoder, suggesting a potential direction for future research in MDS. Furthermore, the experimental results indicate that the repetition problem in the generated summaries has correlations with the high uncertainty scores.">
+        <tr id="Graph data structures offer a versatile and powerful means to model relationships and interconnections in various domains, promising substantial advantages in data representation, analysis, and visualization. In games, graph-based data structures are omnipresent and represent, for example, game economies, skill trees or complex, branching quest lines. With this paper, we propose G-PCGRL, a novel and controllable method for the procedural generation of graph data using reinforcement learning. Therefore, we frame this problem as manipulating a graph's adjacency matrix to fulfill a given set of constraints. Our method adapts and extends the Procedural Content Generation via Reinforcement Learning (PCGRL) framework and introduces new representations to frame the problem of graph data generation as a Markov decision process. We compare the performance of our method with the original PCGRL, the run time with a random search and evolutionary algorithm, and evaluate G-PCGRL on two graph data domains in games: game economies and skill trees. The results show that our method is capable of generating graph-based content quickly and reliably to support and inspire designers in the game creation process. In addition, trained models are controllable in terms of the type and number of nodes to be generated.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/bb81fa6aa9be3d56802cfafdf60fdfeddf4f007c" target='_blank'>
-              Rethinking Transformer-based Multi-document Summarization: An Empirical Investigation
+          <td><a href="https://www.semanticscholar.org/paper/da8186d9c837b3b5140555e1d9904967ed9b8441" target='_blank'>
+              G-PCGRL: Procedural Graph Data Generation via Reinforcement Learning
               </a>
             </td>
           <td>
-            Congbo Ma, Wei Emma Zhang, Dileepa Pitawela, Haojie Zhuang, Yanfeng Shu
+            Florian Rupp, Kai Eckert
           </td>
-          <td>2024-07-16</td>
+          <td>2024-07-15</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>8</td>
-        </tr>
-
-        <tr id="Accurate traffic forecasting is more necessary than ever for transportation departments, especially given its significant role in traffic planning, management, and control. However, most existing methods struggle to address complex spatial correlations on road networks, nonlinear temporal dynamics, and difficult long‐term prediction. This article proposes a novel spatial temporal graph gated transformer (STGGT) to overcome these challenges. The suggested model differs from Google's transformer because it uses a hybrid architecture that integrates graph convolutional networks (GCNs), attention, and gated recurrent units (GRUs) instead of solely relying on attention. Specifically, STGGT uses GCNs to extract spatial dependencies, utilizes attention and GRUs to extract temporal dependencies, and handle long‐term prediction. Experiments indicate that STGGT outperforms the state‐of‐the‐art baseline models on two real‐world traffic datasets of 9%–40%. The proposed model offers a promising solution for accurate traffic forecasting, simultaneously addressing the challenges of complex spatial correlations, nonlinear temporal dynamics, and long‐term prediction.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/64e802ce9b30e768f218018adb39b56cd14ee339" target='_blank'>
-              A spatial-temporal graph gated transformer for traffic forecasting
-              </a>
-            </td>
-          <td>
-            Haroun Bouchemoukha, M. Zennir, Ahmed Alioua
-          </td>
-          <td>2024-06-26</td>
-          <td>Trans. Emerg. Telecommun. Technol.</td>
-          <td>0</td>
-          <td>4</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Tabular synthesis models remain ineffective at capturing complex dependencies, and the quality of synthetic data is still insufficient for comprehensive downstream tasks, such as prediction under distribution shifts, automated decision-making, and cross-table understanding. A major challenge is the lack of prior knowledge about underlying structures and high-order relationships in tabular data. We argue that a systematic evaluation on high-order structural information for tabular data synthesis is the first step towards solving the problem. In this paper, we introduce high-order structural causal information as natural prior knowledge and provide a benchmark framework for the evaluation of tabular synthesis models. The framework allows us to generate benchmark datasets with a flexible range of data generation processes and to train tabular synthesis models using these datasets for further evaluation. We propose multiple benchmark tasks, high-order metrics, and causal inference tasks as downstream tasks for evaluating the quality of synthetic data generated by the trained models. Our experiments demonstrate to leverage the benchmark framework for evaluating the model capability of capturing high-order structural causal information. Furthermore, our benchmarking results provide an initial assessment of state-of-the-art tabular synthesis models. They have clearly revealed significant gaps between ideal and actual performance and how baseline methods differ. Our benchmark framework is available at URL https://github.com/TURuibo/CauTabBench.">
+        <tr id="This paper introduces a new addition to the SPINEX (Similarity-based Predictions with Explainable Neighbors Exploration) family, tailored specifically for time series and forecasting analysis. This new algorithm leverages the concept of similarity and higher-order temporal interactions across multiple time scales to enhance predictive accuracy and interpretability in forecasting. To evaluate the effectiveness of SPINEX, we present comprehensive benchmarking experiments comparing it against 18 algorithms and across 49 synthetic and real datasets characterized by varying trends, seasonality, and noise levels. Our performance assessment focused on forecasting accuracy and computational efficiency. Our findings reveal that SPINEX consistently ranks among the top 5 performers in forecasting precision and has a superior ability to handle complex temporal dynamics compared to commonly adopted algorithms. Moreover, the algorithm's explainability features, Pareto efficiency, and medium complexity (on the order of O(log n)) are demonstrated through detailed visualizations to enhance the prediction and decision-making process. We note that integrating similarity-based concepts opens new avenues for research in predictive analytics, promising more accurate and transparent decision making.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/612b10419f017d20c8b229a25d5e6939dd80c084" target='_blank'>
-              Causality for Tabular Data Synthesis: A High-Order Structure Causal Benchmark Framework
+          <td><a href="https://www.semanticscholar.org/paper/eb8311e78efe8332c0928c44bc76694e1d771836" target='_blank'>
+              SPINEX-TimeSeries: Similarity-based Predictions with Explainable Neighbors Exploration for Time Series and Forecasting Problems
               </a>
             </td>
           <td>
-            Ruibo Tu, Zineb Senane, Lele Cao, Cheng Zhang, H. Kjellström, G. Henter
+            Ahmed Z Naser, MZ Naser
           </td>
-          <td>2024-06-12</td>
+          <td>2024-08-04</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>36</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Multivariate time series anomaly detection is a crucial data mining technique with a wide range of applications in areas such as IT applications. Currently, the majority of anomaly detection methods for time series data rely on unsupervised approaches due to the rarity of anomaly labels. However, in real-world scenarios, obtaining a limited number of anomaly labels is feasible and affordable. Effective usage of these labels can offer valuable insights into the temporal characteristics of anomalies and play a pivotal role in guiding anomaly detection efforts. To improve the performance of multivariate time series anomaly detection, we proposed a novel deep learning model named EDD (Encoder-Decoder-Discriminator) that leverages limited anomaly samples. The EDD model innovatively integrates a graph attention network with long short term memory (LSTM) to extract spatial and temporal features from multivariate time series data. This integrated approach enables the model to capture complex patterns and dependencies within the data. Additionally, the model skillfully maps series data into a latent space, utilizing a carefully crafted loss function to cluster normal data tightly in the latent space while dispersing abnormal data randomly. This innovative design results in distinct probability distributions for normal and abnormal data in the latent space, enabling precise identification of anomalous data. To evaluate the performance of our EDD model, we conducted extensive experimental validation across three diverse datasets. The results demonstrate the significant superiority of our model in multivariate time series anomaly detection. Specifically, the average F1-Score of our model outperformed the second-best method by 2.7% and 73.4% in both evaluation approaches, respectively, highlighting its superior detection capabilities. These findings validate the effectiveness of our proposed EDD model in leveraging limited anomaly samples for accurate and robust anomaly detection in multivariate time series data.">
+        <tr id="Inventory prediction is concerned with the forecasting of future demand for products in order to optimize inventory levels and supply chain management. The challenges include demand volatility, data quality, multi-dimensional interactions, lead time variability, seasonal trends, and dynamic pricing. Nevertheless, these models suffer from numerous shortcomings, and in this research, we propose a new model, MMCW-BiLSTM (modified multi-dimensional collaboratively wrapped BiLSTM), for inventory prediction. The MMCW-BiLSTM model reflects a considerable leap in inventory forecasting by combining a number of components in order to consider intricate temporal dependencies and incorporate feature interactions. The MMCW-BiLSTM makes use of BiLSTM layers, collaborative attention mechanisms, and a multi-dimensional attention approach to learn from augmented datasets consisting of the original features and the extracted time series data. Moreover, adding a Taylor series transformation allows for a more precise description of the features in the model, thus improving the prediction precision. The results show that the models make the least mistakes when they use the AV demand forecasting dataset, with MAE values of 1.75, MAPE values of 2.89, MSE values of 6.76, and RMSE values of 2.6. Similarly, when utilizing the product demand dataset, the model also achieves the lowest error values for these metrics at 1.97, 3.91, 8.76, and 2.96. Likewise, when utilizing the dairy goods sales dataset, the model also achieves the lowest error values for these metrics at 2.54, 3.69, 10.39, and 3.22.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6a0b2af4fae72e31c61e9b23f7aa121732e8dfa5" target='_blank'>
-              An anomaly detection model for multivariate time series with anomaly perception
+          <td><a href="https://www.semanticscholar.org/paper/cccb2c220a6df8c844c4317f0b7f000d6fa902b8" target='_blank'>
+              Inventory Prediction Using a Modified Multi-Dimensional Collaborative Wrapped Bi-Directional Long Short-Term Memory Model
               </a>
             </td>
           <td>
-            Dong Wei, Wu Sun, Xiaofeng Zou, Dan Ma, Huarong Xu, Panfeng Chen, Chaoshu Yang, Mei Chen, Hui Li
+            Said Abualuroug, A. Alzubi, Kolawole Iyiola
           </td>
-          <td>2024-07-31</td>
-          <td>PeerJ Computer Science</td>
-          <td>0</td>
+          <td>2024-07-03</td>
+          <td>Applied Sciences</td>
           <td>0</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Time series forecasting has played an important role in different industries, including economics, energy, weather, and healthcare. RNN-based methods have shown promising potential due to their strong ability to model the interaction of time and variables. However, they are prone to gradient issues like gradient explosion and vanishing gradients. And the prediction accuracy is not high. To address the above issues, this paper proposes a Fractional-order Lipschitz Recurrent Neural Network with a Frequency-domain Gated Attention mechanism (FLRNN-FGA). There are three major components: the Fractional-order Lipschitz Recurrent Neural Network (FLRNN), frequency module, and gated attention mechanism. In the FLRNN, fractional-order integration is employed to describe the dynamic systems accurately. It can capture long-term dependencies and improve prediction accuracy. Lipschitz weight matrices are applied to alleviate the gradient issues. In the frequency module, temporal data are transformed into the frequency domain by Fourier transform. Frequency domain processing can reduce the computational complexity of the model. In the gated attention mechanism, the gated structure can regulate attention information transmission to reduce the number of model parameters. Extensive experimental results on five real-world benchmark datasets demonstrate the effectiveness of FLRNN-FGA compared with the state-of-the-art methods.">
+        <tr id="Dynamic multi-objective optimization problems (DMOPs) exhibit variations in constraints, decision parameter quantities, and the number of objectives over time, leading to changes in their optimal solutions. Prediction-based methods currently stand as the prevailing paradigm for handling DMOPs. Implicit correlations among solutions ob-tained at consecutive time steps while solving DMOPs con-tinuously can guide predictions for future time increments in the time series. Most existing methods rely on a single linear or nonlinear model to capture the correlations of historical optimal solutions. However, a linear model struggles with the nonlinear scenario, and using a nonlinear model to fit the linear relationship of the historical optimal solutions increases the training time because the nonlinear model has more parameters. This paper proposes a novel framework for time series ensemble prediction based on correlation type detection TSEPFCTD. The framework leverages correlation type detection strategy to identify the autocorrelation types in the time series of historical solutions. Subsequently, distinct prediction models are applied for different types, enhancing prediction accuracy. We implement this prediction framework on MOEA/D-DE, constructing a novel algorithm for solving DMOPs. Experimental results on a series of test suites demonstrate the effectiveness of our algorithm in providing robust solution outcomes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/df8abef5d3a79df25da8495db7434b86114030b4" target='_blank'>
-              FLRNN-FGA: Fractional-Order Lipschitz Recurrent Neural Network with Frequency-Domain Gated Attention Mechanism for Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/3ecb29b1ac7c61b9f51aefcec3ff68083f359042" target='_blank'>
+              Dynamic Multi-Objective Optimization Time Series Ensemble Prediction Framework Based on Correlation Type Detection
               </a>
             </td>
           <td>
-            Chunna Zhao, Junjie Ye, Zelong Zhu, Yaqun Huang
+            Lele Xie, Xiaoming Zhang, Ran Hu, Shun Zhang
           </td>
-          <td>2024-07-22</td>
-          <td>Fractal and Fractional</td>
+          <td>2024-06-30</td>
+          <td>2024 IEEE Congress on Evolutionary Computation (CEC)</td>
           <td>0</td>
-          <td>7</td>
+          <td>1</td>
         </tr>
 
-        <tr id="Graph Neural Networks (GNNs) have emerged as powerful tools for supervised machine learning over graph-structured data, while sampling-based node representation learning is widely utilized in unsupervised learning. However, scalability remains a major challenge in both supervised and unsupervised learning for large graphs (e.g., those with over 1 billion nodes). The scalability bottleneck largely stems from the mini-batch sampling phase in GNNs and the random walk sampling phase in unsupervised methods. These processes often require storing features or embeddings in memory. In the context of distributed training, they require frequent, inefficient random access to data stored across different workers. Such repeated inter-worker communication for each mini-batch leads to high communication overhead and computational inefficiency. We propose GraphScale, a unified framework for both supervised and unsupervised learning to store and process large graph data distributedly. The key insight in our design is the separation of workers who store data and those who perform the training. This separation allows us to decouple computing and storage in graph training, thus effectively building a pipeline where data fetching and data computation can overlap asynchronously. Our experiments show that GraphScale outperforms state-of-the-art methods for distributed training of both GNNs and node embeddings. We evaluate GraphScale both on public and proprietary graph datasets and observe a reduction of at least 40% in end-to-end training times compared to popular distributed frameworks, without any loss in performance. While most existing methods don't support billion-node graphs for training node embeddings, GraphScale is currently deployed in production at TikTok enabling efficient learning over such large graphs.">
+        <tr id="Unsupervised Domain Adaptation (UDA) has emerged as a key solution in data-driven fault diagnosis, addressing domain shift where models underperform in changing environments. However, under the realm of continually changing environments, UDA tends to underperform on previously seen domains when adapting to new ones - a problem known as catastrophic forgetting. To address this limitation, we introduce the EverAdapt framework, specifically designed for continuous model adaptation in dynamic environments. Central to EverAdapt is a novel Continual Batch Normalization (CBN), which leverages source domain statistics as a reference point to standardize feature representations across domains. EverAdapt not only retains statistical information from previous domains but also adapts effectively to new scenarios. Complementing CBN, we design a class-conditional domain alignment module for effective integration of target domains, and a Sample-efficient Replay strategy to reinforce memory retention. Experiments on real-world datasets demonstrate EverAdapt superiority in maintaining robust fault diagnosis in dynamic environments. Our code is available: https://github.com/mohamedr002/EverAdapt">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e5115bc6bf426026833b4f7fb72ae6282f678143" target='_blank'>
-              GraphScale: A Framework to Enable Machine Learning over Billion-node Graphs
+          <td><a href="https://www.semanticscholar.org/paper/0ac47f70a5e647f647faa7b42263e7b8c29cd85a" target='_blank'>
+              EverAdapt: Continuous Adaptation for Dynamic Machine Fault Diagnosis Environments
               </a>
             </td>
           <td>
-            Vipul Gupta, Xin Chen, Ruoyun Huang, Fanlong Meng, Jianjun Chen, Yujun Yan
+            Edward, Mohamed Ragab, Yuecong Xu, Min Wu, Zhenghua Chen, Abdulla Alseiari, Xiaoli Li
           </td>
-          <td>2024-07-22</td>
+          <td>2024-07-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>37</td>
         </tr>
 
-        <tr id="Industrial time-series, as a structural data responds to production process information, can be utilized to perform data-driven decision-making for effective monitoring of industrial production process. However, there are some challenges for time-series forecasting in industry, e.g., predicting few-shot caused by data shortage, and decision-confusing caused by unknown treatment policy. To cope with the problems, we propose a novel causal domain adaptation framework, Causal Domain Adaptation (CDA) forecaster to improve the performance on the interested domain with limited data (target). Firstly, we analyze the causality existing along with treatments, and thus ensure the shared causality over time. Subsequently, we propose an answer-based attention mechanism to achieve domain-invariant representation by the shared causality in both domains. Then, a novel domain-adaptation is built to model treatments and outcomes jointly training on source and target domain. The main insights are that our designed answer-based attention mechanism allows the target domain to leverage the existed causality in source time-series even with different treatments, and our forecaster can predict the counterfactual outcome of industrial time-series, meaning a guidance in production process. Compared with commonly baselines, our method on real-world and synthetic oilfield datasets demonstrates the effectiveness in across-domain prediction and the practicality in guiding production process">
+        <tr id="As a pivotal component of the global economic system, the stock market is subject to a multitude of influences, including the macroeconomic environment, market sentiment, and policy changes. Consequently, the ability to forecast stock prices is of paramount importance. Conventional time series forecasting techniques, such asARIMA and GARCH, are ill-equipped to handle complex nonlinear relationships. In contrast, recurrent neural networks, particularly Long Short-Term Memory (LSTM) networks, are particularly adept at handling time-dependent data. In light of recent advances in machine learning and deep learning, this study aims to assess and compare the efficacy of LSTM neural networks and Informer models in stock price forecasting. The objectives of this research are twofold: first, to compare the prediction accuracy using metrics such as Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and R²; and second, to explore fusion strategies to enhance overall prediction performance and computational efficiency. The methodology includes the following steps: data collection and preprocessing, model construction, feature engineering, and model training and evaluation. This study presents a systematic comparison of the effectiveness of LSTM and Informer models in stock price prediction. The findings indicate that a fusion strategy combining the advantages of both models is expected to enhance prediction accuracy and computational efficiency.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/156edecae87bbcc79ee4253c37525b426f87a42a" target='_blank'>
-              Domain Adaptation for Industrial Time-series Forecasting via Counterfactual Inference
+          <td><a href="https://www.semanticscholar.org/paper/1bbcb0bc1d7ecdbcbdff3b237621c2e470bbdce1" target='_blank'>
+              Advanced Stock Price Prediction Using LSTM and Informer Models
               </a>
             </td>
           <td>
-            Chao Min, Guo-quan Wen, Jiangru Yuan, Jun Yi, Xing Guo
+            Chuyang Duan, Wenjun Ke
           </td>
-          <td>2024-07-19</td>
-          <td>ArXiv</td>
+          <td>2024-06-27</td>
+          <td>Journal of Artificial Intelligence General science (JAIGS) ISSN:3006-4023</td>
+          <td>0</td>
           <td>0</td>
-          <td>3</td>
         </tr>
 
-        <tr id="Time series forecasting (TSF) is immensely important in extensive applications, such as electricity transformation, financial trade, medical monitoring, and smart agriculture. Although Transformer-based methods can handle time series data, their ability to predict long-term time series is limited due to the ``anti-order"nature of the self-attention mechanism. To address this problem, we focus on frequency domain to weaken the impact of order in TSF and propose the FreqBlock, where we first obtain frequency representations through the Frequency Transform Module. Subsequently, a newly designed Frequency Cross Attention is used to obtian enhanced frequency representations between the real and imaginary parts, thus establishing a link between the attention mechanism and the inherent Kramer-Kronig relations (KKRs). Our backbone network, FreqTSF, adopts a residual structure by concatenating multiple FreqBlocks to simulate KKRs in the frequency domain and avoid degradation problems. On a theoretical level, we demonstrate that the proposed two modules can significantly reduce the time and memory complexity from $\mathcal{O}(L^2)$ to $\mathcal{O}(L)$ for each FreqBlock computation. Empirical studies on four benchmark datasets show that FreqTSF achieves an overall relative MSE reduction of 15\% and an overall relative MAE reduction of 11\% compared to the state-of-the-art methods. The code will be available soon.">
+        <tr id="Time series classification stands as a pivotal and intricate challenge across various domains, including finance, healthcare, and industrial systems. In contemporary research, there has been a notable upsurge in exploring feature extraction through random sampling. Unlike deep convolutional networks, these methods sidestep elaborate training procedures, yet they often necessitate generating a surplus of features to comprehensively encapsulate time series nuances. Consequently, some features may lack relevance to labels or exhibit multi-collinearity with others. In this paper, we propose a novel hierarchical feature selection method aided by ANOVA variance analysis to address this challenge. Through meticulous experimentation, we demonstrate that our method substantially reduces features by over 94% while preserving accuracy -- a significant advancement in the field of time series analysis and feature selection.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c7a597bc1188e94cf4e9583a7acbceb292b7f71f" target='_blank'>
-              FreqTSF: Time Series Forecasting Via Simulating Frequency Kramer-Kronig Relations
+          <td><a href="https://www.semanticscholar.org/paper/5c07ba99c8d7ae5a1590ce850bbbbc596fbc4609" target='_blank'>
+              HIERVAR: A Hierarchical Feature Selection Method for Time Series Analysis
               </a>
             </td>
           <td>
-            Rujia Shen, Liangliang Liu, Boran Wang, Yi Guan, Yang Yang, Jingchi Jiang
+            Alireza Keshavarzian, S. Valaee
           </td>
-          <td>2024-07-31</td>
+          <td>2024-07-22</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>11</td>
+          <td>44</td>
         </tr>
 
-        <tr id="The modeling of users' behaviors is crucial in modern recommendation systems. A lot of research focuses on modeling users' lifelong sequences, which can be extremely long and sometimes exceed thousands of items. These models use the target item to search for the most relevant items from the historical sequence. However, training lifelong sequences in click through rate (CTR) prediction or personalized search ranking (PSR) is extremely difficult due to the insufficient learning problem of ID embedding, especially when the IDs in the lifelong sequence features do not exist in the samples of training dataset. Additionally, existing target attention mechanisms struggle to learn the multi-modal representations of items in the sequence well. The distribution of multi-modal embedding (text, image and attributes) output of user's interacted items are not properly aligned and there exist divergence across modalities. We also observe that users' search query sequences and item browsing sequences can fully depict users' intents and benefit from each other. To address these challenges, we propose a unified lifelong multi-modal sequence model called SEMINAR-Search Enhanced Multi-Modal Interest Network and Approximate Retrieval. Specifically, a network called Pretraining Search Unit (PSU) learns the lifelong sequences of multi-modal query-item pairs in a pretraining-finetuning manner with multiple objectives: multi-modal alignment, next query-item pair prediction, query-item relevance prediction, etc. After pretraining, the downstream model restores the pretrained embedding as initialization and finetunes the network. To accelerate the online retrieval speed of multi-modal embedding, we propose a multi-modal codebook-based product quantization strategy to approximate the exact attention calculati">
+        <tr id="We developed DyGETViz, a novel framework for effectively visualizing dynamic graphs (DGs) that are ubiquitous across diverse real-world systems. This framework leverages recent advancements in discrete-time dynamic graph (DTDG) models to adeptly handle the temporal dynamics inherent in dynamic graphs. DyGETViz effectively captures both micro- and macro-level structural shifts within these graphs, offering a robust method for representing complex and massive dynamic graphs. The application of DyGETViz extends to a diverse array of domains, including ethology, epidemiology, finance, genetics, linguistics, communication studies, social studies, and international relations. Through its implementation, DyGETViz has revealed or confirmed various critical insights. These include the diversity of content sharing patterns and the degree of specialization within online communities, the chronological evolution of lexicons across decades, and the distinct trajectories exhibited by aging-related and non-related genes. Importantly, DyGETViz enhances the accessibility of scientific findings to non-domain experts by simplifying the complexities of dynamic graphs. Our framework is released as an open-source Python package for use across diverse disciplines. Our work not only addresses the ongoing challenges in visualizing and analyzing DTDG models but also establishes a foundational framework for future investigations into dynamic graph representation and analysis across various disciplines.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/195f4df514f249678776de08ed7e4c15ca90d141" target='_blank'>
-              SEMINAR: Search Enhanced Multi-modal Interest Network and Approximate Retrieval for Lifelong Sequential Recommendation
+          <td><a href="https://www.semanticscholar.org/paper/09cb3de3028ed37e10c48ae40a5a59f3c2e8d14c" target='_blank'>
+              Empowering Interdisciplinary Insights with Dynamic Graph Embedding Trajectories
               </a>
             </td>
           <td>
-            Kaiming Shen, Xichen Ding, Zixiang Zheng, Yuqi Gong, Qianqian Li, Zhongyi Liu, Guannan Zhang
+            Yiqiao Jin, Andrew Zhao, Yeon-Chang Lee, Meng Ye, Ajay Divakaran, Srijan Kumar
           </td>
-          <td>2024-07-15</td>
+          <td>2024-06-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Deep&Cross Network and its derivative models have become an important paradigm in click-through rate (CTR) prediction due to their effective balance between computational cost and performance. However, these models face four major limitations: (1) while most models claim to capture high-order feature interactions, they often do so implicitly and non-interpretably through deep neural networks (DNN), which limits the trustworthiness of the model's predictions; (2) the performance of existing explicit feature interaction methods is often weaker than that of implicit DNN, undermining their necessity; (3) many models fail to adaptively filter noise while enhancing the order of feature interactions; (4) the fusion methods of most models cannot provide suitable supervision signals for their different interaction methods. To address the identified limitations, this paper proposes the next generation Deep Cross Network (DCNv3) and Shallow&Deep Cross Network (SDCNv3). These models ensure interpretability in feature interaction modeling while exponentially increasing the order of feature interactions to achieve genuine Deep Crossing rather than just Deep&Cross. Additionally, we employ a Self-Mask operation to filter noise and reduce the number of parameters in the cross network by half. In the fusion layer, we use a simple yet effective loss weight calculation method called Tri-BCE to provide appropriate supervision signals. Comprehensive experiments on six datasets demonstrate the effectiveness, efficiency, and interpretability of DCNv3 and SDCNv3. The code, running logs, and detailed hyperparameter configurations are available at: https://anonymous.4open.science/r/DCNv3-E352.">
+        <tr id="Learning effective representations for Continuous-Time Dynamic Graphs (CTDGs) has garnered significant research interest, largely due to its powerful capabilities in modeling complex interactions between nodes. A fundamental and crucial requirement for representation learning in CTDGs is the appropriate estimation and preservation of proximity. However, due to the sparse and evolving characteristics of CTDGs, the spatial-temporal properties inherent in high-order proximity remain largely unexplored. Despite its importance, this property presents significant challenges due to the computationally intensive nature of personalized interaction intensity estimation and the dynamic attributes of CTDGs. To this end, we propose a novel Correlated Spatial-Temporal Positional encoding that incorporates a parameter-free personalized interaction intensity estimation under the weak assumption of the Poisson Point Process. Building on this, we introduce the Dynamic Graph Transformer with \Correlated Spatial-Temporal Positional Encoding (CorDGT), which efficiently retains the evolving spatial-temporal high-order proximity for effective node representation learning in CTDGs. Extensive experiments on seven small and two large-scale datasets demonstrate the superior performance and scalability of the proposed CorDGT.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f2fa60a64d31b78148506e3199a554d6b641362c" target='_blank'>
-              DCNv3: Towards Next Generation Deep Cross Network for CTR Prediction
+          <td><a href="https://www.semanticscholar.org/paper/ca3d24ba002ecd938e42d65b10b2f394232325dd" target='_blank'>
+              Dynamic Graph Transformer with Correlated Spatial-Temporal Positional Encoding
               </a>
             </td>
           <td>
-            Honghao Li, Yiwen Zhang, Yi Zhang, Hanwei Li, Lei Sang
+            Zhe Wang, Sheng Zhou, Jiawei Chen, Zhen Zhang, Binbin Hu, Yan Feng, Chun Chen, Can Wang
           </td>
-          <td>2024-07-18</td>
+          <td>2024-07-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>1</td>
+          <td>18</td>
         </tr>
 
-        <tr id="In the era of rapid globalization and digitalization, accurate identification of similar stocks has become increasingly challenging due to the non-stationary nature of financial markets and the ambiguity in conventional regional and sector classifications. To address these challenges, we examine SimStock, a novel temporal self-supervised learning framework that combines techniques from self-supervised learning (SSL) and temporal domain generalization to learn robust and informative representations of financial time series data. The primary focus of our study is to understand the similarities between stocks from a broader perspective, considering the complex dynamics of the global financial landscape. We conduct extensive experiments on four real-world datasets with thousands of stocks and demonstrate the effectiveness of SimStock in finding similar stocks, outperforming existing methods. The practical utility of SimStock is showcased through its application to various investment strategies, such as pairs trading, index tracking, and portfolio optimization, where it leads to superior performance compared to conventional methods. Our findings empirically examine the potential of data-driven approach to enhance investment decision-making and risk management practices by leveraging the power of temporal self-supervised learning in the face of the ever-changing global financial landscape.">
+        <tr id="This study addresses the prediction of CAN bus data, a lesser-explored aspect within unsupervised anomaly detection research. We propose the Fast-Gated Attention (FGA) Transformer, a novel approach designed for accurate and efficient prediction of CAN bus data. This model utilizes a cross-attention window to optimize computational scale and feature extraction, a gated single-head attention mechanism in place of multi-head attention, and shared parameters to minimize model size. Additionally, a generalized unbiased linear attention approximation technique speeds up attention block computation. On three datasets—Car-Hacking, SynCAN, and Automotive Sensors—the FGA Transformer achieves predicted root mean square errors of 1.86 × 10−3, 3.03 × 10−3, and 30.66 × 10−3, with processing speeds of 2178, 2768, and 3062 frames per second, respectively. The FGA Transformer provides the best or comparable accuracy with a speed improvement ranging from 6 to 170 times over existing methods, underscoring its potential for CAN bus data prediction.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c259bc9adf3019870613cbb7888ea4fac4e1929f" target='_blank'>
-              Temporal Representation Learning for Stock Similarities and Its Applications in Investment Management
+          <td><a href="https://www.semanticscholar.org/paper/29ae49c10fdafb110a22645dbea2e2c775a56ed9" target='_blank'>
+              A Multivariate Time Series Prediction Method for Automotive Controller Area Network Bus Data
               </a>
             </td>
           <td>
-            Yoon-Jeong Hwang, Stefan Zohren, Yongjae Lee
+            Dan Yang, Shuya Yang, Junsuo Qu, Ke Wang
           </td>
-          <td>2024-07-18</td>
-          <td>ArXiv</td>
+          <td>2024-07-10</td>
+          <td>Electronics</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="The emerging graph convolutional network (GCN) provides a way to extract additional relationship information and has demonstrated superior performance in fault diagnosis. However, the GCN-based methods have some limitations when applied to cross-domain fault diagnostics. First, the graph topology constructed according to certain criteria remains fixed while it may contain domain-specific information, which could hamper the extraction of domain-invariant features. Second, the non-Euclidean structure of the graph hinders its augmentation through mixing and interpolation, bringing its application challenges in scenarios with small samples. To address these limitations, this article proposes an adaptive topology-aware siamese network (ATA-SN) for cross-domain fault diagnosis with small samples. Specifically, the multichannel data are constructed as a complete graph as input. The adaptive topology-aware module updates and augments the graph simultaneously through biased uncertainty edge perturbation in a nonparametric manner. In combination with a contrastive loss, augmented data with clear class boundaries can be obtained. A statistical metrics-based style loss is used for domain-invariant feature learning. A pair of updated graphs is then fed into the siamese framework, which utilizes the semantic consistency of the paired graphs to recalibrate the contribution of the augmented data to the gradient descent, thus ensuring the effectiveness of the graph augmentation and domain adaptation. Comparative studies and cross-domain fault diagnosis experiments indicate the superiority and effectiveness of the proposed method even in scenarios with extremely limited training data. The code of ATA-SN is released at https://github.com/CQU-ZixuChen/ATA-SN.">
+        <tr id="Predictive analytics with machine learning approaches has widely penetrated and shown great success in system health management over the decade. However, how to convert the prediction to an actionable plan for maintenance is still far from mature. This study investigates how to narrow the gapbetween predictive outcomes and prescriptive descriptions for system maintenance using an agentic approach based on the large language model (LLM). Additionally, with the retrieval-augmented generation (RAG) technique and tool usage capability, the LLM can be context-aware when making decisions in maintenance strategy proposals considering predictions from machine learning. In this way, the proposed method can push forward the boundary of current machine-learning methods from a predictor to an advisor for decision-making workload offload. For verification, a case study on linear actuator fault diagnosis is conducted with the GPT-4 model. The result demonstrates that the proposed method can perform fault detection without extra training or fine-tuning with comparable performance to baseline methods and deliver more informatic diagnosis analysis and suggestions. This research can shed light on the application of large language models in the construction of versatile and flexible artificial intelligence agents for maintenance tasks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/65415f2d9909e8321b7099af8288d9c77f827c26" target='_blank'>
-              Adaptive Topology-Aware Siamese Network for Cross-Domain Fault Diagnosis With Small Samples
+          <td><a href="https://www.semanticscholar.org/paper/40776e2aba7dd99d2dadc993e370a0592a750cb3" target='_blank'>
+              From Prediction to Prescription: Large Language Model Agent for Context-Aware Maintenance Decision Support
               </a>
             </td>
           <td>
-            Zixu Chen, J. Ji, Kai Chen, Qing Ni, Xiaoxi Ding, Wennian Yu
+            Haoxuan Deng, Bernadin Namoano, Bohao Zheng, Samir Khan, John Ahmet Erkoyuncu
           </td>
-          <td>2024-08-01</td>
-          <td>IEEE Sensors Journal</td>
+          <td>2024-06-27</td>
+          <td>PHM Society European Conference</td>
           <td>0</td>
-          <td>15</td>
+          <td>3</td>
         </tr>
 
-        <tr id="Identification of critical nodes is a prominent topic in the study of complex networks. Numerous methods have been proposed, yet most exhibit inherent limitations. Traditional approaches primarily analyze specific structural features of the network; however, node influence is typically the result of a combination of multiple factors. Machine learning-based methods struggle to effectively represent the complex characteristics of network structures through suitable embedding techniques and require substantial data for training, rendering them prohibitively costly for large-scale networks. To address these challenges, this paper presents an active learning model based on GraphSAGE and Transformer, named GNNTAL. This model is initially pre-trained on random or synthetic networks and subsequently fine-tuned on real-world networks by selecting a few representative nodes using K-Means clustering and uncertainty sampling. This approach offers two main advantages: (1) it significantly reduces training costs; (2) it simultaneously incorporates both local and global features. A series of comparative experiments conducted on twelve real-world networks demonstrate that GNNTAL achieves superior performance. Additionally, this paper proposes an influence maximization method based on the predictions of the GNNTAL model, which achieves optimal performance without the need for complex computations. Finally, the paper analyses certain limitations of the GNNTAL model and suggests potential solutions.">
+        <tr id="Building prediction intervals for time series forecasting problems presents a complex challenge, particularly when relying solely on point predictors, a common scenario for practitioners in the industry. While research has primarily focused on achieving increasingly efficient valid intervals, we argue that, when evaluating a set of intervals, traditional measures alone are insufficient. There are additional crucial characteristics: the intervals must vary in length, with this variation directly linked to the difficulty of the prediction, and the coverage of the interval must remain independent of the difficulty of the prediction for practical utility. We propose the Heteroscedastic Quantile Regression (HQR) model and the Width-Adaptive Conformal Inference (WACI) method, providing theoretical coverage guarantees, to overcome those issues, respectively. The methodologies are evaluated in the context of Electricity Price Forecasting and Wind Power Forecasting, representing complex scenarios in time series forecasting. The results demonstrate that HQR and WACI not only improve or achieve typical measures of validity and efficiency but also successfully fulfil the commonly ignored mentioned characteristics.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f2c2569fd1bd2320230e824c982a501344641e9c" target='_blank'>
-              GNNTAL:A Novel Model for Identifying Critical Nodes in Complex Networks
+          <td><a href="https://www.semanticscholar.org/paper/9c18bfd83fa9808cc2d8310863d5b8bcc05f3b70" target='_blank'>
+              Enhancing reliability in prediction intervals using point forecasters: Heteroscedastic Quantile Regression and Width-Adaptive Conformal Inference
               </a>
             </td>
           <td>
-            Hao Wang, Ting Luo, Shuang-ping Yang, Ming Jing, Jian Wang, Na Zhao
+            Carlos Sebasti'an, Carlos E. Gonz'alez-Guill'en, Jes'us Juan
           </td>
-          <td>2024-06-24</td>
+          <td>2024-06-21</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
+          <td>1</td>
         </tr>
 
-        <tr id="This article describes the methods that achieved 4th and 6th place in the forecasting and investment challenges, respectively, of the M6 competition, ultimately securing the 1st place in the overall duathlon ranking. In the forecasting challenge, we tested a novel meta-learning model that utilizes hypernetworks to design a parametric model tailored to a specific family of forecasting tasks. This approach allowed us to leverage similarities observed across individual forecasting tasks while also acknowledging potential heterogeneity in their data generating processes. The model's training can be directly performed with backpropagation, eliminating the need for reliance on higher-order derivatives and is equivalent to a simultaneous search over the space of parametric functions and their optimal parameter values. The proposed model's capabilities extend beyond M6, demonstrating superiority over state-of-the-art meta-learning methods in the sinusoidal regression task and outperforming conventional parametric models on time-series from the M4 competition. In the investment challenge, we adjusted portfolio weights to induce greater or smaller correlation between our submission and that of other participants, depending on the current ranking, aiming to maximize the probability of achieving a good rank.">
+        <tr id="In recent years, deep learning has increasingly gained attention in the field of traffic prediction. Existing traffic prediction models often rely on GCNs or attention mechanisms with O(N^2) complexity to dynamically extract traffic node features, which lack efficiency and are not lightweight. Additionally, these models typically only utilize historical data for prediction, without considering the impact of the target information on the prediction. To address these issues, we propose a Pattern-Matching Dynamic Memory Network (PM-DMNet). PM-DMNet employs a novel dynamic memory network to capture traffic pattern features with only O(N) complexity, significantly reducing computational overhead while achieving excellent performance. The PM-DMNet also introduces two prediction methods: Recursive Multi-step Prediction (RMP) and Parallel Multi-step Prediction (PMP), which leverage the time features of the prediction targets to assist in the forecasting process. Furthermore, a transfer attention mechanism is integrated into PMP, transforming historical data features to better align with the predicted target states, thereby capturing trend changes more accurately and reducing errors. Extensive experiments demonstrate the superiority of the proposed model over existing benchmarks. The source codes are available at: https://github.com/wengwenchao123/PM-DMNet.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/79c059ff368b1797f8ebcd428512691d3f6bcd34" target='_blank'>
-              Designing Time-Series Models With Hypernetworks&Adversarial Portfolios
+          <td><a href="https://www.semanticscholar.org/paper/27093b45b377c53bb3e2360dcde0bd4cae7da8df" target='_blank'>
+              Pattern-Matching Dynamic Memory Network for Dual-Mode Traffic Prediction
               </a>
             </td>
           <td>
-            Filip Stanvek
+            Wenchao Weng, Mei Wu, Hanyu Jiang, Wanzeng Kong, Xiangjie Kong, Feng Xia
           </td>
-          <td>2024-07-29</td>
+          <td>2024-08-12</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>42</td>
         </tr>
 
-        <tr id="Despite progress, deep neural networks still suffer performance declines under distribution shifts between training and test domains, leading to a substantial decrease in Quality of Experience (QoE) for multimedia applications. Existing test-time adaptation (TTA) methods are challenged by dynamic, multiple test distributions within batches. This work provides a new perspective on analyzing batch normalization techniques through class-related and class-irrelevant features, our observations reveal combining source and test batch normalization statistics robustly characterizes target distributions. However, test statistics must have high similarity. We thus propose Discover Your Neighbours (DYN), the first backward-free approach specialized for dynamic TTA. The core innovation is identifying similar samples via instance normalization statistics and clustering into groups which provides consistent class-irrelevant representations. Specifically, Our DYN consists of layer-wise instance statistics clustering (LISC) and cluster-aware batch normalization (CABN). In LISC, we perform layer-wise clustering of approximate feature samples at each BN layer by calculating the cosine similarity of instance normalization statistics across the batch. CABN then aggregates SBN and TCN statistics to collaboratively characterize the target distribution, enabling more robust representations. Experimental results validate DYN's robustness and effectiveness, demonstrating maintained performance under dynamic data stream patterns.">
+        <tr id="Fuzzy neural network (FNN) is regarded as a prominent approach in application of time-series modeling. With the capability of fuzzy reasoning, FNN can capture temporal patterns from the time-series samples. However, the existing FNNs may suffer from the temporal pattern distortion because possibly multiscale features cannot be explored sufficiently. To address this problem, a time-aware fuzzy neural network, based on the frequency-enhanced modulation mechanism (FEM-TAFNN), is developed for time-series prediction in this article. First, a Fourier-based decoder is established to extract the multiscale features. This decoder employs the frequency-domain model to orthogonally separate the time-scale features with different frequencies into independent temporal patterns based on the Fourier basis, which prevents the overlap of temporal patterns using time-domain analysis. Second, a frequency-enhanced modulation mechanism is designed to shape fuzzy rules of FNN based on the contribution of different temporal patterns in the frequency spectrum. It enables FEM-TAFNN to modulate out the realistic multiscale temporal patterns. Finally, the proposed FEM-TAFNN is tested on four multiscale time-series datasets. The empirical results confirm its superior prediction performance than other methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2f3e4495adba4ec10ffc5c3233a5282065d4d9bb" target='_blank'>
-              Discover Your Neighbors: Advanced Stable Test-Time Adaptation in Dynamic World
+          <td><a href="https://www.semanticscholar.org/paper/ce803c3df8b377a910569d38f5c6288c1fad84ce" target='_blank'>
+              Time-Aware Fuzzy Neural Network Based on Frequency-Enhanced Modulation Mechanism
               </a>
             </td>
           <td>
-            Qinting Jiang, Chuyang Ye, Dongyan Wei, Yuan Xue, Jingyan Jiang, Zhi Wang
+            Hong-gui Han, Zecheng Tang, Xiaolong Wu, Hongyan Yang, Jun-Li Qiao
           </td>
-          <td>2024-06-08</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>IEEE Transactions on Fuzzy Systems</td>
           <td>0</td>
-          <td>1</td>
+          <td>40</td>
         </tr>
 
-        <tr id="In the wild, we often encounter collections of sequential data such as electrocardiograms, motion capture, genomes, and natural language, and sequences may be multichannel or symbolic with nonlinear dynamics. We introduce a new method to learn low-dimensional representations of nonlinear time series without supervision and can have provable recovery guarantees. The learned representation can be used for downstream machine-learning tasks such as clustering and classification. The method is based on the assumption that the observed sequences arise from a common domain, but each sequence obeys its own autoregressive models that are related to each other through low-rank regularization. We cast the problem as a computationally efficient convex matrix parameter recovery problem using monotone Variational Inequality and encode the common domain assumption via low-rank constraint across the learned representations, which can learn the geometry for the entire domain as well as faithful representations for the dynamics of each individual sequence using the domain information in totality. We show the competitive performance of our method on real-world time-series data with the baselines and demonstrate its effectiveness for symbolic text modeling and RNA sequence clustering.">
+        <tr id="Forecast reconciliation has become a prominent topic in recent forecasting literature, with a primary distinction made between cross-sectional and temporal hierarchies. This work focuses on temporal hierarchies, such as aggregating monthly time series data to annual data. We explore the impact of various forecast reconciliation methods on temporally aggregated ARIMA models, thereby bridging the fields of hierarchical forecast reconciliation and temporal aggregation both theoretically and experimentally. Our paper is the first to theoretically examine the effects of temporal hierarchical forecast reconciliation, demonstrating that the optimal method aligns with a bottom-up aggregation approach. To assess the practical implications and performance of the reconciled forecasts, we conduct a series of simulation studies, confirming that the findings extend to more complex models. This result helps explain the strong performance of the bottom-up approach observed in many prior studies. Finally, we apply our methods to real data examples, where we observe similar results.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/374d6dcbbd6b7bc58c4e0fdbbfe9c1648975a899" target='_blank'>
-              Nonlinear time-series embedding by monotone variational inequality
+          <td><a href="https://www.semanticscholar.org/paper/985e5918331ffab3f0ab26045d8e9e749f6655c6" target='_blank'>
+              Rediscovering Bottom-Up: Effective Forecasting in Temporal Hierarchies
               </a>
             </td>
           <td>
-            Jonathan Y. Zhou, Yao Xie
+            Lukas Neubauer, Peter Filzmoser
           </td>
-          <td>2024-06-11</td>
+          <td>2024-07-02</td>
           <td>ArXiv</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse problem with a smoothness promoting objective and rely on iterative methods to obtain a solution. In supervised settings where graph labels are available, one can unroll and truncate these iterations into a deep network that is trained end-to-end. Such a network is parameter efficient and inherits inductive bias from the optimization formulation, an appealing aspect for data constrained settings in, e.g., medicine, finance, and the natural sciences. But typically such settings care equally about uncertainty over edge predictions, not just point estimates. Here we introduce novel iterations with independently interpretable parameters, i.e., parameters whose values - independent of other parameters' settings - proportionally influence characteristics of the estimated graph, such as edge sparsity. After unrolling these iterations, prior knowledge over such graph characteristics shape prior distributions over these independently interpretable network parameters to yield a Bayesian neural network (BNN) capable of graph structure learning (GSL) from smooth signal observations. Fast execution and parameter efficiency allow for high-fidelity posterior approximation via Markov Chain Monte Carlo (MCMC) and thus uncertainty quantification on edge predictions. Synthetic and real data experiments corroborate this model's ability to provide well-calibrated estimates of uncertainty, in test cases that include unveiling economic sector modular structure from S$\&$P$500$ data and recovering pairwise digit similarities from MNIST images. Overall, this framework enables GSL in modest-scale applications where uncertainty on the data structure is paramount.">
+        <tr id="In an era where machine learning permeates every facet of human existence, and data evolves incessantly, the application of machine learning models transcends mere data processing. It involves navigating constant changes exemplified by the phenomenon of concept drift, which often affects model performance.
+
+These drifts can be recurrent due to the cyclic nature of the underlying data generation processes, which could be influenced by recurrent phenomena such as weather and time of the day. 
+
+Stream Learning on data streams with recurrent concept drifts attempts to learn from such streams of data.
+
+The survey underscores the significance of the field and its practical applications, delving into nuanced definitions of machine learning for data streams afflicted by recurrent concept drifts. It explores diverse methodological approaches, elucidating their key design components. Additionally, it examines various evaluation techniques, benchmark datasets, and available software tailored for simulating and analysing data streams with recurrent concept drifts. Concluding, the survey offers insights into potential avenues for future research in the field.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d4a2a2d1e598080f8f15315512f0885aeba3c17a" target='_blank'>
-              Graph Structure Learning with Interpretable Bayesian Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/cf06b11f144b00a4ce791a494e6563e109b2d5e9" target='_blank'>
+              Recurrent Concept Drifts on Data Streams
               </a>
             </td>
           <td>
-            Max Wasserman, Gonzalo Mateos
+            N. Gunasekara, Bernhard Pfahringer, Heitor Murilo Gomes, A. Bifet, Yun Sing Koh
           </td>
-          <td>2024-06-20</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>Proceedings of the Thirty-ThirdInternational Joint Conference on Artificial Intelligence</td>
           <td>0</td>
-          <td>3</td>
+          <td>50</td>
         </tr>
 
-        <tr id="The reward model has become increasingly important in alignment, assessment, and data construction for large language models (LLMs). Most existing researchers focus on enhancing reward models through data improvements, following the conventional training framework for reward models that directly optimizes the predicted rewards. In this paper, we propose a hybrid alignment framework HaF-RM for reward model training by introducing an additional constraint on token-level policy probabilities in addition to the reward score. It can simultaneously supervise the internal preference model at the token level and optimize the mapping layer of the reward model at the sequence level. Theoretical justifications and experiment results on five datasets show the validity and effectiveness of our proposed hybrid framework for training a high-quality reward model. By decoupling the reward modeling procedure and incorporating hybrid supervision, our HaF-RM framework offers a principled and effective approach to enhancing the performance and alignment of reward models, a critical component in the responsible development of powerful language models. We release our code at https://haf-rm.github.io.">
+        <tr id="Deep learning (DL) has been widely applied to forecast the sales volume of household appliances with high accuracy. Unfortunately, in small towns, due to the limited amount of historical sales data, it is difficult to forecast household appliance sales accurately. To overcome the above-mentioned challenge, we propose a novel household appliance sales forecasting algorithm based on transfer learning, temporal convolutional network (TCN), long short-term memory (LSTM), and attention mechanism (called “TransTLA”). Firstly, we combine TCN and LSTM to exploit the spatiotemporal correlation of sales data. Secondly, we utilize the attention mechanism to make full use of the features of sales data. Finally, in order to mitigate the impact of data scarcity and regional differences, a transfer learning technique is used to improve the predictive performance in small towns, with the help of the learning experience from the megacity. The experimental outcomes reveal that the proposed TransTLA model significantly outperforms traditional forecasting methods in predicting small town household appliance sales volumes. Specifically, TransTLA achieves an average mean absolute error (MAE) improvement of 27.60% over LSTM, 9.23% over convolutional neural networks (CNN), and 11.00% over the CNN-LSTM-Attention model across one to four step-ahead predictions. This study addresses the data scarcity problem in small town sales forecasting, helping businesses improve inventory management, enhance customer satisfaction, and contribute to a more efficient supply chain, benefiting the overall economy.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/581d831fcea84501bec33161c716d5bf94a8a345" target='_blank'>
-              HAF-RM: A Hybrid Alignment Framework for Reward Model Training
+          <td><a href="https://www.semanticscholar.org/paper/0b9ca38d56c22558ee1fb94ba33b348585bf6d14" target='_blank'>
+              TransTLA: A Transfer Learning Approach with TCN-LSTM-Attention for Household Appliance Sales Forecasting in Small Towns
               </a>
             </td>
           <td>
-            Shujun Liu, Xiaoyu Shen, Yuhang Lai, Siyuan Wang, Shengbin Yue, Zengfeng Huang, Xuanjing Huang, Zhongyu Wei
+            Zhijie Huang, Jianfeng Liu
           </td>
-          <td>2024-07-04</td>
-          <td>ArXiv</td>
+          <td>2024-07-28</td>
+          <td>Applied Sciences</td>
+          <td>0</td>
           <td>0</td>
-          <td>14</td>
         </tr>
 
-        <tr id="Time series analysis is pivotal for business and financial decision making, especially with the increasing integration of the Internet of Things (IoT). However, leveraging time series data for forecasting requires extensive preprocessing to address challenges such as missing values, heteroscedasticity, seasonality, outliers, and noise. Different approaches are necessary for univariate and multivariate time series, Gaussian and non-Gaussian time series, and stationary versus non-stationary time series. Handling missing data alone is complex, demanding unique solutions for each type. Extracting statistical features, identifying data quality issues, and selecting appropriate cleaning and forecasting techniques require significant effort, time, and expertise. To streamline this process, we propose an automated strategy called Preptimize, which integrates statistical and machine learning techniques and recommends prediction model blueprints, suggesting the most suitable approaches for a given dataset as an initial step towards further analysis. Preptimize reads a sample from a large dataset and recommends the blueprint model based on optimization, making it easy to use even for non-experts. The results of various experiments indicated that Preptimize either outperformed or had comparable performance to benchmark models across multiple sectors, including stock prices, cryptocurrency, and power consumption prediction. This demonstrates the framework’s effectiveness in recommending suitable prediction models for various time series datasets, highlighting its broad applicability across different domains in time series forecasting.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/228a2e2a0f2984f0be41b8a4718860d9d8b020d5" target='_blank'>
-              Preptimize: Automation of Time Series Data Preprocessing and Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/1e7d935a1fd72ec0c78f76e9366ac22a96bd7a77" target='_blank'>
+              A Meta-learner approach to multistep-ahead time series prediction
               </a>
             </td>
           <td>
-            Mehak Usmani, Z. Memon, Adil Zulfiqar, Rizwan Qureshi
+            Fouad Bahrpeyma, V. M. Ngo, M. Roantree, A. Mccarren
           </td>
-          <td>2024-08-01</td>
-          <td>Algorithms</td>
+          <td>2024-07-09</td>
+          <td>International Journal of Data Science and Analytics</td>
           <td>0</td>
-          <td>18</td>
+          <td>17</td>
         </tr>
 
-        <tr id="We study the problem of continual test-time adaption where the goal is to adapt a source pre-trained model to a sequence of unlabelled target domains at test time. Existing methods on test-time training suffer from several limitations: (1) Mismatch between the feature extractor and classifier; (2) Interference between the main and self-supervised tasks; (3) Lack of the ability to quickly adapt to the current distribution. In light of these challenges, we propose a cascading paradigm that simultaneously updates the feature extractor and classifier at test time, mitigating the mismatch between them and enabling long-term model adaptation. The pre-training of our model is structured within a meta-learning framework, thereby minimizing the interference between the main and self-supervised tasks and encouraging fast adaptation in the presence of limited unlabelled data. Additionally, we introduce innovative evaluation metrics, average accuracy and forward transfer, to effectively measure the model's adaptation capabilities in dynamic, real-world scenarios. Extensive experiments and ablation studies demonstrate the superiority of our approach in a range of tasks including image classification, text classification, and speech recognition.">
+        <tr id="Solar energy has become a promising renewable energy source, offering significant opportunities for photovoltaic (PV) systems. Accurate and reliable PV generation forecasts are crucial for efficient grid integration and optimized system planning. However, the complexity of environmental factors, including seasonal and daily patterns, as well as social behaviors and user habits, presents significant challenges. Traditional prediction models often struggle with capturing the complex nonlinear dynamics in multivariate time series, leading to low prediction accuracy. To address this issue, this paper proposes a new PV power prediction method that considers factors such as light, air pressure, wind direction, and social behavior, assigning different weights to them to accurately extract nonlinear feature relationships. The framework integrates long short-term memory (LSTM) and gated recurrent units (GRU) to capture local time features, while bidirectional LSTM (BiLSTM) and an attention mechanism extract global spatiotemporal relationships, effectively capturing key features related to historical output. This improves the accuracy of multi-step predictions. To verify the feasibility of the method for multivariate time series, we conducted experiments using PV power prediction as a scenario and compared the results with LSTM, CNN, BiLSTM, CNN-LSTM and GRU models. The experimental results show that the proposed method outperforms these models, with a mean absolute error (MAE) of 12.133, root mean square error (RMSE) of 14.234, mean absolute percentage error (MAPE) of 2.1%, and a coefficient of determination (R2) of 0.895. These results indicate the effectiveness and potential of the method in PV prediction tasks.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/42da121759bed6f46e98e9f1ae95fd5c034906ec" target='_blank'>
-              Adaptive Cascading Network for Continual Test-Time Adaptation
+          <td><a href="https://www.semanticscholar.org/paper/5cd0c75b48f548d60683a1e8ab48e8b00609e962" target='_blank'>
+              A Photovoltaic Prediction Model with Integrated Attention Mechanism
               </a>
             </td>
           <td>
-            Kien X. Nguyen, Fengchun Qiao, Xi Peng
+            Xiangshu Lei
           </td>
-          <td>2024-07-17</td>
-          <td>ArXiv</td>
+          <td>2024-07-04</td>
+          <td>Mathematics</td>
+          <td>0</td>
           <td>0</td>
-          <td>6</td>
         </tr>
 
-        <tr id="One of the crucial tasks in Remaining useful life prediction is to effectively extract key sensor information from numerous sensor signals. In this article, a novel dual-attention enhanced deep residual LSTM (DRLSTM-DA) is developed to deeply optimize multidimensional sensor signals. First, two LSTM layers are designed to compress and reconstruct representative degradation information from input multidimensional time series data, to generate a new feature space. Second, a novel channel adaptive soft threshold module is designed to assign different weights according to the importance of different sensor information, and simultaneously eliminate the noise information in the signal. Thirdly, a temporal attention mechanism is designed to automatically highlight moments containing important decay information while suppressing unimportant moments. Finally, compared with other SOTA methods, our architecture achieves RMSE of 11.55, 13.74, 11.25, and 14.19 on four sub-datasets of the C-MAPSS dataset, with scores of 234.24, 465.49, 202.23, and 537.66, respectively. Meanwhile, in real aeroengine operation dataset, our architecture achieved the smallest RMSE (8.62). These results all validate the good predictive performance of our model.">
+        <tr id="
+ Data-driven methodologies have been used in reservoir management and production forecasting, particularly demonstrating remarkable efficacy in short-term oil production forecasts. However, there is space to improve its prediction, especially in tackling the complexities of challenging reservoirs, such as the heterogeneous carbonate reservoirs from Brazilian Pre-salt fields. Methods for oil production forecasting in the petroleum literature generally consider linear correlations or recurrent neural networks (RNNs). In this paper, we propose a new strategy to improve short-term forecasting for oil production through attention mechanisms that boost state-of-the-art methods. Traditional data-driven techniques generally do not consider static data or planned activities. However, we address this critical gap by leveraging the Temporal Fusion Transformer (TFT) to integrate such information into our short-term forecasting. Transformers, the architectural inspiration behind ChatGPT, employ attention mechanisms to establish relationships between different time series data points, assigning weights to these connections. We jointly explore oil, gas, and water production, pressure, and the ratios between them. This method includes static data (e.g., geographical coordinates) as well as known side reservoir information. Such side information can be, for instance, another predicted future production or planned well shut-ins. We also investigate which side information improves the obtained forecasting. This paper presents two main findings. First, it shows how using certain side information can improve the overall predictive capability of a model. For example, using predicted gas production as side information can significantly improve the oil production forecast. This is logical and in line with expectations, as there is an intimate connection between oil and gas production. In the second application of TFT, we considered well closures as the side information. We used an anomaly detection tool to identify well closures in the history period and converted it to usable side information for the TFT model. The distribution of these well closures is used as a guide to predict our target oil production. As we considered the distribution of well closures as side information, we framed our results in terms of cumulative oil production rather than daily forecast rates. The results of this work show that the cumulative production gets very close to the ground-truth data, better than linear and proposed baselines. In summary, the second key result shows and underscores the significance of incorporating side information within our TFT approach.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/be275ed41dc976b223c1af7df7af60f1ac5ead3d" target='_blank'>
-              DRLSTM-DA: a novel aeroengine remaining useful life prediction method based on deep optimization of multiple sensors information
+          <td><a href="https://www.semanticscholar.org/paper/28c1d2d657f6cc3f0791a67fb06a1d435e895eea" target='_blank'>
+              Watch the Reservoir! Improving Short-Term Production Forecast Through Transformers
               </a>
             </td>
           <td>
-            Shiwei Suo, Song Fu, Lin Lin, Sihao Zhang, Yikun Liu, Guolei Hu, Changsheng Hu
+            R. Werneck, L. A. Lusquino Filho, A. Lustosa, A. Loomba, M. M. Gonçalves, A. Esmin, S. Salavati, E. Morais, P. R. Mendes Junior, M. Zampieri, M. Amaral, O. C. Linares, M. Castro, R. Moura, D. J. Schiozer, A. M. Ferreira, A. Davolio, A. Rocha
           </td>
-          <td>2024-06-17</td>
-          <td>Measurement Science and Technology</td>
+          <td>2024-06-26</td>
+          <td>Day 3 Fri, June 28, 2024</td>
           <td>0</td>
-          <td>7</td>
+          <td>10</td>
         </tr>
 
-        <tr id="The growing demand for air travel requires technological advancements in air traffic management as well as mechanisms for monitoring and ensuring safe and efficient operations. In terminal airspaces, predictive models of future movements and traffic flows can help with proactive planning and efficient coordination; however, varying airport topologies, and interactions with other agents, among other factors, make accurate predictions challenging. Data-driven predictive models have shown promise for handling numerous variables to enable various downstream tasks, including collision risk assessment, taxi-out time prediction, departure metering, and emission estimations. While data-driven methods have shown improvements in these tasks, prior works lack large-scale curated surface movement datasets within the public domain and the development of generalizable trajectory forecasting models. In response to this, we propose two contributions: (1) Amelia-48, a large surface movement dataset collected using the System Wide Information Management (SWIM) Surface Movement Event Service (SMES). With data collection beginning in Dec 2022, the dataset provides more than a year's worth of SMES data (~30TB) and covers 48 airports within the US National Airspace System. In addition to releasing this data in the public domain, we also provide post-processing scripts and associated airport maps to enable research in the forecasting domain and beyond. (2) Amelia-TF model, a transformer-based next-token-prediction large multi-agent multi-airport trajectory forecasting model trained on 292 days or 9.4 billion tokens of position data encompassing 10 different airports with varying topology. The open-sourced model is validated on unseen airports with experiments showcasing the different prediction horizon lengths, ego-agent selection strategies, and training recipes to demonstrate the generalization capabilities.">
+        <tr id="With the rapid digitization of the world, an increasing number of real-world applications are turning to non-Euclidean data, modeled as graphs. Due to their intrinsic high complexity and irregularity, learning from graph data demands tremendous computational power. Recently, CMOS-compatible Ising machines, i.e., dynamical systems fabricated with CMOS technologies, have emerged as a new approach that harnesses the inherent power of nature within dynamical systems to efficiently resolve binary optimization problems and have been adopted for traditional graph computation, such as max-cut. However, when performing complex Graph Learning (GL) tasks, Ising machines face significant hurdles: (i) they are binary and thus ill-suited for real-valued problems; (ii) their expensive all-to-all coupling network that guarantees generality for optimization problems poses daunting scalability concerns.To address these challenges, this paper proposes a nature-powered graph learning framework dubbed DS-GL, which is the first effort to transform the process of solving graph learning problems into the natural annealing process within a parameterized dynamical system embodied as a CMOS chip. To tackle the two major hurdles, DS-GL first augments the Ising machine architecture to modify the self-reaction term of its Hamiltonian function from linear to quadratic, effectively serving as an energy regulator. This adjustment maintains the system’s original physical interpretation while enabling it to process continuous, real-valued data. Second, to address the scaling issue, DS-GL further upgrades the real-valued dense Ising machine by decomposing it into a mesh-based multi-PE dynamical system that supports efficient distributed spatial-temporal co-annealing across different PEs through sparse interconnects. By exploiting the inherent sparsity and community structures in real-world graphs, DS-GL is able to map complex graph learning tasks onto the scalable dynamical system while maintaining high accuracy. Evaluations with four diverse GL applications across seven real-world datasets, including traffic flow and COVID-19 prediction, show that DS-GL can deliver from 103 × to 105 × speedups over Graph Neural Networks on GPUs while operating at a power 2 orders of magnitude lower than GPUs, with 5% – 30% accuracy enhancement.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/fe29091a5f28ae9c53d07479551f034ed3c2e387" target='_blank'>
-              Amelia: A Large Model and Dataset for Airport Surface Movement Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/f5c8f2bb9d71e3bd5704dfdfc3c6c83338cf48fc" target='_blank'>
+              DS-GL: Advancing Graph Learning via Harnessing Nature’s Power within Scalable Dynamical Systems
               </a>
             </td>
           <td>
-            Ingrid Navarro, Pablo Ortega-Kral, Jay Patrikar, Haichuan Wang, Zelin Ye, Jong Hoon Park, Jean Oh, Sebastian Scherer
+            Ruibing Song, Chunshu Wu, Chuan Liu, Ang Li, Michael C. Huang, Tong Geng
           </td>
-          <td>2024-07-30</td>
-          <td>ArXiv</td>
+          <td>2024-06-29</td>
+          <td>2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture (ISCA)</td>
           <td>0</td>
-          <td>9</td>
+          <td>8</td>
         </tr>
 
-        <tr id="Financial market simulation (FMS) serves as a promising tool for understanding market anomalies and the underlying trading behaviors. To ensure high-fidelity simulations, it is crucial to calibrate the FMS model for generating data closely resembling the observed market data. Previous efforts primarily focused on calibrating the mid-price data, leading to essential information loss of the market activities and thus biasing the calibrated model. The Limit Order Book (LOB) data is the fundamental data fully capturing the market micro-structure and is adopted by worldwide exchanges. However, LOB is not applicable to existing calibration objective functions due to its tabular structure not suitable for the vectorized input requirement. This paper proposes to explicitly learn the vectorized representations of LOB with a Transformer-based autoencoder. Then the latent vector, which captures the major information of LOB, can be applied for calibration. Extensive experiments show that the learned latent representation not only preserves the non-linear auto-correlation in the temporal axis, but the precedence between successive price levels of LOB. Besides, it is verified that the performance of the representation learning stage is consistent with the downstream calibration tasks. Thus, this work also progresses the FMS on LOB data, for the first time.">
+        <tr id="In the modern transport industry, vast and diverse information arrays, particularly those including time series data, are rapidly expanding. This growth presents an opportunity to improve the quality of forecasting. Researchers and practitioners are continuously developing innovative tools to predict their future values. The goal of the research is to improve the performance of automated forecasting environments in a systematic and structured way. This paper investigates the effect of substituting the initial time series with another of a similar nature, during the training phase of the model’s development. A financial data set and the Prophet model are employed for this objective. It is observed that the impact on the accuracy of the predicted future values is promising, albeit not significant. Based on the obtained results, valuable conclusions are drawn, and recommendations for further improvements are provided. By highlighting the importance of diverse data incorporation, this research assists in making informed choices and leveraging the full potential of available information for more precise forecasting outcomes.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/df3a27179dd89dd0a9a9b62d5ac1b218eae8f825" target='_blank'>
-              SimLOB: Learning Representations of Limited Order Book for Financial Market Simulation
+          <td><a href="https://www.semanticscholar.org/paper/c8cdf9821562b0563c9797fb5821a5a46f40c681" target='_blank'>
+              Time Series Cross-Sequence Prediction
               </a>
             </td>
           <td>
-            Yuanzhe Li, Yue Wu, Peng Yang
+            K. Koparanov, E. Antonova, D. Minkovska, K. Georgiev
           </td>
-          <td>2024-06-27</td>
-          <td>ArXiv</td>
-          <td>0</td>
+          <td>2024-07-19</td>
+          <td>WSEAS TRANSACTIONS ON BUSINESS AND ECONOMICS</td>
           <td>0</td>
+          <td>3</td>
         </tr>
 
-        <tr id="In this paper, we apply a supervised machine-learning approach to solve a fundamental problem in queueing theory: estimating the transient distribution of the number in the system for a G(t)/GI/1. We develop a neural network mechanism that provides a fast and accurate predictor of these distributions for moderate horizon lengths and practical settings. It is based on using a Recurrent Neural Network (RNN) architecture based on the first several moments of the time-dependant inter-arrival and the stationary service time distributions; we call it the Moment-Based Recurrent Neural Network (RNN) method (MBRNN ). Our empirical study suggests MBRNN requires only the first four inter-arrival and service time moments. We use simulation to generate a substantial training dataset and present a thorough performance evaluation to examine the accuracy of our method using two different test sets. We show that even under the configuration with the worst performance errors, the mean number of customers over the entire timeline has an error of less than 3%. While simulation modeling can achieve high accuracy, the advantage of the MBRNN over simulation is runtime, while the MBRNN analyzes hundreds of systems within a fraction of a second. This paper focuses on a G(t)/GI/1; however, the MBRNN approach demonstrated here can be extended to other queueing systems, as the training data labeling is based on simulations (which can be applied to more complex systems) and the training is based on deep learning, which can capture very complex time sequence tasks. In summary, the MBRNN can potentially revolutionize our ability to perform transient analyses of queueing systems.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f691dfd4dff3b3fb9b91bf5e89d6572368165f58" target='_blank'>
-              Approximating G(t)/GI/1 queues with deep learning
+          <td><a href="https://www.semanticscholar.org/paper/a983ac7de996a0c2a264e2986905402146c015e0" target='_blank'>
+              Unlocking Online Insights: LSTM Exploration and Transfer Learning Prospects
               </a>
             </td>
           <td>
-            Eliran Sherzer, Opher Baron, Dmitry Krass, Yehezkel S. Resheff
+            Muhammad Tahir, Sufyan Ali, A. Sohail, Ying Zhang, Xiaohua Jin
           </td>
-          <td>2024-07-11</td>
-          <td>ArXiv</td>
+          <td>2024-07-08</td>
+          <td>Annals of Data Science</td>
           <td>0</td>
-          <td>14</td>
+          <td>21</td>
         </tr>
 
-        <tr id="One-class learning (OCL) comprises a set of techniques applied when real-world problems have a single class of interest. The usual procedure for OCL is learning a hypersphere that comprises instances of this class and, ideally, repels unseen instances from any other classes. Besides, several OCL algorithms for graphs have been proposed since graph representation learning has succeeded in various fields. These methods may use a two-step strategy, initially representing the graph and, in a second step, classifying its nodes. On the other hand, end-to-end methods learn the node representations while classifying the nodes in one learning process. We highlight three main gaps in the literature on OCL for graphs: (i) non-customized representations for OCL; (ii) the lack of constraints on hypersphere parameters learning; and (iii) the methods' lack of interpretability and visualization. We propose One-cLass Graph Autoencoder (OLGA). OLGA is end-to-end and learns the representations for the graph nodes while encapsulating the interest instances by combining two loss functions. We propose a new hypersphere loss function to encapsulate the interest instances. OLGA combines this new hypersphere loss with the graph autoencoder reconstruction loss to improve model learning. OLGA achieved state-of-the-art results and outperformed six other methods with a statistically significant difference from five methods. Moreover, OLGA learns low-dimensional representations maintaining the classification performance with an interpretable model representation learning and results.">
+        <tr id="Change point detection in time series seeks to identify times when the probability distribution of time series changes. It is widely applied in many areas, such as human-activity sensing and medical science. In the context of multivariate time series, this typically involves examining the joint distribution of high-dimensional data: If any one variable changes, the whole time series is assumed to have changed. However, in practical applications, we may be interested only in certain components of the time series, exploring abrupt changes in their distributions in the presence of other time series. Here, assuming an underlying structural causal model that governs the time-series data generation, we address this problem by proposing a two-stage non-parametric algorithm that first learns parts of the causal structure through constraint-based discovery methods. The algorithm then uses conditional relative Pearson divergence estimation to identify the change points. The conditional relative Pearson divergence quantifies the distribution disparity between consecutive segments in the time series, while the causal discovery method enables a focus on the causal mechanism, facilitating access to independent and identically distributed (IID) samples. Theoretically, the typical assumption of samples being IID in conventional change point detection methods can be relaxed based on the Causal Markov Condition. Through experiments on both synthetic and real-world datasets, we validate the correctness and utility of our approach.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/732e70a34d887a6cc73f56cb1ac0dab09160a46f" target='_blank'>
-              OLGA: One-cLass Graph Autoencoder
+          <td><a href="https://www.semanticscholar.org/paper/010ab97fc0f4c786a8c27a35f6bd53cf9efb60a2" target='_blank'>
+              Causal Discovery-Driven Change Point Detection in Time Series
               </a>
             </td>
           <td>
-            M. Gôlo, José Gilberto Barbosa de Medeiros Junior, Diego Furtado Silva, R. Marcacini
+            Shanyun Gao, Raghavendra Addanki, Tong Yu, Ryan Rossi, Murat Kocaoglu
           </td>
-          <td>2024-06-13</td>
+          <td>2024-07-10</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>14</td>
+          <td>7</td>
         </tr>
 
-        <tr id="Generating synthetic financial time series data that accurately reflects real-world market dynamics holds tremendous potential for various applications, including portfolio optimization, risk management, and large scale machine learning. We present an approach for training generative models for financial time series using the maximum mean discrepancy (MMD) with a signature kernel. Our method leverages the expressive power of the signature transform to capture the complex dependencies and temporal structures inherent in financial data. We employ a moving average model to model the variance of the noise input, enhancing the model's ability to reproduce stylized facts such as volatility clustering. Through empirical experiments on S&P 500 index data, we demonstrate that our model effectively captures key characteristics of financial time series and outperforms a comparable GAN-based approach. In addition, we explore the application of the synthetic data generated to train a reinforcement learning agent for portfolio management, achieving promising results. Finally, we propose a method to add robustness to the generative model by tweaking the noise input so that the generated sequences can be adjusted to different market environments with minimal data.">
+        <tr id="Background: Biomedical data are usually collections of longitudinal data assessed at certain points in time. Clinical observations assess the presences and severity of symptoms, which are the basis for the description and modeling of disease progression. Deciphering potential underlying unknowns from the distinct observation would substantially improve the understanding of pathological cascades. Hidden Markov Models (HMMs) have been successfully applied to the processing of possibly noisy continuous signals. We apply ensembles of HMMs to categorically distributed multivariate time series data, leaving space for expert domain knowledge in the prediction process. Methods: We use an ensemble of HMMs to predict the loss of free walking ability as one major clinical deterioration in the most common autosomal dominantly inherited ataxia disorder worldwide. Results: We present a prediction pipeline that processes data paired with a configuration file, enabling us to train, validate and query an ensemble of HMMs. In particular, we provide a theoretical and practical framework for multivariate time-series inference based on HMMs that includes constructing multiple HMMs, each to predict a particular observable variable. Our analysis is conducted on pseudo-data, but also on biomedical data based on Spinocerebellar ataxia type 3 disease. Conclusions: We find that the model shows promising results for the data we tested. The strength of this approach is that HMMs are well understood, probabilistic and interpretable models, setting it apart from most Deep Learning approaches. We publish all code and evaluation pseudo-data in an open-source repository.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/492d244da8647554a7439883786cfe931ec4c342" target='_blank'>
-              Generative model for financial time series trained with MMD using a signature kernel
+          <td><a href="https://www.semanticscholar.org/paper/75eb137d735a965284db79b60d1396e83205c3ac" target='_blank'>
+              Ensemble of HMMs for Sequence Prediction on Multivariate Biomedical Data
               </a>
             </td>
           <td>
-            Chung I Lu, Julian Sester
+            Richard Fechner, Jens Dörpinghaus, R. Rockenfeller, J. Faber
           </td>
-          <td>2024-07-29</td>
-          <td>ArXiv</td>
-          <td>0</td>
+          <td>2024-07-03</td>
+          <td>BioMedInformatics</td>
           <td>0</td>
+          <td>9</td>
         </tr>
 
-        <tr id="In remote control systems, transmitting large data volumes (e.g. video feeds) from wireless sensors to faraway controllers is challenging when the uplink channel capacity is limited (e.g. RedCap devices or massive wireless sensor networks). Furthermore, the controllers often only need the information-rich components of the original data. To address this, we propose a Time-Series Joint Embedding Predictive Architecture (TS-JEPA) and a semantic actor trained through self-supervised learning. This approach harnesses TS-JEPA's semantic representation power and predictive capabilities by capturing spatio-temporal correlations in the source data. We leverage this to optimize uplink channel utilization, while the semantic actor calculates control commands directly from the encoded representations, rather than from the original data. We test our model through multiple parallel instances of the well-known inverted cart-pole scenario, where the approach is validated through the maximization of stability under constrained uplink channel capacity.">
+        <tr id="Constructing accurate spatiotemporal correlations is a challenging task in joint prediction of multiple photovoltaic sites. Some advanced algorithms for incorporating other surrounding site information have been proposed, such as graph neural network-based methods, which are usually based on static or dynamic graphs to build spatial dependencies between sites. However, the possibility of the simultaneous existence of multiple spatial dependencies is not considered. This paper establishes a spatiotemporal prediction model based on hybrid spatiotemporal graph neural network. In this model, we apply adaptive hybrid graph learning to learn composite spatial correlations among multiple sites. A temporal convolution module with multi-subsequence temporal data input is used to extract local semantic information to better predict future nonlinear temporal dependencies. A spatiotemporal adaptive fusion module is added to address the issue of integrating diverse spatiotemporal trends among multiple sites. To assess the model's predictive performance, nine solar radiation observation stations were selected in two different climatic environments. The average root mean square error (RMSE) of the constructed model was 38.51 and 49.90 W/m2, with average mean absolute error (MAE) of 14.72 and 23.06 W/m2, respectively. Single-site and multi-site prediction models were selected as baseline models. Compared with the baseline models, the RMSE and MAE reduce by 3.1%–20.8% and 8.9%–32.8%, respectively, across all sites. The proposed model demonstrates the effectiveness of improving accuracy in forecasting solar irradiance through multi-site predictions.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/2b01bab0902da79eaca5c6b606b61a45a527c55a" target='_blank'>
-              Time-Series JEPA for Predictive Remote Control under Capacity-Limited Networks
+          <td><a href="https://www.semanticscholar.org/paper/9f5975f5f85d9f8b58520410f9d2fb8ae33faa1d" target='_blank'>
+              Multi-site solar irradiance prediction based on hybrid spatiotemporal graph neural network
               </a>
             </td>
           <td>
-            Abanoub M. Girgis, Álvaro Valcarce, Mehdi Bennis
+            Yunjun Yu, Zejie Cheng, Biao Xiong, Qian Li
           </td>
-          <td>2024-06-07</td>
-          <td>ArXiv</td>
+          <td>2024-07-01</td>
+          <td>Journal of Renewable and Sustainable Energy</td>
           <td>0</td>
-          <td>4</td>
+          <td>10</td>
         </tr>
 
-        <tr id="Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is known to be far from trivial. In this work we introduce a methodology for zero-shot inference of Markov jump processes (MJPs), on bounded state spaces, from noisy and sparse observations, which consists of two components. First, a broad probability distribution over families of MJPs, as well as over possible observation times and noise mechanisms, with which we simulate a synthetic dataset of hidden MJPs and their noisy observation process. Second, a neural network model that processes subsets of the simulated observations, and that is trained to output the initial condition and rate matrix of the target MJP in a supervised way. We empirically demonstrate that one and the same (pretrained) model can infer, in a zero-shot fashion, hidden MJPs evolving in state spaces of different dimensionalities. Specifically, we infer MJPs which describe (i) discrete flashing ratchet systems, which are a type of Brownian motors, and the conformational dynamics in (ii) molecular simulations, (iii) experimental ion channel data and (iv) simple protein folding models. What is more, we show that our model performs on par with state-of-the-art models which are finetuned to the target datasets.">
+        <tr id="Studying low-likelihood high-impact extreme weather events in a warming world is a significant and challenging task for current ensemble forecasting systems. While these systems presently use up to 100 members, larger ensembles could enrich the sampling of internal variability. They may capture the long tails associated with climate hazards better than traditional ensemble sizes. Due to computational constraints, it is infeasible to generate huge ensembles (comprised of 1,000-10,000 members) with traditional, physics-based numerical models. In this two-part paper, we replace traditional numerical simulations with machine learning (ML) to generate hindcasts of huge ensembles. In Part I, we construct an ensemble weather forecasting system based on Spherical Fourier Neural Operators (SFNO), and we discuss important design decisions for constructing such an ensemble. The ensemble represents model uncertainty through perturbed-parameter techniques, and it represents initial condition uncertainty through bred vectors, which sample the fastest growing modes of the forecast. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (IFS) as a baseline, we develop an evaluation pipeline composed of mean, spectral, and extreme diagnostics. Using large-scale, distributed SFNOs with 1.1 billion learned parameters, we achieve calibrated probabilistic forecasts. As the trajectories of the individual members diverge, the ML ensemble mean spectra degrade with lead time, consistent with physical expectations. However, the individual ensemble members' spectra stay constant with lead time. Therefore, these members simulate realistic weather states, and the ML ensemble thus passes a crucial spectral test in the literature. The IFS and ML ensembles have similar Extreme Forecast Indices, and we show that the ML extreme weather forecasts are reliable and discriminating.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7c0b656d096263106b058f6c7ea137ae4421227d" target='_blank'>
-              Foundation Inference Models for Markov Jump Processes
+          <td><a href="https://www.semanticscholar.org/paper/de58dea585a06935529ae1f31353338f254df5af" target='_blank'>
+              Huge Ensembles Part I: Design of Ensemble Weather Forecasts using Spherical Fourier Neural Operators
               </a>
             </td>
           <td>
-            David Berghaus, K. Cvejoski, Patrick Seifner, C. Ojeda, Ramses J. Sanchez
+            Ankur Mahesh, William Collins, B. Bonev, Noah D. Brenowitz, Y. Cohen, Joshua Elms, Peter Harrington, K. Kashinath, Thorsten Kurth, Joshua North, Travis OBrien, Michael S. Pritchard, David Pruitt, Mark Risser, Shashank Subramanian, Jared Willard
           </td>
-          <td>2024-06-10</td>
+          <td>2024-08-06</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>7</td>
+          <td>25</td>
         </tr>
 
-        <tr id="Accurate modeling of car-following behaviors is essential for various applications in traffic management and autonomous driving systems. However, current approaches often suffer from limitations like high sensitivity to data quality and lack of interpretability. In this study, we propose GenFollower, a novel zero-shot prompting approach that leverages large language models (LLMs) to address these challenges. We reframe car-following behavior as a language modeling problem and integrate heterogeneous inputs into structured prompts for LLMs. This approach achieves improved prediction performance and interpretability compared to traditional baseline models. Experiments on the Waymo Open datasets demonstrate GenFollower's superior performance and ability to provide interpretable insights into factors influencing car-following behavior. This work contributes to advancing the understanding and prediction of car-following behaviors, paving the way for enhanced traffic management and autonomous driving systems.">
+        <tr id="Graph neural networks (GNNs) have gained significant attention in diverse domains, ranging from urban planning to pandemic management. Ensuring both accuracy and robustness in GNNs remains a challenge due to insufficient quality data that contains sufficient features. With sufficient training data where all spatiotemporal patterns are well-represented, existing GNN models can make reasonably accurate predictions. However, existing methods fail when the training data are drawn from different circumstances (e.g., traffic patterns on regular days) than test data (e.g., traffic patterns after a natural disaster). Such challenges are usually classified under domain generalization. In this work, we show that one way to address this challenge in the context of spatiotemporal prediction is by incorporating domain differential equations into graph convolutional networks (GCNs). We theoretically derive conditions where GCNs incorporating such domain differential equations are robust to mismatched training and testing data compared to baseline domain agnostic models. To support our theory, we propose two domain-differential-equation-informed networks: Reaction-Diffusion Graph Convolutional Network (RDGCN), which incorporates differential equations for traffic speed evolution, and the Susceptible-Infectious-Recovered Graph Convolutional Network (SIRGCN), which incorporates a disease propagation model. Both RDGCN and SIRGCN are based on reliable and interpretable domain differential equations that allow the models to generalize to unseen patterns. We experimentally show that RDGCN and SIRGCN are more robust with mismatched testing data than state-of-the-art deep learning methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3c2dc1a2b947f863938dfbf2e05352e7bff43498" target='_blank'>
-              GenFollower: Enhancing Car-Following Prediction with Large Language Models
+          <td><a href="https://www.semanticscholar.org/paper/0ce74ab023edbff0d9a6fad7e1a98a69c76287cb" target='_blank'>
+              On the generalization discrepancy of spatiotemporal dynamics-informed graph convolutional networks
               </a>
             </td>
           <td>
-            Xianda Chen, Mingxing Peng, PakHin Tiu, Yuanfei Wu, Junjie Chen, Meixin Zhu, Xinhu Zheng
+            Yue Sun, Chao Chen, Yuesheng Xu, Sihong Xie, Rick S. Blum, Parv Venkitasubramaniam
           </td>
-          <td>2024-07-08</td>
-          <td>ArXiv</td>
+          <td>2024-07-12</td>
+          <td>Frontiers in Mechanical Engineering</td>
+          <td>0</td>
           <td>1</td>
-          <td>4</td>
         </tr>
 
-        <tr id="Financial institutions desperately need accurate credit default prediction tools to minimize losses, optimize lending and foster responsible borrowing. Existing methods often rely on complex ensemble approaches which are computationally intensive. This paper proposes a relatively lightweight solution: a simple encoder-only transformer which extracts latent features directly from credit card transaction data, followed by a simple neural network for the credit default prediction. The proposed approach achieves comparable performance on the American Express (AMEX) Default Prediction Kaggle Competition dataset against state-of-the-art (SOTA) ensemble techniques such as 3-Ensemble Modules with Gradient Boosting Decision Tree (GBDT) and 3-LightGBM with Dropouts meet Multiple Additive Regression Trees (DART) and pseudo-labelling ensemble methods. It achieves better performance than LightGBM based method.">
+        <tr id="With the vigorous development of e-commerce, accurately modeling and predicting user behavior has become a key factor in improving business efficiency. Precisely understanding user behavior not only enables companies to provide personalized services but also allows them to stand out in the intense market competition. This study aims to explore the effectiveness of applying end-to-end models, Long Short-Term Memory (LSTM), and attention mechanisms in time series modeling to enhance the performance of modeling and predicting user behavior in e-commerce. In the methodology section, we first introduce the basic principles of the end-to-end model, which extracts features directly from raw data for prediction, avoiding the need for intricate feature engineering. Simultaneously, we introduce Long Short-Term Memory (LSTM) to better capture long-term dependencies in time series data.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/7211f434decf5b1594c3d63c116941a8bba4a6e6" target='_blank'>
-              A Lightweight Neural Network with Transformer to Predict Credit Default
+          <td><a href="https://www.semanticscholar.org/paper/0da5e0a0f8f43013d568bfc235ed44504eef00ce" target='_blank'>
+              End-to-End Modeling and Long Short-Term Memory Application in Time Series Modeling
               </a>
             </td>
           <td>
-            Zongqi Hu, Chai Kiat Yeo
+            Guodong Yang, Kuangyu Li, Yunfan Zhang, Qindi Feng
           </td>
-          <td>2024-06-25</td>
-          <td>2024 IEEE Conference on Artificial Intelligence (CAI)</td>
+          <td>2024-07-30</td>
+          <td>Journal of Organizational and End User Computing</td>
           <td>0</td>
           <td>0</td>
         </tr>
 
-        <tr id="Clinical trials need to recruit a sufficient number of volunteer patients to demonstrate the statistical power of the treatment (e.g., a new drug) in curing a certain disease. Clinical trial recruitment has a significant impact on trial success. Forecasting whether the recruitment process would be successful before we run the trial would save many resources and time. This paper develops a novel deep&cross network with large language model (LLM)-augmented text feature that learns semantic information from trial eligibility criteria and predicts enrollment success. The proposed method enables interpretability by understanding which sentence/word in eligibility criteria contributes heavily to prediction. We also demonstrate the empirical superiority of the proposed method (0.7002 PR-AUC) over a bunch of well-established machine learning methods. The code and curated dataset are publicly available at https://anonymous.4open.science/r/TrialEnroll-7E12.">
+        <tr id="The COVID-19 pandemic has posed significant chal-lenges to global health, economies, and social structures since its emergence in late 2019. Southern California, a region with unique characteristics and diverse communities, has experienced difficul-ties in controlling the virus's spread. Understanding the factors that influence COVID-19 transmission in Southern California is crucial for informing public health policies and mitigating the virus's impact on the communities. In this study, we collected weekly zip code level data from March to December 2020 in Southern California and applied various machine learning algorithms, such as graph neural networks (GNN), multi-layer perceptrons (MLP), and gradient boosting trees (XGBoost), to model the spread of COVID-19. Our main contributions include the development of various COVID-19 forecasting models that incorporate socioeconomically significant variables and zip code level mobility data, coupled with variable impact assessments to provide valuable insights for informing future public health policies and strategies. Our predictive model not only attains high levels of accuracy in forecasting but also facilitates the understanding of how each variable contributes to the final outcome. These findings have the potential to enhance our understanding of COVID-19 transmission patterns and inform targeted mitigation strategies in the region.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/8b0084ee93fc8c700058b3d5d2d7c58de05f753a" target='_blank'>
-              TrialEnroll: Predicting Clinical Trial Enrollment Success with Deep&Cross Network and Large Language Models
+          <td><a href="https://www.semanticscholar.org/paper/e3a3a205cede5dc9ee960274ff3f51815bbca1ea" target='_blank'>
+              Predicting COVID-19 Transmission in Southern California with Machine Learning Methods
               </a>
             </td>
           <td>
-            Ling Yue, Sixue Xing, Jintai Chen, Tianfan Fu
+            Han Li, Ran Wei, Wenyu Wang, Nanpeng Yu
           </td>
-          <td>2024-07-18</td>
-          <td>ArXiv</td>
+          <td>2024-03-16</td>
+          <td>2024 9th International Conference on Big Data Analytics (ICBDA)</td>
           <td>0</td>
-          <td>2</td>
+          <td>6</td>
         </tr>
 
-        <tr id="Recent works have shown that transformers can solve contextual reasoning tasks by internally executing computational graphs called circuits. Circuits often use attention to logically match information from subspaces of the representation, e.g. using position-in-sequence to identify the previous token. In this work, we consider a semantic subspace to be any independent subspace of the latent representation that can fully determine an attention distribution. We show that Pre-Norm, the placement of normalisation layer used by state-of-the-art transformers, violates this ability unless the model learns a strict representation structure of orthogonal spheres. This is because it causes linear subspaces to interfere through their common normalisation factor. Theoretically, we analyse circuit stability by modelling this interference as random noise on the $L_2$-norms of the query/key/value vectors, predicting a phenomenon of circuit collapse when sparse-attention shifts to a different token. Empirically, we investigate the sensitivity of real-world models trained for mathematical addition, observing a 1% rate of circuit collapse when the norms are artificially perturbed by $\lesssim$10%. We contrast Pre-Norm with QKV-Norm, which places normalisation after the attention head's linear operators. Theoretically this relaxes the representational constraints. Empirically we observe comparable in-distribution but worse out-of-distribution performance.">
+        <tr id="Most state-of-the-art AI applications in atmospheric science are based on classic deep learning approaches. However, such approaches cannot automatically integrate multiple complicated procedures to construct an intelligent agent, since each functionality is enabled by a separate model learned from independent climate datasets. The emergence of foundation models, especially multimodal foundation models, with their ability to process heterogeneous input data and execute complex tasks, offers a substantial opportunity to overcome this challenge. In this report, we want to explore a central question - how the state-of-the-art foundation model, i.e., GPT-4o, performs various atmospheric scientific tasks. Toward this end, we conduct a case study by categorizing the tasks into four main classes, including climate data processing, physical diagnosis, forecast and prediction, and adaptation and mitigation. For each task, we comprehensively evaluate the GPT-4o's performance along with a concrete discussion. We hope that this report may shed new light on future AI applications and research in atmospheric science.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5e969b6c033a3ec1665fc16296110d76be357f80" target='_blank'>
-              Transformer Normalisation Layers and the Independence of Semantic Subspaces
+          <td><a href="https://www.semanticscholar.org/paper/18a501f9bccb6fcfbb0d37e1ac9f7d535942b340" target='_blank'>
+              On the Opportunities of (Re)-Exploring Atmospheric Science by Foundation Models: A Case Study
               </a>
             </td>
           <td>
-            S. Menary, Samuel Kaski, Andre Freitas
+            Lujia Zhang, Hanzhe Cui, Yurong Song, Chenyue Li, Binhang Yuan, Mengqian Lu
           </td>
-          <td>2024-06-25</td>
+          <td>2024-07-25</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>50</td>
+          <td>2</td>
         </tr>
 
-        <tr id="Flood prediction is a critical challenge in the context of climate change, with significant implications for ecosystem preservation, human safety, and infrastructure protection. In this study, we tackle this problem by applying the Quantum-Train (QT) technique to a forecasting Long Short-Term Memory (LSTM) model trained by Quantum Machine Learning (QML) with significant parameter reduction. The QT technique, originally successful in the A Matter of Taste challenge at QHack 2024, leverages QML to reduce the number of trainable parameters to a polylogarithmic function of the number of parameters in a classical neural network (NN). This innovative framework maps classical NN weights to a Hilbert space, altering quantum state probability distributions to adjust NN parameters. Our approach directly processes classical data without the need for quantum embedding and operates independently of quantum computing resources post-training, making it highly practical and accessible for real-world flood prediction applications. This model aims to improve the efficiency of flood forecasts, ultimately contributing to better disaster preparedness and response.">
+        <tr id="The cinematic metaverse aims to create a virtual space with the context of a film. Users can enter this space in the form of avatars, experiencing the cinematic plot firsthand in an immersive manner. This requires us to design a rational computation resource allocation and synchronization algorithm to meet the demands of multi‐objective joint optimization, such as low latency and high throughput, which ensures that users can seamlessly switch between virtual and real worlds and acquire immersive experiences. Unfortunately, the explosive growth in the number of users makes it difficult to jointly optimize multiple objectives. Predicting traffic generated by the users' avatars in the cinematic metaverse is significant for the optimization process. Although graph neural networks‐based traffic prediction models achieve superior prediction accuracy, these methods rely only on physical distances‐based topological graph information, while failing to comprehensively reflect the real relationships between avatars in the cinematic metaverse. To address this issue, we present a novel Multi‐Graph Representation Spatio‐Temporal Attention Networks (MGRSTANet) for traffic prediction in the cinematic metaverse. Specifically, based on multiple topological graph information (e.g., physical distances, centerity, and similarity), we first design Multi‐Graph Embedding (MGE) module to generate multiple graph representations, thus reflecting on the real relationships between avatars more comprehensively. The Spatio‐Temporal Attention (STAtt) module is then proposed to extract spatio‐temporal correlations in each graph representations, thus improving prediction accuracy. We conduct simulation experiments to evaluate the effectiveness of MGRSTANet. The experimental results demonstrate that our proposed model outperforms the state‐of‐the‐art baselines in terms of prediction accuracy, making it appropriate for traffic forecasting in the cinematic metaverse.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c6070c93b2e55353e37efc3cde9139fec8b0debb" target='_blank'>
-              Quantum-Train Long Short-Term Memory: Application on Flood Prediction Problem
+          <td><a href="https://www.semanticscholar.org/paper/7a17e82d53c5d1ce27349fc52790d7c9df247a47" target='_blank'>
+              Multi-graph representation spatio-temporal attention networks for traffic forecasting in the cinematic metaverse
               </a>
             </td>
           <td>
-            Chu-Hsuan Abraham Lin, Chen-Yu Liu, Kuan-Cheng Chen
+            Ke Li, Xiaoming He, Yinqiu Liu, Meng Chen
           </td>
-          <td>2024-07-11</td>
-          <td>ArXiv</td>
+          <td>2024-07-01</td>
+          <td>Trans. Emerg. Telecommun. Technol.</td>
+          <td>0</td>
           <td>1</td>
-          <td>2</td>
         </tr>
 
-        <tr id="Travel choice analysis is crucial for understanding individual travel behavior to develop appropriate transport policies and recommendation systems in Intelligent Transportation Systems (ITS). Despite extensive research, this domain faces two critical challenges: a) modeling with limited survey data, and b) simultaneously achieving high model explainability and accuracy. In this paper, we introduce a novel prompt-learning-based Large Language Model(LLM) framework that significantly improves prediction accuracy and provides explicit explanations for individual predictions. This framework involves three main steps: transforming input variables into textual form; building of demonstrations similar to the object, and applying these to a well-trained LLM. We tested the framework's efficacy using two widely used choice datasets: London Passenger Mode Choice (LPMC) and Optima-Mode collected in Switzerland. The results indicate that the LLM significantly outperforms state-of-the-art deep learning methods and discrete choice models in predicting people's choices. Additionally, we present a case of explanation illustrating how the LLM framework generates understandable and explicit explanations at the individual level.">
+        <tr id="Diffusion Transformer, the backbone of Sora for video generation, successfully scales the capacity of diffusion models, pioneering new avenues for high-fidelity sequential data generation. Unlike static data such as images, sequential data consists of consecutive data frames indexed by time, exhibiting rich spatial and temporal dependencies. These dependencies represent the underlying dynamic model and are critical to validate the generated data. In this paper, we make the first theoretical step towards bridging diffusion transformers for capturing spatial-temporal dependencies. Specifically, we establish score approximation and distribution estimation guarantees of diffusion transformers for learning Gaussian process data with covariance functions of various decay patterns. We highlight how the spatial-temporal dependencies are captured and affect learning efficiency. Our study proposes a novel transformer approximation theory, where the transformer acts to unroll an algorithm. We support our theoretical results by numerical experiments, providing strong evidence that spatial-temporal dependencies are captured within attention layers, aligning with our approximation theory.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/d6c15845a955d6a89c45684ba61801c976943999" target='_blank'>
-              Enhancing Travel Choice Modeling with Large Language Models: A Prompt-Learning Approach
+          <td><a href="https://www.semanticscholar.org/paper/29e9034e1e9a82b3bffe33d3460d002e29d5958c" target='_blank'>
+              Diffusion Transformer Captures Spatial-Temporal Dependencies: A Theory for Gaussian Process Data
               </a>
             </td>
           <td>
-            Xuehao Zhai, Hanlin Tian, Lintong Li, Tianyu Zhao
+            Hengyu Fu, Zehao Dou, Jiawei Guo, Mengdi Wang, Minshuo Chen
           </td>
-          <td>2024-06-19</td>
+          <td>2024-07-23</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>0</td>
+          <td>4</td>
         </tr>
 
-        <tr id="Time series data complexity presents new challenges in clustering analysis across fields such as electricity, energy, industry, and finance. Despite advances in representation learning and clustering with Variational Autoencoders (VAE) based deep learning techniques, issues like the absence of discriminative power in feature representation, the disconnect between instance reconstruction and clustering objectives, and scalability challenges with large datasets persist. This paper introduces a novel deep time series clustering approach integrating VAE with metric learning. It leverages a VAE based on Gated Recurrent Units for temporal feature extraction, incorporates metric learning for joint optimization of latent space representation, and employs the sum of log likelihoods as the clustering merging criterion, markedly improving clustering accuracy and interpretability. Experimental findings demonstrate a 27.16% improvement in average clustering accuracy and a 47.15% increase in speed on industrial load data. This study offers novel insights and tools for the thorough analysis and application of time series data, with further exploration of VAE’s potential in time series clustering anticipated in future research.">
+        <tr id="Continual graph learning (CGL) is an important and challenging task that aims to extend static GNNs to dynamic task flow scenarios. As one of the mainstream CGL methods, the experience replay (ER) method receives widespread attention due to its superior performance. However, existing ER methods focus on identifying samples by feature significance or topological relevance, which limits their utilization of comprehensive graph data. In addition, the topology-based ER methods only consider local topological information and add neighboring nodes to the buffer, which ignores the global topological information and increases memory overhead. To bridge these gaps, we propose a novel method called Feature-Topology Fusion-based Experience Replay (FTF-ER) to effectively mitigate the catastrophic forgetting issue with enhanced efficiency. Specifically, from an overall perspective to maximize the utilization of the entire graph data, we propose a highly complementary approach including both feature and global topological information, which can significantly improve the effectiveness of the sampled nodes. Moreover, to further utilize global topological information, we propose Hodge Potential Score (HPS) as a novel module to calculate the topological importance of nodes. HPS derives a global node ranking via Hodge decomposition on graphs, providing more accurate global topological information compared to neighbor sampling. By excluding neighbor sampling, HPS significantly reduces buffer storage costs for acquiring topological information and simultaneously decreases training time. Compared with state-of-the-art methods, FTF-ER achieves a significant improvement of 3.6% in AA and 7.1% in AF on the OGB-Arxiv dataset, demonstrating its superior performance in the class-incremental learning setting.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/5c8bdd5e4eb0940f762713b94bd43e70c528c42c" target='_blank'>
-              Research on load clustering algorithm based on variational autoencoder and hierarchical clustering
+          <td><a href="https://www.semanticscholar.org/paper/5a0f6d19e56c93eb398b62ebfdf9a94a5c5b4bed" target='_blank'>
+              FTF-ER: Feature-Topology Fusion-Based Experience Replay Method for Continual Graph Learning
               </a>
             </td>
           <td>
-            Miaozhuang Cai, Yin Zheng, Zhengyang Peng, Chunyan Huang, Haoxia Jiang
+            Jinhui Pang, Changqing Lin, Xiaoshuai Hao, Rong Yin, Zixuan Wang, Zhihui Zhang, Jinglin He, Huang Tai Sheng
           </td>
-          <td>2024-06-13</td>
-          <td>PLOS ONE</td>
+          <td>2024-07-28</td>
+          <td>ArXiv</td>
           <td>0</td>
           <td>1</td>
         </tr>
 
-        <tr id="This paper addresses the challenge of creating a neural architecture for very long sequences that requires constant time for processing new information at each time step. Our approach, Associative Recurrent Memory Transformer (ARMT), is based on transformer self-attention for local context and segment-level recurrence for storage of task specific information distributed over a long context. We demonstrate that ARMT outperfors existing alternatives in associative retrieval tasks and sets a new performance record in the recent BABILong multi-task long-context benchmark by answering single-fact questions over 50 million tokens with an accuracy of 79.9%. The source code for training and evaluation is available on github.">
+        <tr id="Accurate streamflow forecasting is crucial for effectively managing water resources, particularly in countries like Colombia, where hydroelectric power generation significantly contributes to the national energy grid. Although highly interpretable, traditional deterministic, physically-driven models often suffer from complexity and require extensive parameterization. Data-driven models like Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) networks offer simplicity and performance but cannot quantify uncertainty. This work introduces Sparse Variational Gaussian Processes (SVGPs) for forecasting streamflow contributions. The proposed SVGP model reduces computational complexity compared to traditional Gaussian Processes, making it highly scalable for large datasets. The methodology employs optimal hyperparameters and shared inducing points to capture short-term and long-term relationships among reservoirs. Training, validation, and analysis of the proposed approach consider the streamflow dataset from 23 geographically dispersed reservoirs recorded during twelve years in Colombia. Performance assessment reveals that the proposal outperforms baseline Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) models in three key aspects: adaptability to changing dynamics, provision of informative confidence intervals through Bayesian inference, and enhanced forecasting accuracy. Therefore, the SVGP-based forecasting methodology offers a scalable and interpretable solution for multi-output streamflow forecasting, thereby contributing to more effective water resource management and hydroelectric planning.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/1085ddc5028be0a6f517bde6c44029abc208c63f" target='_blank'>
-              Associative Recurrent Memory Transformer
+          <td><a href="https://www.semanticscholar.org/paper/82ecf0c70aa07f89d48d8aa7c5d4ec1674f0475d" target='_blank'>
+              Scalable and Interpretable Forecasting of Hydrological Time Series Based on Variational Gaussian Processes
               </a>
             </td>
           <td>
-            Ivan Rodkin, Yuri Kuratov, Aydar Bulatov, Mikhail Burtsev
+            J. D. Pastrana-Cortés, J. Gil-González, A. Álvarez-Meza, D. Cárdenas-Peña, Á. Orozco-Gutiérrez
           </td>
-          <td>2024-07-05</td>
-          <td>ArXiv</td>
+          <td>2024-07-15</td>
+          <td>Water</td>
           <td>0</td>
-          <td>8</td>
+          <td>15</td>
         </tr>
 
-        <tr id="We present our work on developing and training scalable graph foundation models (GFM) using HydraGNN, a multi-headed graph convolutional neural network architecture. HydraGNN expands the boundaries of graph neural network (GNN) in both training scale and data diversity. It abstracts over message passing algorithms, allowing both reproduction of and comparison across algorithmic innovations that define convolution in GNNs. This work discusses a series of optimizations that have allowed scaling up the GFM training to tens of thousands of GPUs on datasets that consist of hundreds of millions of graphs. Our GFMs use multi-task learning (MTL) to simultaneously learn graph-level and node-level properties of atomistic structures, such as the total energy and atomic forces. Using over 150 million atomistic structures for training, we illustrate the performance of our approach along with the lessons learned on two United States Department of Energy (US-DOE) supercomputers, namely the Perlmutter petascale system at the National Energy Research Scientific Computing Center and the Frontier exascale system at Oak Ridge National Laboratory. The HydraGNN architecture enables the GFM to achieve near-linear strong scaling performance using more than 2,000 GPUs on Perlmutter and 16,000 GPUs on Frontier. Hyperparameter optimization (HPO) was performed on over 64,000 GPUs on Frontier to select GFM architectures with high accuracy. Early stopping was applied on each GFM architecture for energy awareness in performing such an extreme-scale task. The training of an ensemble of highest-ranked GFM architectures continued until convergence to establish uncertainty quantification (UQ) capabilities with ensemble learning. Our contribution opens the door for rapidly developing, training, and deploying GFMs using large-scale computational resources to enable AI-accelerated materials discovery and design.">
+        <tr id="In recent years, sequential recommendation has received widespread attention for its role in enhancing user experience and driving personalized content recommendations. However, it also encounters challenges, including the limitations of modeling information and the variability of user preferences. A novel time-aware Long-Short Term Transformer (TLSTSRec) for sequential recommendation is introduced in this paper to address these challenges. TLSTSRec has two major innovative features. (1) Accurate modeling of users is achieved by fully leveraging temporal information. Time information is modeled by creating a trainable timestamp matrix from both the perspectives of time duration and time spectrum. (2) A novel time-aware Transformer model is proposed. To address the inherent variability of user preferences over time, the model combines long-term and short-term temporal information and adjusts the personalized trade-offs between long-term and short-term sequences using adaptive fusion layers. Subsequently, newly designed encoders and decoders are employed to model timestamps and interaction items. Finally, extensive experiments substantiate the effectiveness of TLSTSRec relative to various state-of-the-art sequential recommendation models based on MC/RNN/GNN/SA across a spectrum of widely used metrics. Furthermore, experiments are conducted to validate the rationality of the TLSTSRec structure.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e9774ce8071dd76506106d6eb3572ff746d40b01" target='_blank'>
-              Scalable Training of Graph Foundation Models for Atomistic Materials Modeling: A Case Study with HydraGNN
+          <td><a href="https://www.semanticscholar.org/paper/417f89b6992377e3e5d706672bfa4da837f011df" target='_blank'>
+              TLSTSRec: Time-aware long short-term attention neural network for sequential recommendation
               </a>
             </td>
           <td>
-            Massimiliano Lupo Pasini, Jong Youl Choi, Kshitij Mehta, Pei Zhang, David Rogers, Jonghyun Bae, Khaled Ibrahim, Ashwin M. Aji, Karl W. Schulz, Jorda Polo, Prasanna Balaprakash
+            Hongwei Chen, Luanxuan Liu, Zexi Chen
           </td>
-          <td>2024-06-12</td>
-          <td>ArXiv</td>
+          <td>2024-08-01</td>
+          <td>Intelligent Data Analysis</td>
+          <td>0</td>
           <td>0</td>
-          <td>6</td>
         </tr>
 
-        <tr id="The significance of modeling long-term user interests for CTR prediction tasks in large-scale recommendation systems is progressively gaining attention among researchers and practitioners. Existing work, such as SIM and TWIN, typically employs a two-stage approach to model long-term user behavior sequences for efficiency concerns. The first stage rapidly retrieves a subset of sequences related to the target item from a long sequence using a search-based mechanism namely the General Search Unit (GSU), while the second stage calculates the interest scores using the Exact Search Unit (ESU) on the retrieved results. Given the extensive length of user behavior sequences spanning the entire life cycle, potentially reaching up to 10^6 in scale, there is currently no effective solution for fully modeling such expansive user interests. To overcome this issue, we introduced TWIN-V2, an enhancement of TWIN, where a divide-and-conquer approach is applied to compress life-cycle behaviors and uncover more accurate and diverse user interests. Specifically, a hierarchical clustering method groups items with similar characteristics in life-cycle behaviors into a single cluster during the offline phase. By limiting the size of clusters, we can compress behavior sequences well beyond the magnitude of 10^5 to a length manageable for online inference in GSU retrieval. Cluster-aware target attention extracts comprehensive and multi-faceted long-term interests of users, thereby making the final recommendation results more accurate and diverse. Extensive offline experiments on a multi-billion-scale industrial dataset and online A/B tests have demonstrated the effectiveness of TWIN-V2. Under an efficient deployment framework, TWIN-V2 has been successfully deployed to the primary traffic that serves hundreds of millions of daily active users at Kuaishou.">
+        <tr id="Literature abounds with various statistical and machine learning techniques for stock market forecasting. However, Reinforcement Learning (RL) is conspicuous by its absence in this field and is little explored despite its potential to address the dynamic and uncertain nature of the stock market. In a first-of-its-kind study, this research precisely bridges this gap, by forecasting stock prices using RL, in the static as well as streaming contexts using deep RL techniques. In the static context, we employed three deep RL algorithms for forecasting the stock prices: Deep Deterministic Policy Gradient (DDPG), Proximal Policy Optimisation (PPO) and Recurrent Deterministic Policy Gradient (RDPG) and compared their performance with Multi-Layer Perceptron (MLP), Support Vector Regression (SVR) and General Regression Neural Network (GRNN). In addition, we proposed a generic streaming analytics-based forecasting approach leveraging the real-time processing capabilities of Spark streaming for all six methods. This approach employs a sliding window technique for real-time forecasting or nowcasting using the above-mentioned algorithms. We demonstrated the effectiveness of the proposed approach on the daily closing prices of four different financial time series dataset as well as the Mackey–Glass time series, a benchmark chaotic time series dataset. We evaluated the performance of these methods using three metrics: Symmetric Mean Absolute Percentage (SMAPE), Directional Symmetry statistic (DS) and Theil’s U Coefficient. The results are promising for DDPG in the static context and GRNN turned out to be the best in streaming context. We performed the Diebold–Mariano (DM) test to assess the statistical significance of the best-performing models.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c5859754c1f6c099199d42b488415b04a7bfd527" target='_blank'>
-              TWIN V2: Scaling Ultra-Long User Behavior Sequence Modeling for Enhanced CTR Prediction at Kuaishou
+          <td><a href="https://www.semanticscholar.org/paper/399a8108ea6cff24099de6a2388ecbb9069a00fa" target='_blank'>
+              Deep Reinforcement Learning for Financial Forecasting in Static and Streaming Cases
               </a>
             </td>
           <td>
-            Zihua Si, Lin Guan, ZhongXiang Sun, Xiaoxue Zang, Jing Lu, Yiqun Hui, Xingchao Cao, Zeyu Yang, Yichen Zheng, Dewei Leng, Kai Zheng, Chenbin Zhang, Ya-Ling Niu, Yang Song, Kun Gai
+            Aravilli Atchuta Ram, Sandarbh Yadav, Yelleti Vivek, V. Ravi
           </td>
-          <td>2024-07-23</td>
-          <td>ArXiv</td>
+          <td>2024-06-27</td>
+          <td>Journal of Information &amp; Knowledge Management</td>
           <td>0</td>
-          <td>10</td>
+          <td>40</td>
         </tr>
 
-        <tr id="None">
+        <tr id="High precision in forecasting travel demand for online car-hailing is crucial for traffic management to schedule vehicles, hence reducing energy consumption and achieving sustainable development. Netflix demand forecasting relies on the capture of spatiotemporal correlations. To extract the spatiotemporal information more fully, this study designs and develops a novel spatiotemporal prediction model with multidimensional inputs (MSACL) by embedding a self-attention memory (SAM) module into a convolutional long short-term memory neural network (ConvLSTM). The SAM module can extract features with long-range spatiotemporal dependencies. The experimental data are derived from the Chengdu City online car-hailing trajectory data set and the external factors data set. Comparative experiments demonstrate that the proposed model has higher accuracy. The proposed model outperforms the Sa-ConvLSTM model and has the highest prediction accuracy, shows a reduction in the mean absolute error (MAE) by 1.72, a reduction in the mean squared error (MSE) by 0.43, and an increase in the R-squared (R2) by 4%. In addition, ablation experiments illustrate the effectiveness of each component, where the external factor inputs have the least impact on the model accuracy, but the removal of the SAM module results in the most significant decrease in model accuracy.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4ccc940a891f74aa82e4a858d918d21d59774433" target='_blank'>
-              A binary-domain recurrent-like architecture-based dynamic graph neural network
+          <td><a href="https://www.semanticscholar.org/paper/ea2c249a41fa5eff75101cd3187bb7f3b33e1f26" target='_blank'>
+              Prediction on Demand for Regional Online Car-Hailing Travel Based on Self-Attention Memory and ConvLSTM
               </a>
             </td>
           <td>
-            Zi-chao Chen, Sui Lin
+            Jianqi Li, Wenbao Zeng, Weiqi Liu, Rongjun Cheng
           </td>
-          <td>2024-06-25</td>
-          <td>Auton. Intell. Syst.</td>
-          <td>0</td>
+          <td>2024-07-04</td>
+          <td>Sustainability</td>
           <td>0</td>
+          <td>1</td>
         </tr>
 
-        <tr id="The dynamic characteristics of multiphase industrial processes present significant challenges in the field of industrial big data modeling. Traditional soft sensing models frequently neglect the process dynamics and have difficulty in capturing transient phenomena like phase transitions. To address this issue, this article introduces a causality-driven sequence segmentation (CDSS) model. This model first identifies the local dynamic properties of the causal relationships between variables, which are also referred to as causal mechanisms. It then segments the sequence into different phases based on the sudden shifts in causal mechanisms that occur during phase transitions. Additionally, a novel metric, similarity distance, is designed to evaluate the temporal consistency of causal mechanisms, which includes both causal similarity distance and stable similarity distance. The discovered causal relationships in each phase are represented as a temporal causal graph (TCG). Furthermore, a soft sensing model called temporal-causal graph convolutional network (TC-GCN) is trained for each phase, by using the time-extended data and the adjacency matrix of TCG. The numerical examples are utilized to validate the proposed CDSS model, and the segmentation results demonstrate that CDSS has excellent performance on segmenting both stable and unstable multiphase series. Especially, it has higher accuracy in separating non-stationary time series compared to other methods. The effectiveness of the proposed CDSS model and the TC-GCN model is also verified through a penicillin fermentation process. Experimental results indicate that the breakpoints discovered by CDSS align well with the reaction mechanisms and TC-GCN significantly has excellent predictive accuracy.">
+        <tr id="Echo state network (ESN) implements an alternative paradigm called reservoir computing to train recurrent neural networks (RNNs), where internal weights are randomly generated and kept fixed, and only readout weights need to be trained, which greatly reduces the training complexity of RNNs. ESN not only facilitates the practical implementation of RNNs but also shows superior performance over fully trained RNNs across a range of applications. However, the conventional ESN suffers from the drawbacks of stringent conditions for weight convergence and slow convergence speed. This paper proposes a memory regressor extended learning method to update the readout weights of ESNs. By constructing and incorporating a generalized prediction error based on regressor extension and filtering, the capacity of ESN to utilize historical data can be greatly improved. In the discrete-time domain, it is proven that exponential convergence of readout weights is achieved under a condition termed interval excitation that is strictly weaker than the classical condition of persistent excitation. Simulation results on modeling a 10th-order nonlinear autoregressive moving-average (NARMA) system have revealed that the proposed approach accelerates weight convergence speed almost ten times higher compared to the conventional ESN.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/f4b2b1a8bce30a394b4fb8eac0b13365c9a406b2" target='_blank'>
-              Causality-driven Sequence Segmentation for Enhancing Multiphase Industrial Process Data Analysis and Soft Sensing
+          <td><a href="https://www.semanticscholar.org/paper/4e0fa7b7dfe357970b3e72acb8d86266f028d299" target='_blank'>
+              Memory Regressor Extended Echo State Networks for Nonlinear Dynamics Modeling
               </a>
             </td>
           <td>
-            Yimeng He, Le Yao, Xinmin Zhang, Xiangyin Kong, Zhihuan Song
+            Kai Hu, Qian Wang, Tian Shi, Kohei Nakajima, Yongping Pan
           </td>
-          <td>2024-06-30</td>
-          <td>ArXiv</td>
+          <td>2024-06-25</td>
+          <td>2024 European Control Conference (ECC)</td>
           <td>0</td>
-          <td>7</td>
+          <td>2</td>
         </tr>
 
-        <tr id="We present a logic based interpretable model for learning on graphs and an algorithm to distill this model from a Graph Neural Network (GNN). Recent results have shown connections between the expressivity of GNNs and the two-variable fragment of first-order logic with counting quantifiers (C2). We introduce a decision-tree based model which leverages an extension of C2 to distill interpretable logical classifiers from GNNs. We test our approach on multiple GNN architectures. The distilled models are interpretable, succinct, and attain similar accuracy to the underlying GNN. Furthermore, when the ground truth is expressible in C2, our approach outperforms the GNN.">
+        <tr id="With technological advancements, much data is being captured by sensors, smartphones, wearable devices, and so forth. These vast datasets are stored in data centres and utilized to forge data‐driven models for the condition monitoring of infrastructures and systems through future data mining tasks. However, these datasets often surpass the processing capabilities of traditional information systems and methodologies due to their significant size. Additionally, not all samples within these datasets contribute valuable information during the model training phase, leading to inefficiencies. The processing and training of Machine Learning algorithms become time‐consuming, and storing all the data demands excessive space, contributing to the Big Data challenge. In this paper, we propose two novel techniques to reduce large time‐series datasets into more compact versions without undermining the predictive performance of the resulting models. These methods also aim to decrease the time required for training the models and the storage space needed for the condensed datasets. We evaluated our techniques on five public datasets, employing three Machine Learning algorithms: Holt‐Winters, SARIMA, and LSTM. The outcomes indicate that for most of the datasets examined, our techniques maintain, and in several instances enhance, the forecasting accuracy of the models. Moreover, we significantly reduced the time required to train the Machine Learning algorithms employed.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/799f87515867c928d15d035609e77fa59d1339e5" target='_blank'>
-              Logical Distillation of Graph Neural Networks
+          <td><a href="https://www.semanticscholar.org/paper/33d3e765763fbda62c139a833d2484281eec1ade" target='_blank'>
+              Sampling approaches to reduce very frequent seasonal time series
               </a>
             </td>
           <td>
-            Alexander Pluska, Pascal Welke, Thomas Gärtner, Sagar Malhotra
+            Afonso Baldo, Paulo J. S. Ferreira, João Mendes‐Moreira
           </td>
-          <td>2024-06-11</td>
-          <td>ArXiv</td>
-          <td>0</td>
+          <td>2024-07-25</td>
+          <td>Expert Systems</td>
           <td>0</td>
+          <td>2</td>
         </tr>
 
-        <tr id="
- One of the core assumptions of most deep-learning-based data-driven models is that samples are independent. However, this assumption poses a key challenge in production forecasting—performance is influenced by well interference and reservoir connectivity. Most shale gas wells are hydraulically fractured and exist in complex fracture systems, and the neighboring well characteristics should also be considered when constructing data-driven forecast models. Researchers have explored using the graph convolutional network (GCN) to address this issue by incorporating neighboring well characteristics into production forecasting models. However, applying GCN to field-scale studies is problematic, as it requires training on a full batch, leading to gigantic cache allocation. In addition, the transductive nature of GCN poses challenges for direct generalization to unseen nodes. To overcome these limitations, we adopt the graph sampling and aggregation (GraphSAGE) network architecture, which allows training large graphs with batches and generalizing predictions for previously unseen nodes. By utilizing the gated recurrent unit (GRU) network, the proposed spatial-temporal (ST)-GraphSAGE model can capture cross-time relationships between the target and the neighboring wells and generate promising prediction time series for the target wells, even if they are newly drilled wells.
- The proposed approach is validated and tested using the field data from 2,240 Montney shale gas wells, including formation properties, hydraulic fracture parameters, production history, and operational data. The algorithm aggregates the first-hop information to the target node for each timestep. The encoder-decoder (ED) architecture is used to generate forecasts for the subsequent 3-year production rate by using the 1-year production history of the wells. The trained model enables the evaluation of production predictions for newly developed wells at any location. We evaluate the model’s performance using P10, P50, and P90 of the test data set’s root mean square error (RMSE). Our method preserves the topological characteristics of wells and generalizes the prediction to unseen nodes while significantly reducing training complexity, making it applicable to larger data sets. By incorporating information from adjacent wells and integrating ST data, our ST-GraphSAGE model outperforms the traditional GRU-ED model and shows enhanced interpretability.">
+        <tr id="Climaate prediction plays a vital role in various sectors, including agriculture, disaster management, and urban planning. Traditional methods for climate forecasting often rely on complex physical models, which require substantial computational resources and may not accurately capture local weather patterns. This study explores the potential of Long Short-Term Memory (LSTM) networks, a type of recurrent neural network, for predicting daily climate variables such as temperature, precipitation, and humidity. Utilizing historical climate data from the city of Delhi, we developed an LSTM model to forecast short-term climate trends. The model consists of two LSTM layers followed by three Dense layers and is compiled with the Adam optimizer, mean squared error loss, and mean absolute error as a metric. Our results demonstrate the model's capability to capture temporal dependencies in climate data, achieving a satisfactory level of accuracy in temperature forecasting. This research underscores the potential of machine learning techniques, particularly LSTM networks, in enhancing climate prediction and contributing to more informed decision-making in weather-sensitive sectors.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/3acb14c12dea5fe005f993df58cb0487b23127f2" target='_blank'>
-              Shale Gas Production Forecasting with Well Interference Based on Spatial-Temporal Graph Convolutional Network
+          <td><a href="https://www.semanticscholar.org/paper/3b6d06cad165e6e886fa69a86af54e02218c3b53" target='_blank'>
+              Prediction of Daily Climate Using Long Short-Term Memory (LSTM) Model
               </a>
             </td>
           <td>
-            Ziming Xu, Juliana Y. Leung
+            Jinxin Xu, Zhuoyue Wang, Xinjin Li, Zichao Li, Zhenglin Li
           </td>
-          <td>2024-07-01</td>
-          <td>SPE Journal</td>
+          <td>2024-07-12</td>
+          <td>International Journal of Innovative Science and Research Technology (IJISRT)</td>
+          <td>2</td>
+          <td>2</td>
+        </tr>
+
+        <tr id="Out-of-stock prediction refers to the activity of forecasting the time when a product will not be available for purchase because of an inventory deficiency. Due to difficulties, out-of-stock forecasting models now face certain challenges. Incorrect demand forecasting may result in a lack or excess of goods in stock, a factor that affects client satisfaction and the profitability of companies. Accordingly, the new approach BCHO-TCN LightGBM, which is based on Buzzard Coney Hawk Optimization with a deep temporal convolutional neural network and the Light Gradient-Boosting Machine framework, is developed to deal with all challenges in the existing models in the field of out-of-stock prediction. The role that BCHO plays in the LightGBM-based deep temporal CNNis rooted in modifying the classifier to improve both accuracy and speed. Integrating BCHO into the model training process allows us to optimize and adjust the hyperparameters and the weights of the CNN linked with the temporal DNN, which, in turn, makes the model perform better in the extraction of temporal features from time-series data. This optimization strategy, which derives from the cooperative behaviors and evasion tactics of BCHO, is a powerful source of information for the computational optimization agent. This leads to a faster convergence of the model towards optimal solutions and therefore improves the overall accuracy and predictive abilities of the temporal CNN with the LightGBM algorithm. The results indicate that when using data from Amazon India’s product listings, the model shows a high degree of accuracy, as well as excellent net present value (NPV), present discounted value (PDV), and threat scores, with values reaching 94.52%, 95.16%, 94.81%, and 95.76%, respectively. Likewise, in a k-fold 10 scenario, the model achieves values of 94.81%, 95.60%, 96.28%, and 95.86% for the same metrics.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/96cb7b1001e9b5ba05e22ee7aaa6f6de94c16dcd" target='_blank'>
+              Out-of-Stock Prediction Model Using Buzzard Coney Hawk Optimization-Based LightGBM-Enabled Deep Temporal Convolutional Neural Network
+              </a>
+            </td>
+          <td>
+            Ahmed Elghadghad, A. Alzubi, Kolawole Iyiola
+          </td>
+          <td>2024-07-05</td>
+          <td>Applied Sciences</td>
           <td>0</td>
-          <td>1</td>
+          <td>4</td>
         </tr>
 
-        <tr id="User interests can be viewed over different time scales, mainly including stable long-term preferences and changing short-term intentions, and their combination facilitates the comprehensive sequential recommendation. However, existing work that focuses on different time scales of user modeling has ignored the negative effects of different time-scale noise, which hinders capturing actual user interests and cannot be resolved by conventional sequential denoising methods. In this paper, we propose a Long- and Short-term Interest Denoising Network (LSIDN), which employs different encoders and tailored denoising strategies to extract long- and short-term interests, respectively, achieving both comprehensive and robust user modeling. Specifically, we employ a session-level interest extraction and evolution strategy to avoid introducing inter-session behavioral noise into long-term interest modeling; we also adopt contrastive learning equipped with a homogeneous exchanging augmentation to alleviate the impact of unintentional behavioral noise on short-term interest modeling. Results of experiments on two public datasets show that LSIDN consistently outperforms state-of-the-art models and achieves significant robustness.">
+        <tr id="This paper presents a novel neuro-fuzzy model, termed fuzzy recurrent stochastic configuration networks (F-RSCNs), for industrial data analytics. Unlike the original recurrent stochastic configuration network (RSCN), the proposed F-RSCN is constructed by multiple sub-reservoirs, and each sub-reservoir is associated with a Takagi-Sugeno-Kang (TSK) fuzzy rule. Through this hybrid framework, first, the interpretability of the model is enhanced by incorporating fuzzy reasoning to embed the prior knowledge into the network. Then, the parameters of the neuro-fuzzy model are determined by the recurrent stochastic configuration (RSC) algorithm. This scheme not only ensures the universal approximation property and fast learning speed of the built model but also overcomes uncertain problems, such as unknown dynamic orders, arbitrary structure determination, and the sensitivity of learning parameters in modelling nonlinear dynamics. Finally, an online update of the output weights is performed using the projection algorithm, and the convergence analysis of the learning parameters is given. By integrating TSK fuzzy inference systems into RSCNs, F-RSCNs have strong fuzzy inference capability and can achieve sound performance for both learning and generalization. Comprehensive experiments show that the proposed F-RSCNs outperform other classical neuro-fuzzy and non-fuzzy models, demonstrating great potential for modelling complex industrial systems.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/a7e09202c47cdded6de935dcde3e9dc2bbfedd3d" target='_blank'>
-              Denoising Long- and Short-term Interests for Sequential Recommendation
+          <td><a href="https://www.semanticscholar.org/paper/011103f067ff8221c76b025cca9c174b3d93244b" target='_blank'>
+              Fuzzy Recurrent Stochastic Configuration Networks for Industrial Data Analytics
               </a>
             </td>
           <td>
-            Xinyu Zhang, Beibei Li, Beihong Jin
+            Dianhui Wang, Gang Dang
           </td>
-          <td>2024-07-20</td>
-          <td>DBLP, ArXiv</td>
+          <td>2024-07-06</td>
+          <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
+          <td>1</td>
         </tr>
 
-        <tr id="None">
+        <tr id="PurposeTo optimize train operations, dispatchers currently rely on experience for quick adjustments when delays occur. However, delay predictions often involve imprecise shifts based on known delay times. Real-time and accurate train delay predictions, facilitated by data-driven neural network models, can significantly reduce dispatcher stress and improve adjustment plans. Leveraging current train operation data, these models enable swift and precise predictions, addressing challenges posed by train delays in high-speed rail networks during unforeseen events.Design/methodology/approachThis paper proposes CBLA-net, a neural network architecture for predicting late arrival times. It combines CNN, Bi-LSTM, and attention mechanisms to extract features, handle time series data, and enhance information utilization. Trained on operational data from the Beijing-Tianjin line, it predicts the late arrival time of a target train at the next station using multidimensional input data from the target and preceding trains.FindingsThis study evaluates our model's predictive performance using two data approaches: one considering full data and another focusing only on late arrivals. Results show precise and rapid predictions. Training with full data achieves a MAE of approximately 0.54 minutes and a RMSE of 0.65 minutes, surpassing the model trained solely on delay data (MAE: is about 1.02 min, RMSE: is about 1.52 min). Despite superior overall performance with full data, the model excels at predicting delays exceeding 15 minutes when trained exclusively on late arrivals. For enhanced adaptability to real-world train operations, training with full data is recommended.Originality/valueThis paper introduces a novel neural network model, CBLA-net, for predicting train delay times. It innovatively compares and analyzes the model's performance using both full data and delay data formats. Additionally, the evaluation of the network's predictive capabilities considers different scenarios, providing a comprehensive demonstration of the model's predictive performance.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/27f9fcb6735817e02fa4201e2f161c1213de1d4e" target='_blank'>
-              An adaptive composite time series forecasting model for short-term traffic flow
+          <td><a href="https://www.semanticscholar.org/paper/e57a492ae484333d79b26e0ab06d19a0ae256575" target='_blank'>
+              Short-term train arrival delay prediction: a data-driven approach
               </a>
             </td>
           <td>
-            Qitan Shao, Xinglin Piao, Xiangyu Yao, Yuqiu Kong, Yongli Hu, Baocai Yin, Yong Zhang
+            Qingyun Fu, Shuxin Ding, Tao Zhang, Rongsheng Wang, Ping Hu, Cunlai Pu
           </td>
-          <td>2024-08-03</td>
-          <td>Journal of Big Data</td>
+          <td>2024-07-02</td>
+          <td>Railway Sciences</td>
           <td>0</td>
-          <td>9</td>
+          <td>14</td>
         </tr>
 
-        <tr id="Time series data is fundamentally important for describing many critical domains such as healthcare, finance, and climate, where explainable models are necessary for safe automated decision-making. To develop eXplainable AI (XAI) in these domains therefore implies explaining salient information in the time series. Current methods for obtaining saliency maps assumes localized information in the raw input space. In this paper, we argue that the salient information of a number of time series is more likely to be localized in the frequency domain. We propose FreqRISE, which uses masking based methods to produce explanations in the frequency and time-frequency domain, which shows the best performance across a number of tasks.">
+        <tr id="This paper proposes a deep recurrent neural network (DRNN) approach to model the one-hour-ahead wind speed forecasting by using various meteorological sensory data from the North Wyke farm platform (NWFP). To refine model input, mutual information analysis is applied to eliminate irrelevant sensory data. The DRNN architecture employs three recurrent layers Long-Short Term Memory (LSTM), Gated Recurrent Unit (GRU), and simple Recurrent Neural Network (RNN) to capture temporal relationships. The proposed networks are tested using real-life, one-year data from the NWFP. The results showed a strong correlation between the actual and predicted wind speed for LSTM, GRU, and RNN layers-based DRNN, however, simple RNN slightly outperformed the other two recurrent layers. The distribution of the network errors over the year is also analyzed. Although the observed meteorological data between the years was from different distributions, the proposed network generalized well even though these data were altered due to global warming.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/96f14090fbcfee008626ce8a8d563732fe1519ce" target='_blank'>
-              Explaining time series models using frequency masking
+          <td><a href="https://www.semanticscholar.org/paper/85208f740e1c9925156ec820fb1175b1cb13df77" target='_blank'>
+              Wind Speed Prediction Using Deep Recurrent Neural Networks and Farm Platform Features for One-Hour-Ahead Forecast
               </a>
             </td>
           <td>
-            Thea Brusch, Kristoffer Wickstrøm, Mikkel N. Schmidt, T. S. Alstrøm, Robert Jenssen
+            Emre Özbilge, Yonal Kırsal
           </td>
-          <td>2024-06-19</td>
-          <td>ArXiv</td>
+          <td>2024-06-27</td>
+          <td>Çukurova Üniversitesi Mühendislik Fakültesi Dergisi</td>
           <td>0</td>
-          <td>12</td>
+          <td>9</td>
         </tr>
 
-        <tr id="In the rapidly evolving Next-Generation Networking (NGN) era, the adoption of zero-trust architectures has become increasingly crucial to protect security. However, provisioning zero-trust services in NGNs poses significant challenges, primarily due to the environmental complexity and dynamics. Motivated by these challenges, this paper explores efficient zero-trust service provisioning using hierarchical micro-segmentations. Specifically, we model zero-trust networks via hierarchical graphs, thereby jointly considering the resource- and trust-level features to optimize service efficiency. We organize such zero-trust networks through micro-segmentations, which support granular zero-trust policies efficiently. To generate the optimal micro-segmentation, we present the Large Language Model-Enhanced Graph Diffusion (LEGD) algorithm, which leverages the diffusion process to realize a high-quality generation paradigm. Additionally, we utilize policy boosting and Large Language Models (LLM) to enable LEGD to optimize the generation policy and understand complicated graphical features. Moreover, realizing the unique trustworthiness updates or service upgrades in zero-trust NGN, we further present LEGD-Adaptive Maintenance (LEGD-AM), providing an adaptive way to perform task-oriented fine-tuning on LEGD. Extensive experiments demonstrate that the proposed LEGD achieves 90% higher efficiency in provisioning services compared with other baselines. Moreover, the LEGD-AM can reduce the service outage time by over 50%.">
+        <tr id="The Path-dependent Neural Jump ODE (PD-NJ-ODE) is a model for online prediction of generic (possibly non-Markovian) stochastic processes with irregular (in time) and potentially incomplete (with respect to coordinates) observations. It is a model for which convergence to the $L^2$-optimal predictor, which is given by the conditional expectation, is established theoretically. Thereby, the training of the model is solely based on a dataset of realizations of the underlying stochastic process, without the need of knowledge of the law of the process. In the case where the underlying process is deterministic, the conditional expectation coincides with the process itself. Therefore, this framework can equivalently be used to learn the dynamics of ODE or PDE systems solely from realizations of the dynamical system with different initial conditions. We showcase the potential of our method by applying it to the chaotic system of a double pendulum. When training the standard PD-NJ-ODE method, we see that the prediction starts to diverge from the true path after about half of the evaluation time. In this work we enhance the model with two novel ideas, which independently of each other improve the performance of our modelling setup. The resulting dynamics match the true dynamics of the chaotic system very closely. The same enhancements can be used to provably enable the PD-NJ-ODE to learn long-term predictions for general stochastic datasets, where the standard model fails. This is verified in several experiments.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/9c8c139f33667170dc0fa673b2932966b3d4af49" target='_blank'>
-              Hierarchical Micro-Segmentations for Zero-Trust Services via Large Language Model (LLM)-enhanced Graph Diffusion
+          <td><a href="https://www.semanticscholar.org/paper/ba851d147a33cf0c6fcf639b5d4990df283a0b23" target='_blank'>
+              Learning Chaotic Systems and Long-Term Predictions with Neural Jump ODEs
               </a>
             </td>
           <td>
-            Yinqiu Liu, Guangyuan Liu, Hongyang Du, D. Niyato, Jiawen Kang, Zehui Xiong, Dong In Kim, X. Shen
+            F. Krach, Josef Teichmann
           </td>
-          <td>2024-06-20</td>
+          <td>2024-07-26</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>112</td>
+          <td>13</td>
         </tr>
 
-        <tr id="Macroeconomic data are crucial for monitoring countries' performance and driving policy. However, traditional data acquisition processes are slow, subject to delays, and performed at a low frequency. We address this 'ragged-edge' problem with a two-step framework. The first step is a supervised learning model predicting observed low-frequency figures. We propose a neural-network-based nowcasting model that exploits mixed-frequency, high-dimensional data. The second step uses the elasticities derived from the previous step to interpolate unobserved high-frequency figures. We apply our method to nowcast countries' yearly research and development (R&D) expenditure series. These series are collected through infrequent surveys, making them ideal candidates for this task. We exploit a range of predictors, chiefly Internet search volume data, and document the relevance of these data in improving out-of-sample predictions. Furthermore, we leverage the high frequency of our data to derive monthly estimates of R&D expenditures, which are currently unobserved. We compare our results with those obtained from the classical regression-based and the sparse temporal disaggregation methods. Finally, we validate our results by reporting a strong correlation with monthly R&D employment data.">
+        <tr id="This paper explores the prediction of the dynamics of piecewise smooth maps using various deep learning models. We have shown various novel ways of predicting the dynamics of piecewise smooth maps using deep learning models. Moreover, we have used machine learning models such as Decision Tree Classifier, Logistic Regression, K-Nearest Neighbor, Random Forest, and Support Vector Machine for predicting the border collision bifurcation in the 1D normal form map and the 1D tent map. Further, we classified the regular and chaotic behaviour of the 1D tent map and the 2D Lozi map using deep learning models like Convolutional Neural Network (CNN), ResNet50, and ConvLSTM via cobweb diagram and phase portraits. We also classified the chaotic and hyperchaotic behaviour of the 3D piecewise smooth map using deep learning models such as the Feed Forward Neural Network (FNN), Long Short-Term Memory (LSTM), and Recurrent Neural Network (RNN). Finally, deep learning models such as Long Short-Term Memory (LSTM) and Recurrent Neural Network (RNN) are used for reconstructing the two parametric charts of 2D border collision bifurcation normal form map.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/755d4e35574496bb86e54a9124bcf609f8663ce7" target='_blank'>
-              Nowcasting R&D Expenditures: A Machine Learning Approach
+          <td><a href="https://www.semanticscholar.org/paper/aac95c6cb783f8093374db2d5a3d6f429f49bbfd" target='_blank'>
+              Deep Learning for Prediction and Classifying the Dynamical behaviour of Piecewise Smooth Maps
               </a>
             </td>
           <td>
-            Atin Aboutorabi, Gaétan de Rassenfosse
+            S. VismayaV, Bharath V Nair, S. S. Muni
           </td>
-          <td>2024-07-16</td>
+          <td>2024-06-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>22</td>
+          <td>10</td>
         </tr>
 
-        <tr id="In the era of data-intensive edge computing, the orchestration of Data Distributed Inferencing (DDI) tasks poses a formidable challenge, demanding real-time adaptability to varying network conditions and compute resources. This study introduces an innovative approach to address this challenge, leveraging Gradient Boosting Regression (GBR) as the core predictive modeling technique. The primary objective is to estimate inferencing time based on crucial factors, including bandwidth, compute device type, and the number of compute nodes, allowing for dynamic task placement and optimization in a DDI environment. Our model employs an online learning framework, continuously updating itself as new data streams in, enabling it to swiftly adapt to changing conditions and consistently deliver accurate inferencing time predictions. This research marks a significant step forward in enhancing the efficiency and performance of DDI systems, with implications for real-world applications across various domains, including IoT, edge computing, and distributed machine learning.">
+        <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/de22a295e7e50639f555b3c0a46f0ba9fc9c115b" target='_blank'>
-              Adaptive predictive modeling with online learning: addressing data drift challenges in historical data for distributed inferencing
+          <td><a href="https://www.semanticscholar.org/paper/d1bae805ccd830107d647947cbe64aa0294f9638" target='_blank'>
+              A Kernel Attention-based Transformer Model for Survival Prediction of Heart Disease Patients.
               </a>
             </td>
           <td>
-            Cleon Anderson, Scott E. Brown, David Harman, M. Dwyer
+            Palak Kaushal, Shailendra Singh, Rajesh Vijayvergiya
           </td>
-          <td>2024-06-07</td>
-          <td>None</td>
+          <td>2024-08-05</td>
+          <td>Journal of cardiovascular translational research</td>
           <td>0</td>
-          <td>3</td>
+          <td>1</td>
         </tr>
 
-        <tr id="aeon is a unified Python 3 library for all machine learning tasks involving time series. The package contains modules for time series forecasting, classification, extrinsic regression and clustering, as well as a variety of utilities, transformations and distance measures designed for time series data. aeon also has a number of experimental modules for tasks such as anomaly detection, similarity search and segmentation. aeon follows the scikit-learn API as much as possible to help new users and enable easy integration of aeon estimators with useful tools such as model selection and pipelines. It provides a broad library of time series algorithms, including efficient implementations of the very latest advances in research. Using a system of optional dependencies, aeon integrates a wide variety of packages into a single interface while keeping the core framework with minimal dependencies. The package is distributed under the 3-Clause BSD license and is available at https://github.com/ aeon-toolkit/aeon. This version was submitted to the JMLR journal on 02 Nov 2023 for v0.5.0 of aeon. At the time of this preprint aeon has released v0.9.0, and has had substantial changes.">
+        <tr id="Graph Neural Networks (GNNs) excel in diverse tasks, yet their applications in high-stakes domains are often hampered by unreliable predictions. Although numerous uncertainty quantification methods have been proposed to address this limitation, they often lack \textit{rigorous} uncertainty estimates. This work makes the first attempt to introduce a distribution-free and model-agnostic uncertainty quantification approach to construct a predictive interval with a statistical guarantee for GNN-based link prediction. We term it as \textit{conformalized link prediction.} Our approach builds upon conformal prediction (CP), a framework that promises to construct statistically robust prediction sets or intervals. We first theoretically and empirically establish a permutation invariance condition for the application of CP in link prediction tasks, along with an exact test-time coverage. Leveraging the important structural information in graphs, we then identify a novel and crucial connection between a graph's adherence to the power law distribution and the efficiency of CP. This insight leads to the development of a simple yet effective sampling-based method to align the graph structure with a power law distribution prior to the standard CP procedure. Extensive experiments demonstrate that for conformalized link prediction, our approach achieves the desired marginal coverage while significantly improving the efficiency of CP compared to baseline methods.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6664110bc4fee7c79dd1928d2a37dd9222295260" target='_blank'>
-              aeon: a Python toolkit for learning from time series
+          <td><a href="https://www.semanticscholar.org/paper/046f6abdbf63fbb80d831102e7889c6801ad3545" target='_blank'>
+              Conformalized Link Prediction on Graph Neural Networks
               </a>
             </td>
           <td>
-            Matthew Middlehurst, Ali Ismail-Fawaz, Antoine Guillaume, Christopher Holder, David Guijo Rubio, Guzal Bulatova, Leonidas Tsaprounis, Lukasz Mentel, Martin Walter, Patrick Schäfer, Anthony J. Bagnall
+            Tianyi Zhao, Jian Kang, Lu Cheng
           </td>
-          <td>2024-06-20</td>
+          <td>2024-06-26</td>
           <td>ArXiv</td>
-          <td>2</td>
-          <td>8</td>
+          <td>1</td>
+          <td>1</td>
         </tr>
 
-        <tr id="The increasing rate of road accidents worldwide results not only in significant loss of life but also imposes billions financial burdens on societies. Current research in traffic crash frequency modeling and analysis has predominantly approached the problem as classification tasks, focusing mainly on learning-based classification or ensemble learning methods. These approaches often overlook the intricate relationships among the complex infrastructure, environmental, human and contextual factors related to traffic crashes and risky situations. In contrast, we initially propose a large-scale traffic crash language dataset, named CrashEvent, summarizing 19,340 real-world crash reports and incorporating infrastructure data, environmental and traffic textual and visual information in Washington State. Leveraging this rich dataset, we further formulate the crash event feature learning as a novel text reasoning problem and further fine-tune various large language models (LLMs) to predict detailed accident outcomes, such as crash types, severity and number of injuries, based on contextual and environmental factors. The proposed model, CrashLLM, distinguishes itself from existing solutions by leveraging the inherent text reasoning capabilities of LLMs to parse and learn from complex, unstructured data, thereby enabling a more nuanced analysis of contributing factors. Our experiments results shows that our LLM-based approach not only predicts the severity of accidents but also classifies different types of accidents and predicts injury outcomes, all with averaged F1 score boosted from 34.9% to 53.8%. Furthermore, CrashLLM can provide valuable insights for numerous open-world what-if situational-awareness traffic safety analyses with learned reasoning features, which existing models cannot offer. We make our benchmark, datasets, and model public available for further exploration.">
+        <tr id="End-of-life vehicle (ELV) forecasting constitutes a crucial aspect of sustainable waste management and resource allocation strategies. While the existing literature predominantly employs time-series forecasting and machine learning methodologies, a dearth of studies leveraging deep learning techniques, particularly Long Short-Term Memory (LSTM) networks, is evident. Moreover, the focus on localized contexts within national or municipal boundaries overlooks the imperative of addressing ELV generation dynamics at an international scale, particularly within entities such as the EU-27. Furthermore, the absence of methodologies to reconcile missing historical data presents a significant limitation in forecasting accuracy. In response to these critical gaps, this study proposes a pioneering framework that integrates grey systems theory (GST)-based backcasting with LSTM-based deep learning methodologies for forecasting ELV generation within the EU until 2040. By introducing this innovative approach, this study not only extends the methodological repertoire within the field but also enhances the applicability of findings to supranational regulatory frameworks. Moreover, the incorporation of backcasting techniques addresses data limitations, ensuring more robust and accurate forecasting outcomes. The results indicate an anticipated decline in the recovery and recycling of ELVs, underscoring the urgent need for intervention by policymakers and stakeholders in the waste management sector. Through these contributions, this study enriches our understanding of ELV generation dynamics and facilitates informed decision-making processes in environmental sustainability and resource management domains.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/97b78591f4a2da17cc4a28e40f7388bdae45fb86" target='_blank'>
-              Learning Traffic Crashes as Language: Datasets, Benchmarks, and What-if Causal Analyses
+          <td><a href="https://www.semanticscholar.org/paper/f77631c5d497447eda2ed5efa6e1eb40e0a25f2e" target='_blank'>
+              Forecasting End-of-Life Vehicle Generation in the EU-27: A Hybrid LSTM-Based Forecasting and Grey Systems Theory-Based Backcasting Approach
               </a>
             </td>
           <td>
-            Zhiwen Fan, Pu Wang, Yang Zhao, Yibo Zhao, B. Ivanovic, Zhangyang Wang, Marco Pavone, H. Yang
+            Selman Karagoz
           </td>
-          <td>2024-06-16</td>
-          <td>ArXiv</td>
+          <td>2024-07-02</td>
+          <td>Pollutants</td>
+          <td>0</td>
           <td>0</td>
-          <td>20</td>
         </tr>
 
-        <tr id="The Transformer model has shown leading performance in time series forecasting. Nevertheless, in some complex scenarios, it tends to learn low-frequency features in the data and overlook high-frequency features, showing a frequency bias. This bias prevents the model from accurately capturing important high-frequency data features. In this paper, we undertook empirical analyses to understand this bias and discovered that frequency bias results from the model disproportionately focusing on frequency features with higher energy. Based on our analysis, we formulate this bias and propose Fredformer, a Transformer-based framework designed to mitigate frequency bias by learning features equally across different frequency bands. This approach prevents the model from overlooking lower amplitude features important for accurate forecasting. Extensive experiments show the effectiveness of our proposed approach, which can outperform other baselines in different real-world time-series datasets. Furthermore, we introduce a lightweight variant of the Fredformer with an attention matrix approximation, which achieves comparable performance but with much fewer parameters and lower computation costs. The code is available at: https://github.com/chenzRG/Fredformer">
+        <tr id="In this paper we introduce a method for significantly improving the signal to noise ratio in financial data. The approach relies on combining a target variable with different context variables and use auto-encoders (AEs) to learn reconstructions of the combined inputs. The objective is to obtain agreement among pairs of AEs which are trained on related but different inputs and for which they are forced to find common ground. The training process is set up as a"conversation"where the models take turns at producing a prediction (speaking) and reconciling own predictions with the output of the other AE (listening), until an agreement is reached. This leads to a new way of constraining the complexity of the data representation generated by the AE. Unlike standard regularization whose strength needs to be decided by the designer, the proposed mutual regularization uses the partner network to detect and amend the lack of generality of the learned representation of the data. The integration of alternative perspectives enhances the de-noising capacity of a single AE and allows us to discover new regularities in financial time-series which can be converted into profitable trading strategies.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/937461ab8d8ec3b550a31ce461e668fc910bf25e" target='_blank'>
-              Fredformer: Frequency Debiased Transformer for Time Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/88138df593fb8ebbfe08e9779a37bd6bdc468272" target='_blank'>
+              Strong denoising of financial time-series
               </a>
             </td>
           <td>
-            Xihao Piao, Zheng Chen, Taichi Murayama, Yasuko Matsubara, Yasushi Sakurai
+            Matthias J. Feiler
           </td>
-          <td>2024-06-13</td>
+          <td>2024-08-11</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>13</td>
+          <td>0</td>
         </tr>
 
-        <tr id="Long-term time series forecasting is a long-standing challenge in various applications. A central issue in time series forecasting is that methods should expressively capture long-term dependency. Furthermore, time series forecasting methods should be flexible when applied to different scenarios. Although Fourier analysis offers an alternative to effectively capture reusable and periodic patterns to achieve long-term forecasting in different scenarios, existing methods often assume high-frequency components represent noise and should be discarded in time series forecasting. However, we conduct a series of motivation experiments and discover that the role of certain frequencies varies depending on the scenarios. In some scenarios, removing high-frequency components from the original time series can improve the forecasting performance, while in others scenarios, removing them is harmful to forecasting performance. Therefore, it is necessary to treat the frequencies differently according to specific scenarios. To achieve this, we first reformulate the time series forecasting problem as learning a transfer function of each frequency in the Fourier domain. Further, we design Frequency Dynamic Fusion (FreDF), which individually predicts each Fourier component, and dynamically fuses the output of different frequencies. Moreover, we provide a novel insight into the generalization ability of time series forecasting and propose the generalization bound of time series forecasting. Then we prove FreDF has a lower bound, indicating that FreDF has better generalization ability. Extensive experiments conducted on multiple benchmark datasets and ablation studies demonstrate the effectiveness of FreDF.">
+        <tr id="To predict the future movements of stock markets, numerous studies concentrate on daily data and employ various machine learning (ML) models as benchmarks that often vary and lack standardization across different research works. This paper tries to solve the problem from a fresh standpoint by aiming to predict the weekly movements, and introducing a novel benchmark of random traders. This benchmark is independent of any ML model, thus making it more objective and potentially serving as a commonly recognized standard. During training process, apart from the basic features such as technical indicators, scaling laws and directional changes are introduced as additional features, furthermore, the training datasets are also adjusted by assigning varying weights to different samples, the weighting approach allows the models to emphasize specific samples. On back-testing, several trained models show good performance, with the multi-layer perception (MLP) demonstrating stability and robustness across extensive and comprehensive data that include upward, downward and cyclic trends. The unique perspective of this work that focuses on weekly movements, incorporates new features and creates an objective benchmark, contributes to the existing literature on stock market prediction.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/180860f60e6655bebc9757b695b4fbc18a0c39ee" target='_blank'>
-              Not All Frequencies Are Created Equal:Towards a Dynamic Fusion of Frequencies in Time-Series Forecasting
+          <td><a href="https://www.semanticscholar.org/paper/7a0bb044a3d1045d39d6d28a519d37fb7ac7b36d" target='_blank'>
+              Machine learning in weekly movement prediction
               </a>
             </td>
           <td>
-            Xingyu Zhang, Siyu Zhao, Zeen Song, Huijie Guo, Jianqi Zhang, Changwen Zheng, Wenwen Qiang
+            Han Gui
           </td>
-          <td>2024-07-17</td>
+          <td>2024-07-13</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>8</td>
+          <td>0</td>
         </tr>
 
     </tbody>
@@ -4906,7 +4733,7 @@ <h3 id="recommended_articles">Recommended articles on <i>Time-series forecasting
 
   var trace1 = {
     x: ['2023', '2024'],
-    y: [0, 42],
+    y: [0, 13],
     name: 'Num of citations',
     yaxis: 'y1',
     type: 'scatter'
diff --git a/site/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378/index.html b/site/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378/index.html
index 94d13230..f729d0a4 100644
--- a/site/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378/index.html
+++ b/site/recommendations/06a0ba437d41a7c82c08a9636a4438c1b5031378/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:07 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:28 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -485,7 +485,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-03-15</td>
           <td>PLOS Computational Biology</td>
           <td>3</td>
-          <td>54</td>
+          <td>55</td>
         </tr>
 
         <tr id="High-throughput data acquisition in synthetic biology leads to an abundance of data that need to be processed and aggregated into useful biological models. Building dynamical models based on this wealth of data is of paramount importance to understand and optimize designs of synthetic biology constructs. However, building models manually for each data set is inconvenient and might become infeasible for highly complex synthetic systems. In this paper, we present state-of-the-art system identification techniques and combine them with chemical reaction network theory (CRNT) to generate dynamic models automatically. On the system identification side, Sparse Bayesian Learning offers methods to learn from data the sparsest set of dictionary functions necessary to capture the dynamics of the system into ODE models; on the CRNT side, building on such sparse ODE models, all possible network structures within a given parameter uncertainty region can be computed. Additionally, the system identification process can be complemented with constraints on the parameters to, for example, enforce stability or non-negativity-thus offering relevant physical constraints over the possible network structures. In this way, the wealth of data can be translated into biologically relevant network structures, which then steers the data acquisition, thereby providing a vital step for closed-loop system identification.">
@@ -497,7 +497,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2018-09-24</td>
           <td>2018 IEEE Conference on Decision and Control (CDC)</td>
           <td>3</td>
-          <td>34</td>
+          <td>35</td>
         </tr>
 
         <tr id="Reconstruction of biochemical reaction networks (BRN) and genetic regulatory networks (GRN) in particular is a central topic in systems biology which raises crucial theoretical challenges in system identification. Nonlinear Ordinary Differential Equations (ODEs) that involve polynomial and rational functions are typically used to model biochemical reaction networks. Such nonlinear models make the problem of determining the connectivity of biochemical networks from time-series experimental data quite difficult. In this paper, we present a network reconstruction algorithm that can deal with ODE model descriptions containing polynomial and rational functions. Rather than identifying the parameters of linear or nonlinear ODEs characterised by pre-defined equation structures, our methodology allows us to determine the nonlinear ODEs structure together with their associated parameters. To solve the network reconstruction problem, we cast it as a compressive sensing (CS) problem and use sparse Bayesian learning (SBL) algorithms as a computationally efficient and robust way to obtain its solution.">
@@ -509,7 +509,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2012-05-08</td>
           <td>2012 IEEE 51st IEEE Conference on Decision and Control (CDC)</td>
           <td>33</td>
-          <td>34</td>
+          <td>35</td>
         </tr>
 
         <tr id="None">
@@ -544,8 +544,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-06-01</td>
           <td>Nonlinear Dynamics</td>
-          <td>27</td>
-          <td>90</td>
+          <td>28</td>
+          <td>91</td>
         </tr>
 
         <tr id="Systems biology is a new discipline built upon the premise that an understanding of how cells and organisms carry out their functions cannot be gained by looking at cellular components in isolation. Instead, consideration of the interplay between the parts of systems is indispensable for analyzing, modeling, and predicting systems' behavior. Studying biological processes under this premise, systems biology combines experimental techniques and computational methods in order to construct predictive models. Both in building and utilizing models of biological systems, inverse problems arise at several occasions, for example, (i) when experimental time series and steady state data are used to construct biochemical reaction networks, (ii) when model parameters are identified that capture underlying mechanisms or (iii) when desired qualitative behavior such as bistability or limit cycle oscillations is engineered by proper choices of parameter combinations. In this paper we review principles of the modeling process in systems biology and illustrate the ill-posedness and regularization of parameter identification problems in that context. Furthermore, we discuss the methodology of qualitative inverse problems and demonstrate how sparsity enforcing regularization allows the determination of key reaction mechanisms underlying the qualitative behavior.">
diff --git a/site/recommendations/0acd117521ef5aafb09fed02ab415523b330b058/index.html b/site/recommendations/0acd117521ef5aafb09fed02ab415523b330b058/index.html
index e7c80886..1231c0f3 100644
--- a/site/recommendations/0acd117521ef5aafb09fed02ab415523b330b058/index.html
+++ b/site/recommendations/0acd117521ef5aafb09fed02ab415523b330b058/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:11 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:36 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-11-01</td>
           <td>Chaos</td>
-          <td>2</td>
+          <td>3</td>
           <td>11</td>
         </tr>
 
@@ -508,8 +508,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3159</td>
-          <td>63</td>
+          <td>3190</td>
+          <td>65</td>
         </tr>
 
         <tr id="None">
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>234</td>
+          <td>238</td>
           <td>12</td>
         </tr>
 
@@ -569,7 +569,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2017-12-01</td>
           <td>2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)</td>
           <td>12</td>
-          <td>63</td>
+          <td>65</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b/index.html b/site/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b/index.html
index c62e1846..6248cb3a 100644
--- a/site/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b/index.html
+++ b/site/recommendations/0d01d21137a5af9f04e4b16a55a0f732cb8a540b/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:44 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:04:58 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -485,7 +485,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-10-24</td>
           <td>ArXiv</td>
           <td>4</td>
-          <td>49</td>
+          <td>50</td>
         </tr>
 
         <tr id="Graph neural networks (GNNs) have been widely applied in multi-variate time-series forecasting (MTSF) tasks because of their capability in capturing the correlations among different time-series. These graph-based learning approaches improve the forecasting performance by discovering and understanding the underlying graph structures, which represent the data correlation. When the explicit prior graph structures are not available, most existing works cannot guarantee the sparsity of the generated graphs that make the overall model computational expensive and less interpretable. In this work, we propose a decoupled training method, which includes a graph generating module and a GNNs forecasting module. First, we use Graphical Lasso (or GraphLASSO) to directly exploit the sparsity pattern from data to build graph structures in both static and time-varying cases. Second, we fit these graph structures and the input data into a Graph Convolutional Recurrent Network (GCRN) to train a forecasting model. The experimental results on three real-world datasets show that our novel approach has competitive performance against existing state-of-the-art forecasting algorithms while providing sparse, meaningful and explainable graph structures and reducing training time by approximately 40%. Our PyTorch implementation is publicly available at https://github.com/HySonLab/GraphLASSO">
@@ -533,7 +533,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2021-09-10</td>
           <td>ArXiv</td>
           <td>12</td>
-          <td>45</td>
+          <td>46</td>
         </tr>
 
         <tr id="Multivariate time-series forecasting is a critical task for many applications, and graph time-series network is widely studied due to its capability to capture the spatial-temporal correlation simultaneously. However, most existing works focus more on learning with the explicit prior graph structure, while ignoring potential information from the implicit graph structure, yielding incomplete structure modeling. Some recent works attempts to learn the intrinsic or implicit graph structure directly, while lacking a way to combine explicit prior structure with implicit structure together. In this paper, we propose Regularized Graph Structure Learning (RGSL) model to incorporate both explicit prior structure and implicit structure together, and learn the forecasting deep networks along with the graph structure. RGSL consists of two innovative modules. First, we derive an implicit dense similarity matrix through node embedding, and learn the sparse graph structure using the Regularized Graph Generation (RGG) based on the Gumbel Softmax trick. Second, we propose a Laplacian Matrix Mixed-up Module (LM3) to fuse the explicit graph and implicit graph together. We conduct experiments on three real-word datasets. Results show that the proposed RGSL model outperforms existing graph forecasting algorithms with a notable margin, while learning meaningful graph structure simultaneously. Our code and models are made publicly available at https://github.com/alipay/RGSL.git.">
@@ -543,9 +543,9 @@ <h3 data-intro='Recommendations for the article'>
             Hongyuan Yu, Ting Li, Weichen Yu, Jianguo Li, Yan Huang, Liang Wang, A. Liu
           </td>
           <td>2022-07-01</td>
-          <td>DBLP, ArXiv</td>
+          <td>ArXiv, DBLP</td>
           <td>37</td>
-          <td>33</td>
+          <td>34</td>
         </tr>
 
         <tr id="Time series forecasting is an extensively studied subject in statistics, economics, and computer science. Exploration of the correlation and causation among the variables in a multivariate time series shows promise in enhancing the performance of a time series model. When using deep neural networks as forecasting models, we hypothesize that exploiting the pairwise information among multiple (multivariate) time series also improves their forecast. If an explicit graph structure is known, graph neural networks (GNNs) have been demonstrated as powerful tools to exploit the structure. In this work, we propose learning the structure simultaneously with the GNN if the graph is unknown. We cast the problem as learning a probabilistic graph model through optimizing the mean performance over the graph distribution. The distribution is parameterized by a neural network so that discrete graphs can be sampled differentiably through reparameterization. Empirical evaluations show that our method is simpler, more efficient, and better performing than a recently proposed bilevel learning approach for graph structure learning, as well as a broad array of forecasting models, either deep or non-deep learning based, and graph or non-graph based.">
@@ -556,8 +556,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-01-18</td>
           <td>ArXiv</td>
-          <td>174</td>
-          <td>36</td>
+          <td>177</td>
+          <td>37</td>
         </tr>
 
         <tr id="Multi-variate time series forecasting is an important problem with a wide range of applications. Recent works model the relations between time-series as graphs and have shown that propagating information over the relation graph can improve time series forecasting. However, in many cases, relational information is not available or is noisy and reliable. Moreover, most works ignore the underlying uncertainty of time-series both for structure learning and deriving the forecasts resulting in the structure not capturing the uncertainty resulting in forecast distributions with poor uncertainty estimates. We tackle this challenge and introduce STOIC, that leverages stochastic correlations between time-series to learn underlying structure between time-series and to provide well-calibrated and accurate forecasts. Over a wide-range of benchmark datasets STOIC provides around 16% more accurate and 14% better-calibrated forecasts. STOIC also shows better adaptation to noise in data during inference and captures important and useful relational information in various benchmarks.">
diff --git a/site/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b/index.html b/site/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b/index.html
index 23ca7052..3dd2f8c8 100644
--- a/site/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b/index.html
+++ b/site/recommendations/123acfbccca0460171b6b06a4012dbb991cde55b/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:46 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:04:59 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>23</td>
+          <td>27</td>
           <td>18</td>
         </tr>
 
@@ -497,7 +497,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2024-02-04</td>
           <td>ArXiv</td>
           <td>3</td>
-          <td>65</td>
+          <td>66</td>
         </tr>
 
         <tr id="Large language models (LLMs) are being applied to time series tasks, particularly time series forecasting. However, are language models actually useful for time series? After a series of ablation studies on three recent and popular LLM-based time series forecasting methods, we find that removing the LLM component or replacing it with a basic attention layer does not degrade the forecasting results -- in most cases the results even improved. We also find that despite their significant computational cost, pretrained LLMs do no better than models trained from scratch, do not represent the sequential dependencies in time series, and do not assist in few-shot settings. Additionally, we explore time series encoders and reveal that patching and attention structures perform similarly to state-of-the-art LLM-based forecasters.">
@@ -520,8 +520,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-04</td>
           <td>ArXiv</td>
-          <td>6</td>
-          <td>65</td>
+          <td>5</td>
+          <td>66</td>
         </tr>
 
         <tr id="In this paper, we introduce TimeGPT, the first foundation model for time series, capable of generating accurate predictions for diverse datasets not seen during training. We evaluate our pre-trained model against established statistical, machine learning, and deep learning methods, demonstrating that TimeGPT zero-shot inference excels in performance, efficiency, and simplicity. Our study provides compelling evidence that insights from other domains of artificial intelligence can be effectively applied to time series analysis. We conclude that large-scale time series models offer an exciting opportunity to democratize access to precise predictions and reduce uncertainty by leveraging the capabilities of contemporary advancements in deep learning.">
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-05</td>
           <td>ArXiv</td>
-          <td>39</td>
+          <td>40</td>
           <td>1</td>
         </tr>
 
@@ -556,7 +556,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-03</td>
           <td>ArXiv</td>
-          <td>109</td>
+          <td>120</td>
           <td>9</td>
         </tr>
 
@@ -580,7 +580,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-06-19</td>
           <td>ArXiv</td>
-          <td>32</td>
+          <td>35</td>
           <td>8</td>
         </tr>
 
diff --git a/site/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277/index.html b/site/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277/index.html
index a5fd90ab..014594c2 100644
--- a/site/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277/index.html
+++ b/site/recommendations/16f01c1b3ddd0b2abd5ddfe4fdb3f74767607277/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:49 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:02 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -508,7 +508,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-09-20</td>
           <td>IEEE Transactions on Knowledge and Data Engineering</td>
-          <td>55</td>
+          <td>58</td>
           <td>17</td>
         </tr>
 
@@ -580,7 +580,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-14</td>
           <td>ArXiv</td>
-          <td>44</td>
+          <td>48</td>
           <td>14</td>
         </tr>
 
@@ -593,7 +593,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2024-02-04</td>
           <td>ArXiv</td>
           <td>3</td>
-          <td>65</td>
+          <td>66</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f/index.html b/site/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f/index.html
index 3952dc0e..b88c0836 100644
--- a/site/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f/index.html
+++ b/site/recommendations/1df04f33a8ef313cc2067147dbb79c3ca7c5c99f/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:47 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:00 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -496,8 +496,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-13</td>
           <td>ArXiv</td>
-          <td>30</td>
-          <td>8</td>
+          <td>32</td>
+          <td>9</td>
         </tr>
 
         <tr id="Message-passing graph neural networks (GNNs), while excelling at capturing local relationships, often struggle with long-range dependencies on graphs. Conversely, graph transformers (GTs) enable information exchange between all nodes but oversimplify the graph structure by treating them as a set of fixed-length vectors. This work proposes a novel architecture, NeuralWalker, that overcomes the limitations of both methods by combining random walks with message passing. NeuralWalker achieves this by treating random walks as sequences, allowing for the application of recent advances in sequence models in order to capture long-range dependencies within these walks. Based on this concept, we propose a framework that offers (1) more expressive graph representations through random walk sequences, (2) the ability to utilize any sequence model for capturing long-range dependencies, and (3) the flexibility by integrating various GNN and GT architectures. Our experimental evaluations demonstrate that NeuralWalker achieves significant performance improvements on 19 graph and node benchmark datasets, notably outperforming existing methods by up to 13% on the PascalVoc-SP and COCO-SP datasets. Code is available at https://github.com/BorgwardtLab/NeuralWalker.">
@@ -520,8 +520,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-06-09</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>2</td>
+          <td>1</td>
+          <td>3</td>
         </tr>
 
         <tr id="Graph representation learning (GRL) is fundamental in multi-graph applications like molecular property prediction. Graph neural networks (GNNs) have emerged as a popular method for GRL. However, existing GRL methods primarily focus on designing GNN models with enhanced expressiveness while overlooking the memory efficiency of algorithms during training. The memory inefficiency problem is caused by a contextual constraint imposed on node representations, which requires each node to be context-dependent on its input graph. In this paper, we propose a novel method, called context sketching (COS), for memory-efficient graph representation learning in multi-graph scenarios. We first formally define the contextual constraint based on the enclosed $\infty-$hop subgraphs of nodes. Subsequently, we propose to relax the original contextual constraint by requiring each node to be context-dependent on its enclosed $k-$hop subgraph $(k \ll \infty)$ which is a contextual sketch of the enclosed $\infty$-hop subgraph. Lastly, we prove that COS constructs an optimal solution to a memory-related objective associated with graph coarsening. Experiments on four widely used benchmark datasets demonstrate that COS can reduce the memory footprint of baselines by a large margin with almost no accuracy loss.">
@@ -545,7 +545,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2024-06-17</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>6</td>
+          <td>7</td>
         </tr>
 
         <tr id="The Transformer architecture has achieved remarkable success in a number of domains including natural language processing and computer vision. However, when it comes to graph-structured data, transformers have not achieved competitive performance, especially on large graphs. In this paper, we identify the main deficiencies of current graph transformers:(1) Existing node sampling strategies in Graph Transformers are agnostic to the graph characteristics and the training process. (2) Most sampling strategies only focus on local neighbors and neglect the long-range dependencies in the graph. We conduct experimental investigations on synthetic datasets to show that existing sampling strategies are sub-optimal. To tackle the aforementioned problems, we formulate the optimization strategies of node sampling in Graph Transformer as an adversary bandit problem, where the rewards are related to the attention weights and can vary in the training procedure. Meanwhile, we propose a hierarchical attention scheme with graph coarsening to capture the long-range interactions while reducing computational complexity. Finally, we conduct extensive experiments on real-world datasets to demonstrate the superiority of our method over existing graph transformers and popular GNNs.">
@@ -556,8 +556,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-10-08</td>
           <td>ArXiv</td>
-          <td>56</td>
-          <td>17</td>
+          <td>59</td>
+          <td>19</td>
         </tr>
 
         <tr id="Transformer-based models have recently shown success in representation learning on graph-structured data beyond natural language processing and computer vision. However, the success is limited to small-scale graphs due to the drawbacks of full dot-product attention on graphs such as the quadratic complexity with respect to the number of nodes and message aggregation from enormous irrelevant nodes. To address these issues, we propose Deformable Graph Transformer (DGT) that performs sparse attention via dynamically sampled relevant nodes for efficiently handling large-scale graphs with a linear complexity in the number of nodes. Specifically, our framework first constructs multiple node sequences with various criteria to consider both structural and semantic proximity. Then, combining with our learnable Katz Positional Encodings, the sparse attention is applied to the node sequences for learning node representations with a significantly reduced computational cost. Extensive experiments demonstrate that our DGT achieves state-of-the-art performance on 7 graph benchmark datasets with 2.5 - 449 times less computational cost compared to transformer-based graph models with full attention.">
@@ -569,7 +569,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-06-29</td>
           <td>ArXiv</td>
           <td>6</td>
-          <td>27</td>
+          <td>28</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68/index.html b/site/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68/index.html
index 9ff2d186..ae046141 100644
--- a/site/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68/index.html
+++ b/site/recommendations/279cd637b7e38bba1dd8915b5ce68cbcacecbe68/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:53 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:09 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -483,7 +483,7 @@ <h3 data-intro='Recommendations for the article'>
             Andreas Doerr, Christian Daniel, Martin Schiegg, D. Nguyen-Tuong, S. Schaal, Marc Toussaint, Sebastian Trimpe
           </td>
           <td>2018-01-31</td>
-          <td>DBLP, ArXiv, MAG</td>
+          <td>ArXiv, MAG, DBLP</td>
           <td>110</td>
           <td>93</td>
         </tr>
@@ -521,7 +521,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-05-26</td>
           <td>J. Mach. Learn. Res.</td>
           <td>11</td>
-          <td>49</td>
+          <td>50</td>
         </tr>
 
         <tr id="Real-world dynamical systems often consist of multiple stochastic subsystems that interact with each other. Modeling and forecasting the behavior of such dynamics are generally not easy, due to the inherent hardness in understanding the complicated interactions and evolutions of their constituents. This paper introduces the relational state-space model (R-SSM), a sequential hierarchical latent variable model that makes use of graph neural networks (GNNs) to simulate the joint state transitions of multiple correlated objects. By letting GNNs cooperate with SSM, R-SSM provides a flexible way to incorporate relational information into the modeling of multi-object dynamics. We further suggest augmenting the model with normalizing flows instantiated for vertex-indexed random variables and propose two auxiliary contrastive objectives to facilitate the learning. The utility of R-SSM is empirically evaluated on synthetic and real time series datasets.">
@@ -533,7 +533,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2020-01-13</td>
           <td>ArXiv</td>
           <td>8</td>
-          <td>56</td>
+          <td>57</td>
         </tr>
 
         <tr id="Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered sequence of static graph snapshots observed at discrete time points. Sequence models such as RNNs or Transformers have long been the predominant backbone networks for modeling such temporal graphs. Yet, despite the promising results, RNNs struggle with long-range dependencies, while transformers are burdened by quadratic computational complexity. Recently, state space models (SSMs), which are framed as discretized representations of an underlying continuous-time linear dynamical system, have garnered substantial attention and achieved breakthrough advancements in independent sequence modeling. In this work, we undertake a principled investigation that extends SSM theory to temporal graphs by integrating structural information into the online approximation objective via the adoption of a Laplacian regularization term. The emergent continuous-time system introduces novel algorithmic challenges, thereby necessitating our development of GraphSSM, a graph state space model for modeling the dynamics of temporal graphs. Extensive experimental results demonstrate the effectiveness of our GraphSSM framework across various temporal graph benchmarks.">
@@ -544,8 +544,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-06-03</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>10</td>
+          <td>1</td>
+          <td>11</td>
         </tr>
 
         <tr id="Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs) are classical models for time series, and prior works combine SSMs with deep learning layers for efficient sequence modeling. However, we find fundamental limitations with these prior approaches, proving their SSM representations cannot express autoregressive time series processes. We thus introduce SpaceTime, a new state-space time series architecture that improves all three criteria. For expressivity, we propose a new SSM parameterization based on the companion matrix -- a canonical representation for discrete-time processes -- which enables SpaceTime's SSM layers to learn desirable autoregressive processes. For long horizon forecasting, we introduce a"closed-loop"variation of the companion SSM, which enables SpaceTime to predict many future time-steps by generating its own layer-wise inputs. For efficient training and inference, we introduce an algorithm that reduces the memory and compute of a forward pass with the companion matrix. With sequence length $\ell$ and state-space size $d$, we go from $\tilde{O}(d \ell)$ na\"ively to $\tilde{O}(d + \ell)$. In experiments, our contributions lead to state-of-the-art results on extensive and diverse benchmarks, with best or second-best AUROC on 6 / 7 ECG and speech time series classification, and best MSE on 14 / 16 Informer forecasting tasks. Furthermore, we find SpaceTime (1) fits AR($p$) processes that prior deep SSMs fail on, (2) forecasts notably more accurately on longer horizons than prior state-of-the-art, and (3) speeds up training on real-world ETTh1 data by 73% and 80% relative wall-clock time over Transformers and LSTMs.">
@@ -557,7 +557,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-03-16</td>
           <td>ArXiv</td>
           <td>28</td>
-          <td>43</td>
+          <td>44</td>
         </tr>
 
         <tr id="
@@ -571,8 +571,8 @@ <h3 data-intro='Recommendations for the article'>
             R. G. Krishnan, Uri Shalit, D. Sontag
           </td>
           <td>2016-09-30</td>
-          <td>DBLP, ArXiv, MAG</td>
-          <td>424</td>
+          <td>ArXiv, MAG, DBLP</td>
+          <td>428</td>
           <td>48</td>
         </tr>
 
diff --git a/site/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196/index.html b/site/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196/index.html
index c34b76fc..97dbad3f 100644
--- a/site/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196/index.html
+++ b/site/recommendations/2b2aa13d4959073f61ad70555bc8c7da7d116196/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:08 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:29 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -556,7 +556,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-07-02</td>
           <td>ArXiv</td>
-          <td>126</td>
+          <td>129</td>
           <td>22</td>
         </tr>
 
@@ -581,7 +581,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2019-06-10</td>
           <td>J. Comput. Phys.</td>
           <td>21</td>
-          <td>18</td>
+          <td>19</td>
         </tr>
 
         <tr id="In recent years, we have witnessed a significant shift toward ever-more complex and ever-larger-scale systems in the majority of the grand societal challenges tackled in applied sciences. The need to comprehend and predict the dynamics of complex systems have spurred developments in large-scale simulations and a multitude of methods across several disciplines. The goals of understanding and prediction in complex dynamical systems, however, have been hindered by high dimensionality, complexity and chaotic behaviours. Recent advances in data-driven techniques and machine-learning approaches have revolutionized how we model and analyse complex systems. The integration of these techniques with dynamical systems theory opens up opportunities to tackle previously unattainable challenges in modelling and prediction of dynamical systems. While data-driven prediction methods have made great strides in recent years, it is still necessary to develop new techniques to improve their applicability to a wider range of complex systems in science and engineering. This focus issue shares recent developments in the field of complex dynamical systems with emphasis on data-driven, data-assisted and artificial intelligence-based discovery of dynamical systems. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.">
@@ -592,7 +592,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-06-20</td>
           <td>Philosophical transactions. Series A, Mathematical, physical, and engineering sciences</td>
-          <td>41</td>
+          <td>42</td>
           <td>33</td>
         </tr>
 
diff --git a/site/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220/index.html b/site/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220/index.html
index 6f93dbdf..8f5437df 100644
--- a/site/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220/index.html
+++ b/site/recommendations/35e2571c17246577e0bc1b9de57a314c3b60e220/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:10 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:34 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -485,7 +485,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2019-06-25</td>
           <td>IEEE Access</td>
           <td>95</td>
-          <td>63</td>
+          <td>65</td>
         </tr>
 
         <tr id="Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our neural new-physics detector (NNPhD) aims to detect new physics by decomposing the force field into conservative and nonconservative components, which are represented by a Lagrangian neural network (LNN) and an unconstrained neural network, respectively, trained to minimize the force recovery error plus a constant λ times the magnitude of the predicted nonconservative force. We show that a phase transition occurs at λ=1, universally for arbitrary forces. We demonstrate that NNPhD successfully discovers new physics in toy numerical experiments, rediscovering friction (1493) from a damped double pendulum, Neptune from Uranus' orbit (1846), and gravitational waves (2017) from an inspiraling orbit. We also show how NNPhD coupled with an integrator outperforms both an LNN and an unconstrained neural network for predicting the future of a damped double pendulum.">
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-05-31</td>
           <td>2023 American Control Conference (ACC)</td>
-          <td>15</td>
+          <td>16</td>
           <td>37</td>
         </tr>
 
@@ -543,9 +543,9 @@ <h3 data-intro='Recommendations for the article'>
             Philipp Holl, V. Koltun, Nils Thuerey
           </td>
           <td>2021-09-30</td>
-          <td>DBLP, ArXiv</td>
+          <td>ArXiv, DBLP</td>
           <td>5</td>
-          <td>103</td>
+          <td>105</td>
         </tr>
 
         <tr id="None">
@@ -568,8 +568,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-05-06</td>
           <td>Physical review letters</td>
-          <td>81</td>
-          <td>81</td>
+          <td>82</td>
+          <td>82</td>
         </tr>
 
         <tr id="None">
@@ -592,7 +592,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-07-06</td>
           <td>ArXiv</td>
-          <td>21</td>
+          <td>22</td>
           <td>27</td>
         </tr>
 
diff --git a/site/recommendations/3c9961153493370500020c81527b3548c96f81e0/index.html b/site/recommendations/3c9961153493370500020c81527b3548c96f81e0/index.html
index 021925fe..0af8d0fa 100644
--- a/site/recommendations/3c9961153493370500020c81527b3548c96f81e0/index.html
+++ b/site/recommendations/3c9961153493370500020c81527b3548c96f81e0/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:04 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:22 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,8 +484,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3159</td>
-          <td>63</td>
+          <td>3190</td>
+          <td>65</td>
         </tr>
 
         <tr id="None">
@@ -496,7 +496,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>234</td>
+          <td>238</td>
           <td>12</td>
         </tr>
 
diff --git a/site/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2/index.html b/site/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2/index.html
index 5910c86c..ed241a7b 100644
--- a/site/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2/index.html
+++ b/site/recommendations/3df50e9b73cc2937dfd651f4c3344bc99b7ed3f2/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:05 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:24 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -476,14 +476,14 @@ <h3 data-intro='Recommendations for the article'>
   </thead>
   <tbody>
 
-        <tr id="This article introduces an advanced Koopman mode decomposition (KMD) technique -- coined Featurized Koopman Mode Decomposition (FKMD) -- that uses delay embedding and a learned Mahalanobis distance to enhance analysis and prediction of high dimensional dynamical systems. The delay embedding expands the observation space to better capture underlying manifold structure, while the Mahalanobis distance adjusts observations based on the system's dynamics. This aids in featurizing KMD in cases where good features are not a priori known. We show that FKMD improves predictions for a high-dimensional linear oscillator, a high-dimensional Lorenz attractor that is partially observed, and a cell signaling problem from cancer research.">
+        <tr id="This article introduces an advanced Koopman mode decomposition (KMD) technique—coined Featurized Koopman Mode Decomposition (FKMD)—that uses delay embedding and a learned Mahalanobis distance to enhance analysis and prediction of high-dimensional dynamical systems. The delay embedding expands the observation space to better capture underlying manifold structures, while the Mahalanobis distance adjusts observations based on the system’s dynamics. This aids in featurizing KMD in cases where good features are not a priori known. We show that FKMD improves predictions for a high-dimensional linear oscillator, a high-dimensional Lorenz attractor that is partially observed, and a cell signaling problem from cancer research.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/78f159b92f2f6689b738970dc1ce3a8641b2a534" target='_blank'>Featurizing Koopman Mode Decomposition For Robust Forecasting</a></td>
+          <td><a href="https://www.semanticscholar.org/paper/78f159b92f2f6689b738970dc1ce3a8641b2a534" target='_blank'>Featurizing Koopman mode decomposition for robust forecasting</a></td>
           <td>
             D. Aristoff, J. Copperman, Nathan Mankovich, Alexander Davies
           </td>
           <td>2023-12-14</td>
-          <td>ArXiv</td>
+          <td>The Journal of Chemical Physics</td>
           <td>0</td>
           <td>12</td>
         </tr>
@@ -497,7 +497,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-11-20</td>
           <td>Physical review. E</td>
           <td>8</td>
-          <td>50</td>
+          <td>51</td>
         </tr>
 
         <tr id="A central challenge in data-driven model discovery is the presence of hidden, or latent, variables that are not directly measured but are dynamically important. Takens’ theorem provides conditions for when it is possible to augment partial measurements with time delayed information, resulting in an attractor that is diffeomorphic to that of the original full-state system. This diffeomorphism is typically unknown, and learning the dynamics in the embedding space has remained an open challenge for decades. Here, we design a deep autoencoder network to learn a coordinate transformation from the delay embedded space into a new space, where it is possible to represent the dynamics in a sparse, closed form. We demonstrate this approach on the Lorenz, Rössler and Lotka–Volterra systems, as well as a Lorenz analogue from a video of a chaotic waterwheel experiment. This framework combines deep learning and the sparse identification of nonlinear dynamics methods to uncover interpretable models within effective coordinates.">
@@ -508,8 +508,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-01-13</td>
           <td>Proceedings of the Royal Society A</td>
-          <td>67</td>
-          <td>63</td>
+          <td>69</td>
+          <td>65</td>
         </tr>
 
         <tr id="Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens' delay embedding theory provides a way to transform high-dimensional spatial information into temporal information. In this work, by combining delay embedding theory and deep learning techniques, we propose a novel framework, delay-embedding-based forecast Machine (DEFM), to predict the future values of a target variable in a self-supervised and multistep-ahead manner based on high-dimensional observations. With a three-module spatiotemporal architecture, the DEFM leverages deep neural networks to effectively extract both the spatially and temporally associated information from the observed time series even with time-varying parameters or additive noise. The DEFM can accurately predict future information by transforming spatiotemporal information to the delay embeddings of a target variable. The efficacy and precision of the DEFM are substantiated through applications in three spatiotemporally chaotic systems: a 90-dimensional (90D) coupled Lorenz system, the Lorenz 96 system, and the Kuramoto-Sivashinsky equation with inhomogeneity. Additionally, the performance of the DEFM is evaluated on six real-world datasets spanning various fields. Comparative experiments with five prediction methods illustrate the superiority and robustness of the DEFM and show the great potential of the DEFM in temporal information mining and forecasting.">
@@ -521,7 +521,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2020-05-16</td>
           <td>Chaos</td>
           <td>1</td>
-          <td>78</td>
+          <td>79</td>
         </tr>
 
         <tr id="Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens' delay embedding theory provides a way to transform high-dimensional spatial information into temporal information. In this work, by combining delay embedding theory and deep learning techniques, we propose a novel framework, delay-embedding-based forecast Machine (DEFM), to predict the future values of a target variable in a self-supervised and multistep-ahead manner based on high-dimensional observations. With a three-module spatiotemporal architecture, the DEFM leverages deep neural networks to effectively extract both the spatially and temporally associated information from the observed time series even with time-varying parameters or additive noise. The DEFM can accurately predict future information by transforming spatiotemporal information to the delay embeddings of a target variable. The efficacy and precision of the DEFM are substantiated through applications in three spatiotemporally chaotic systems: a 90-dimensional (90D) coupled Lorenz system, the Lorenz 96 system, and the Kuramoto-Sivashinsky equation with inhomogeneity. Additionally, the performance of the DEFM is evaluated on six real-world datasets spanning various fields. Comparative experiments with five prediction methods illustrate the superiority and robustness of the DEFM and show the great potential of the DEFM in temporal information mining and forecasting.">
@@ -533,7 +533,19 @@ <h3 data-intro='Recommendations for the article'>
           <td>2020-05-16</td>
           <td>Chaos</td>
           <td>1</td>
-          <td>78</td>
+          <td>79</td>
+        </tr>
+
+        <tr id="Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based on empirical measurement is an important step in characterizing and predicting these processes. Classifying a system as chaotic usually requires estimating its largest Lyapunov exponent, which quantifies the average rate of convergence or divergence of initially close trajectories in state space, and for which a positive value is generally accepted as an operational definition of chaos. Estimating the largest Lyapunov exponent from observations of a process is especially challenging in systems affected by dynamical noise, which is the case for many models of real-world processes, in particular models of biological systems. We describe a novel method for estimating the largest Lyapunov exponent from data, based on training Deep Learning models on synthetically generated trajectories, and demonstrate that this method yields accurate and noise-robust predictions given relatively short inputs and across a range of different dynamical systems. Our method is unique in that it can analyze tree-shaped data, a ubiquitous topology in biological settings, and specifically in dynamics over lineages of cells or organisms. We also characterize the types of input information extracted by our models for their predictions, allowing for a deeper understanding into the different ways by which chaos can be analyzed in different topologies.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/9fb357e57624525f27224822502061cc8fb831e1" target='_blank'>Detecting chaos in lineage-trees: A deep learning approach</a></td>
+          <td>
+            H. Rappeport, Irit Levin Reisman, Naftali Tishby, N. Balaban
+          </td>
+          <td>2021-06-08</td>
+          <td>ArXiv</td>
+          <td>2</td>
+          <td>56</td>
         </tr>
 
         <tr id="A generally applicable robust data-driven network modeling strategy offers rapid means to predict and control complex systems. We propose a universal method for data-driven modeling of complex nonlinear dynamics from time-resolved snapshot data without prior knowledge. Complex nonlinear dynamics govern many fields of science and engineering. Data-driven dynamic modeling often assumes a low-dimensional subspace or manifold for the state. We liberate ourselves from this assumption by proposing cluster-based network modeling (CNM) bridging machine learning, network science, and statistical physics. CNM describes short- and long-term behavior and is fully automatable, as it does not rely on application-specific knowledge. CNM is demonstrated for the Lorenz attractor, ECG heartbeat signals, Kolmogorov flow, and a high-dimensional actuated turbulent boundary layer. Even the notoriously difficult modeling benchmark of rare events in the Kolmogorov flow is solved. This automatable universal data-driven representation of complex nonlinear dynamics complements and expands network connectivity science and promises new fast-track avenues to understand, estimate, predict, and control complex systems in all scientific fields.">
@@ -560,30 +572,6 @@ <h3 data-intro='Recommendations for the article'>
           <td>49</td>
         </tr>
 
-        <tr id="Chaotic dynamical systems (DS) are ubiquitous in nature and society. Often we are interested in reconstructing such systems from observed time series for prediction or mechanistic insight, where by reconstruction we mean learning geometrical and invariant temporal properties of the system in question (like attractors). However, training reconstruction algorithms like recurrent neural networks (RNNs) on such systems by gradient-descent based techniques faces severe challenges. This is mainly due to exploding gradients caused by the exponential divergence of trajectories in chaotic systems. Moreover, for (scientific) interpretability we wish to have as low dimensional reconstructions as possible, preferably in a model which is mathematically tractable. Here we report that a surprisingly simple modification of teacher forcing leads to provably strictly all-time bounded gradients in training on chaotic systems, and, when paired with a simple architectural rearrangement of a tractable RNN design, piecewise-linear RNNs (PLRNNs), allows for faithful reconstruction in spaces of at most the dimensionality of the observed system. We show on several DS that with these amendments we can reconstruct DS better than current SOTA algorithms, in much lower dimensions. Performance differences were particularly compelling on real world data with which most other methods severely struggled. This work thus led to a simple yet powerful DS reconstruction algorithm which is highly interpretable at the same time.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/6ca393ee5afbe0e876baae5e428724ffd090efc5" target='_blank'>Generalized Teacher Forcing for Learning Chaotic Dynamics</a></td>
-          <td>
-            F. Hess, Z. Monfared, Manuela Brenner, D. Durstewitz
-          </td>
-          <td>2023-06-07</td>
-          <td>DBLP, ArXiv</td>
-          <td>15</td>
-          <td>36</td>
-        </tr>
-
-        <tr id="Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the system undergoes changes in qualitative behavior. A detailed description of the dynamics can be difficult or impossible to obtain for high-dimensional and chaotic systems. Therefore, a more sensible goal is to recognize and mark transitions of a system between qualitatively different regimes of behavior. In practice, one is interested in developing techniques for detection of such transitions from sparse observations, possibly contaminated by noise. In this paper we develop a framework to accurately tag different regimes of complex systems based on topological features. In particular, our framework works with a high degree of success in picking out a cyclically orbiting regime from a stationary equilibrium regime in high-dimensional stochastic dynamical systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/4201cd896bbab7c98602be04bb744b6c470b0dfb" target='_blank'>Automatic recognition and tagging of topologically different regimes in dynamical systems</a></td>
-          <td>
-            Jesse Berwald, M. Gidea, Mikael Vejdemo-Johansson
-          </td>
-          <td>2013-12-09</td>
-          <td>ArXiv</td>
-          <td>34</td>
-          <td>22</td>
-        </tr>
-
   </tbody>
   <tfoot>
     <tr>
diff --git a/site/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba/index.html b/site/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba/index.html
index 759be728..09369a8d 100644
--- a/site/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba/index.html
+++ b/site/recommendations/455bfc515eb279cc09023faa1f78c6efb61224ba/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:42 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:04:56 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -520,7 +520,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-03-01</td>
           <td>ArXiv</td>
-          <td>8</td>
+          <td>9</td>
           <td>65</td>
         </tr>
 
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-03-01</td>
           <td>ArXiv</td>
-          <td>8</td>
+          <td>9</td>
           <td>65</td>
         </tr>
 
@@ -545,7 +545,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-10-17</td>
           <td>2023 IEEE International Conference on Data Mining (ICDM)</td>
           <td>0</td>
-          <td>8</td>
+          <td>9</td>
         </tr>
 
         <tr id="Irregularly-sampled time series occur in many domains including healthcare. They can be challenging to model because they do not naturally yield a fixed-dimensional representation as required by many standard machine learning models. In this paper, we consider irregular sampling from the perspective of missing data. We model observed irregularly-sampled time series data as a sequence of index-value pairs sampled from a continuous but unobserved function. We introduce an encoder-decoder framework for learning from such generic indexed sequences. We propose learning methods for this framework based on variational autoencoders and generative adversarial networks. For continuous irregularly-sampled time series, we introduce continuous convolutional layers that can efficiently interface with existing neural network architectures. Experiments show that our models are able to achieve competitive or better classification results on irregularly-sampled multivariate time series compared to recent RNN models while offering significantly faster training times.">
@@ -555,9 +555,9 @@ <h3 data-intro='Recommendations for the article'>
             Steven Cheng-Xian Li, Benjamin M Marlin
           </td>
           <td>2020-07-12</td>
-          <td>DBLP, ArXiv, MAG</td>
+          <td>ArXiv, MAG, DBLP</td>
           <td>47</td>
-          <td>32</td>
+          <td>33</td>
         </tr>
 
         <tr id="We consider a sequence of related multivariate time series learning tasks, such as predicting failures for different instances of a machine from time series of multi-sensor data, or activity recognition tasks over different individuals from multiple wearable sensors. We focus on two under-explored practical challenges arising in such settings: (i) Each task may have a different subset of sensors, i.e., providing different partial observations of the underlying ‘system’. This restriction can be due to different manufacturers in the former case, and people wearing more or less measurement devices in the latter (ii) We are not allowed to store or re-access data from a task once it has been observed at the task level. This may be due to privacy considerations in the case of people, or legal restrictions placed by machine owners. Nevertheless, we would like to (a) improve performance on subsequent tasks using experience from completed tasks as well as (b) continue to perform better on past tasks, e.g., update the model and improve predictions on even the first machine after learning from subsequently observed ones. We note that existing continual learning methods do not take into account variability in input dimensions arising due to different subsets of sensors being available across tasks, and struggle to adapt to such variable input dimensions (VID) tasks. In this work, we address this shortcoming of existing methods. To this end, we learn task-specific generative models and classifiers, and use these to augment data for target tasks. Since the input dimensions across tasks vary, we propose a novel conditioning module based on graph neural networks to aid a standard recurrent neural network. We evaluate the efficacy of the proposed approach on three publicly available datasets corresponding to two activity recognition tasks (classification) and one prognostics task (regression). We demonstrate that it is possible to significantly enhance the performance on future and previous tasks while learning continuously from VID tasks without storing data.">
diff --git a/site/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01/index.html b/site/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01/index.html
index e23038f2..219b052c 100644
--- a/site/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01/index.html
+++ b/site/recommendations/4971f9abd024e40fbbdff2e9492745b68a6bca01/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:07 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:29 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -508,8 +508,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-11-12</td>
           <td>J. Open Source Softw.</td>
-          <td>108</td>
-          <td>63</td>
+          <td>109</td>
+          <td>65</td>
         </tr>
 
         <tr id="Data-driven modeling frameworks that adopt sparse regression techniques, such as sparse identification of nonlinear dynamics (SINDy) and its modifications, are developed to resolve difficulties in extracting underlying dynamics from experimental data. In contrast to neural-network-based methods, these methods are designed to obtain white-box analytical models. In this work, we incorporate the concept of SINDy and knowledge in the field of classical mechanics to identify interpretable and sparse expressions of total energy and the Lagrangian that shelters the hidden dynamics. Moreover, our method (hereafter referred as Lagrangian-SINDy) is developed to use knowledge of simple systems that form the system being analyzed to ensure the likelihood of correct results and to improve the learning pace. Lagrangian-SINDy is highly accurate in discovering interpretable dynamics via energy-related physical quantities. Its performance is validated with three popular multi-DOF nonlinear dynamical systems, namely the spherical pendulum, double pendulum and cart-pendulum system. Comparisons with other SINDy-based methods are made and Lagrangian-SINDy is found to provide the most compact analytical models.">
@@ -569,7 +569,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2024-04-24</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>6</td>
+          <td>7</td>
         </tr>
 
         <tr id="In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.">
@@ -580,7 +580,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-01</td>
           <td>ArXiv</td>
-          <td>0</td>
+          <td>1</td>
           <td>1</td>
         </tr>
 
@@ -592,8 +592,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-07-06</td>
           <td>Journal of computational physics</td>
-          <td>119</td>
-          <td>19</td>
+          <td>121</td>
+          <td>20</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/4a111f7a3b56d0468f13104999844885157ef17d/index.html b/site/recommendations/4a111f7a3b56d0468f13104999844885157ef17d/index.html
index 70e48a4b..a5f35a4c 100644
--- a/site/recommendations/4a111f7a3b56d0468f13104999844885157ef17d/index.html
+++ b/site/recommendations/4a111f7a3b56d0468f13104999844885157ef17d/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:48 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:02 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>23</td>
+          <td>27</td>
           <td>18</td>
         </tr>
 
@@ -496,8 +496,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-04</td>
           <td>ArXiv</td>
-          <td>6</td>
-          <td>65</td>
+          <td>5</td>
+          <td>66</td>
         </tr>
 
         <tr id="We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history. Our channel-independent patch time series Transformer (PatchTST) can improve the long-term forecasting accuracy significantly when compared with that of SOTA Transformer-based models. We also apply our model to self-supervised pre-training tasks and attain excellent fine-tuning performance, which outperforms supervised training on large datasets. Transferring of masked pre-trained representation on one dataset to others also produces SOTA forecasting accuracy. Code is available at: https://github.com/yuqinie98/PatchTST.">
@@ -508,10 +508,22 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-11-27</td>
           <td>ArXiv</td>
-          <td>469</td>
+          <td>494</td>
           <td>34</td>
         </tr>
 
+        <tr id="Time series forecasting is a critical and challenging task in practical application. Recent advancements in pre-trained foundation models for time series forecasting have gained significant interest. However, current methods often overlook the multi-scale nature of time series, which is essential for accurate forecasting. To address this, we propose HiMTM, a hierarchical multi-scale masked time series modeling with self-distillation for long-term forecasting. HiMTM integrates four key components: (1) hierarchical multi-scale transformer (HMT) to capture temporal information at different scales; (2) decoupled encoder-decoder (DED) that directs the encoder towards feature extraction while the decoder focuses on pretext tasks; (3) hierarchical self-distillation (HSD) for multi-stage feature-level supervision signals during pre-training; and (4) cross-scale attention fine-tuning (CSA-FT) to capture dependencies between different scales for downstream tasks. These components collectively enhance multi-scale feature extraction in masked time series modeling, improving forecasting accuracy. Extensive experiments on seven mainstream datasets show that HiMTM surpasses state-of-the-art self-supervised and end-to-end learning methods by a considerable margin of 3.16-68.54\%. Additionally, HiMTM outperforms the latest robust self-supervised learning method, PatchTST, in cross-domain forecasting by a significant margin of 2.3\%. The effectiveness of HiMTM is further demonstrated through its application in natural gas demand forecasting.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/d945eae22457648e191742c37bcad88a114ce703" target='_blank'>HiMTM: Hierarchical Multi-Scale Masked Time Series Modeling with Self-Distillation for Long-Term Forecasting</a></td>
+          <td>
+            Shubao Zhao, Ming Jin, Zhaoxiang Hou, Che-Sheng Yang, Zengxiang Li, Qingsong Wen, Yi Wang
+          </td>
+          <td>2024-01-10</td>
+          <td>ArXiv</td>
+          <td>0</td>
+          <td>6</td>
+        </tr>
+
         <tr id="The Transformer is a highly successful deep learning model that has revolutionised the world of artificial neural networks, first in natural language processing and later in computer vision. This model is based on the attention mechanism and is able to capture complex semantic relationships between a variety of patterns present in the input data. Precisely because of these characteristics, the Transformer has recently been exploited for time series forecasting problems, assuming a natural adaptability to the domain of continuous numerical series. Despite the acclaimed results in the literature, some works have raised doubts about the robustness and effectiveness of this approach. In this paper, we further investigate the effectiveness of Transformer-based models applied to the domain of time series forecasting, demonstrate their limitations, and propose a set of alternative models that are better performing and significantly less complex. In particular, we empirically show how simplifying Transformer-based forecasting models almost always leads to an improvement, reaching state of the art performance. We also propose shallow models without the attention mechanism, which compete with the overall state of the art in long time series forecasting, and demonstrate their ability to accurately predict time series over extremely long windows. From a methodological perspective, we show how it is always necessary to use a simple baseline to verify the effectiveness of proposed models, and finally, we conclude the paper with a reflection on recent research paths and the opportunity to follow trends and hypes even where it may not be necessary.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/b98bc7d48357932537fc9ba6035e3b6bd1018ae6" target='_blank'>Two Steps Forward and One Behind: Rethinking Time Series Forecasting with Deep Learning</a></td>
@@ -519,9 +531,9 @@ <h3 data-intro='Recommendations for the article'>
             Riccardo Ughi, Eugenio Lomurno, Matteo Matteucci
           </td>
           <td>2023-04-10</td>
-          <td>DBLP, ArXiv</td>
+          <td>ArXiv, DBLP</td>
           <td>1</td>
-          <td>5</td>
+          <td>6</td>
         </tr>
 
         <tr id="Time series has been left behind in the era of pre-training and transfer learning. While research in the fields of natural language processing and computer vision are enjoying progressively larger datasets to train massive models, the most popular time series datasets consist of only tens of thousands of time steps, limiting our ability to study the effectiveness of pre-training and scaling. Recent studies have also cast doubt on the need for expressive models and scale. To alleviate these issues, we introduce three large-scale time series forecasting datasets from the cloud operations (CloudOps) domain, the largest having billions of observations, enabling further study into pre-training and scaling of time series models. We build the empirical groundwork for studying pre-training and scaling of time series models and pave the way for future research by identifying a promising candidate architecture. We show that it is a strong zero-shot baseline and benefits from further scaling, both in model and dataset size. Accompanying these datasets and results is a suite of comprehensive benchmark results comparing classical and deep learning baselines to our pre-trained method - achieving a 27% reduction in error on the largest dataset. Code and datasets can be found https://github.com/SalesforceAIResearch/pretrain-time-series-cloudops.">
@@ -548,18 +560,6 @@ <h3 data-intro='Recommendations for the article'>
           <td>2</td>
         </tr>
 
-        <tr id="Long-term time-series forecasting (LTSF) plays a crucial role in various practical applications. Transformer and its variants have become the de facto backbone for LTSF, offering exceptional capabilities in processing long sequence data. However, existing Transformer-based models, such as Fedformer and Informer, often achieve their best performances on validation sets after just a few epochs, indicating potential underutilization of the Transformer's capacity. One of the reasons that contribute to this overfitting is data redundancy arising from the rolling forecasting settings in the data augmentation process, particularly evident in longer sequences with highly similar adjacent data. In this paper, we propose a novel approach to address this issue by employing curriculum learning and introducing a memory-driven decoder. Specifically, we progressively introduce Bernoulli noise to the training samples, which effectively breaks the high similarity between adjacent data points. To further enhance forecasting accuracy, we introduce a memory-driven decoder. This component enables the model to capture seasonal tendencies and dependencies in the time-series data and leverages temporal relationships to facilitate the forecasting process. The experimental results on six real-life LTSF benchmarks demonstrate that our approach can be seamlessly plugged into varying Transformer-based models, with our approach enhancing the LTSF performances of various Transformer-based models by maximally 30%.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/e4e01b1059fa20b8fc5817f292fe38466381dc26" target='_blank'>CLMFormer: Mitigating Data Redundancy to Revitalize Transformer-based Long-Term Time Series Forecasting System</a></td>
-          <td>
-            Mingjie Li, Xiaoyun Zhao, R. Liu, Changlin Li, Xiaohan Wang, Xiaojun Chang
-          </td>
-          <td>2022-07-16</td>
-          <td>ArXiv</td>
-          <td>1</td>
-          <td>78</td>
-        </tr>
-
   </tbody>
   <tfoot>
     <tr>
diff --git a/site/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14/index.html b/site/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14/index.html
index 3e6f7448..2ad64683 100644
--- a/site/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14/index.html
+++ b/site/recommendations/5bd2c0acaf58c25f71617db2396188c74d29bf14/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:52 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:06 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -497,7 +497,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-03-15</td>
           <td>ACM Transactions on Knowledge Discovery from Data</td>
           <td>38</td>
-          <td>36</td>
+          <td>37</td>
         </tr>
 
         <tr id="Domain generalization methods aim to learn models robust to domain shift with data from a limited number of source domains and without access to target domain samples during training. Popular domain alignment methods for domain generalization seek to extract domain-invariant features by minimizing the discrepancy between feature distributions across all domains, disregarding inter-domain relationships. In this paper, we instead propose a novel representation learning methodology that selectively enforces prediction consistency between source domains estimated to be closely-related. Specifically, we hypothesize that domains share different class-informative representations, so instead of aligning all domains which can cause negative transfer, we only regularize the discrepancy between closely-related domains. We apply our method to time-series classification tasks and conduct comprehensive experiments on three public real-world datasets. Our method significantly improves over the baseline and achieves better or competitive performance in comparison with state-of-the-art methods in terms of both accuracy and model calibration.">
@@ -519,7 +519,7 @@ <h3 data-intro='Recommendations for the article'>
             Xiaoyong Jin, Youngsuk Park, Danielle C. Maddix, Bernie Wang, Xifeng Yan
           </td>
           <td>2021-02-13</td>
-          <td>DBLP, ArXiv</td>
+          <td>ArXiv, DBLP</td>
           <td>56</td>
           <td>65</td>
         </tr>
diff --git a/site/recommendations/5d150cec2775f9bc863760448f14104cc8f42368/index.html b/site/recommendations/5d150cec2775f9bc863760448f14104cc8f42368/index.html
index 16af42d6..9516f1b8 100644
--- a/site/recommendations/5d150cec2775f9bc863760448f14104cc8f42368/index.html
+++ b/site/recommendations/5d150cec2775f9bc863760448f14104cc8f42368/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:02 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:21 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,8 +484,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2019-03-29</td>
           <td>Proceedings of the National Academy of Sciences of the United States of America</td>
-          <td>595</td>
-          <td>63</td>
+          <td>603</td>
+          <td>65</td>
         </tr>
 
         <tr id="None">
@@ -520,7 +520,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>234</td>
+          <td>238</td>
           <td>12</td>
         </tr>
 
@@ -557,7 +557,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2021-05-11</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
           <td>37</td>
-          <td>53</td>
+          <td>52</td>
         </tr>
 
         <tr id="None">
@@ -569,7 +569,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2014-12-10</td>
           <td>The European Physical Journal Special Topics</td>
           <td>64</td>
-          <td>63</td>
+          <td>65</td>
         </tr>
 
         <tr id="None">
@@ -581,7 +581,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2014-12-01</td>
           <td>The European Physical Journal Special Topics</td>
           <td>7</td>
-          <td>63</td>
+          <td>65</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c/index.html b/site/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c/index.html
index df5078a9..cc566db0 100644
--- a/site/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c/index.html
+++ b/site/recommendations/60d0d998fa038182b3b69a57adb9b2f82d40589c/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:03 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:21 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-07-01</td>
           <td>Nature Computational Science</td>
-          <td>66</td>
+          <td>67</td>
           <td>20</td>
         </tr>
 
@@ -497,7 +497,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2024-05-07</td>
           <td>ArXiv</td>
           <td>1</td>
-          <td>63</td>
+          <td>65</td>
         </tr>
 
         <tr id="None">
@@ -544,10 +544,22 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-12-20</td>
           <td>ArXiv</td>
-          <td>11</td>
+          <td>13</td>
           <td>72</td>
         </tr>
 
+        <tr id="High-resolution reconstruction of flow-field data from low-resolution and noisy measurements is of interest due to the prevalence of such problems in experimental fluid mechanics, where the measurement data are in general sparse, incomplete and noisy. Deep-learning approaches have been shown suitable for such super-resolution tasks. However, a high number of high-resolution examples is needed, which may not be available for many cases. Moreover, the obtained predictions may lack in complying with the physical principles, e.g. mass and momentum conservation. Physics-informed deep learning provides frameworks for integrating data and physical laws for learning. In this study, we apply physics-informed neural networks (PINNs) for super-resolution of flow-field data both in time and space from a limited set of noisy measurements without having any high-resolution reference data. Our objective is to obtain a continuous solution of the problem, providing a physically-consistent prediction at any point in the solution domain. We demonstrate the applicability of PINNs for the super-resolution of flow-field data in time and space through three canonical cases: Burgers’ equation, two-dimensional vortex shedding behind a circular cylinder and the minimal turbulent channel flow. The robustness of the models is also investigated by adding synthetic Gaussian noise. Furthermore, we show the capabilities of PINNs to improve the resolution and reduce the noise in a real experimental dataset consisting of hot-wire-anemometry measurements. Our results show the adequate capabilities of PINNs in the context of data augmentation for experiments in fluid mechanics.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/ecf61b26615fc12f9edc4826dd81a23ac0d72f37" target='_blank'>Physics-informed deep-learning applications to experimental fluid mechanics</a></td>
+          <td>
+            Hamidreza Eivazi, Yuning Wang, R. Vinuesa
+          </td>
+          <td>2022-03-29</td>
+          <td>Measurement Science and Technology</td>
+          <td>21</td>
+          <td>38</td>
+        </tr>
+
         <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/606824bebf4e444fca9b988823883f1ec99f19ec" target='_blank'>A physics-informed operator regression framework for extracting data-driven continuum models</a></td>
@@ -556,7 +568,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-09-25</td>
           <td>ArXiv</td>
-          <td>84</td>
+          <td>86</td>
           <td>17</td>
         </tr>
 
@@ -572,19 +584,6 @@ <h3 data-intro='Recommendations for the article'>
           <td>47</td>
         </tr>
 
-        <tr id="
- In the context of science, the well-known adage “a picture is worth a thousand words” might well be “a model is worth a thousand datasets.” Scientific models, such as Newtonian physics or biological gene regulatory networks, are human-driven simplifications of complex phenomena that serve as surrogates for the countless experiments that validated the models. Recently, machine learning has been able to overcome the inaccuracies of approximate modeling by directly learning the entire set of nonlinear interactions from data. However, without any predetermined structure from the scientific basis behind the problem, machine learning approaches are flexible but data-expensive, requiring large databases of homogeneous labeled training data. A central challenge is reconciling data that is at odds with simplified models without requiring "big data". In this work demonstrate how a mathematical object, which we denote universal differential equations (UDEs), can be utilized as a theoretical underpinning to a diverse array of problems in scientific machine learning to yield efficient algorithms and generalized approaches. The UDE model augments scientific models with machine-learnable structures for scientifically-based learning. We show how UDEs can be utilized to discover previously unknown governing equations, accurately extrapolate beyond the original data, and accelerate model simulation, all in a time and data-efficient manner. This advance is coupled with open-source software that allows for training UDEs which incorporate physical constraints, delayed interactions, implicitly-defined events, and intrinsic stochasticity in the model. Our examples show how a diverse set of computationally-difficult modeling issues across scientific disciplines, from automatically discovering biological mechanisms to accelerating the training of physics-informed neural networks and large-eddy simulations, can all be transformed into UDE training problems that are efficiently solved by a single software methodology.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/696b388ee6221c6dbcfd647a06883b2bfee773d9" target='_blank'>Universal Differential Equations for Scientific Machine Learning</a></td>
-          <td>
-            Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, K. Zubov, R. Supekar, Dominic J. Skinner, A. Ramadhan
-          </td>
-          <td>2020-01-13</td>
-          <td>ArXiv</td>
-          <td>483</td>
-          <td>25</td>
-        </tr>
-
   </tbody>
   <tfoot>
     <tr>
diff --git a/site/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37/index.html b/site/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37/index.html
index 15f35430..5305f20e 100644
--- a/site/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37/index.html
+++ b/site/recommendations/648d90b713997a771e2c49f02cd771e8b7b10b37/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:51 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:04 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-04-23</td>
           <td>Sensors (Basel, Switzerland)</td>
-          <td>20</td>
+          <td>21</td>
           <td>77</td>
         </tr>
 
@@ -521,7 +521,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-06-26</td>
           <td>DBLP</td>
           <td>2</td>
-          <td>139</td>
+          <td>140</td>
         </tr>
 
         <tr id="Contrastive representation learning is crucial in medical time series analysis as it alleviates dependency on labor-intensive, domain-specific, and scarce expert annotations. However, existing contrastive learning methods primarily focus on one single data level, which fails to fully exploit the intricate nature of medical time series. To address this issue, we present COMET, an innovative hierarchical framework that leverages data consistencies at all inherent levels in medical time series. Our meticulously designed model systematically captures data consistency from four potential levels: observation, sample, trial, and patient levels. By developing contrastive loss at multiple levels, we can learn effective representations that preserve comprehensive data consistency, maximizing information utilization in a self-supervised manner. We conduct experiments in the challenging patient-independent setting. We compare COMET against six baselines using three diverse datasets, which include ECG signals for myocardial infarction and EEG signals for Alzheimer's and Parkinson's diseases. The results demonstrate that COMET consistently outperforms all baselines, particularly in setup with 10% and 1% labeled data fractions across all datasets. These results underscore the significant impact of our framework in advancing contrastive representation learning techniques for medical time series. The source code is available at https://github.com/DL4mHealth/COMET.">
@@ -532,8 +532,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-21</td>
           <td>ArXiv</td>
-          <td>18</td>
-          <td>2</td>
+          <td>19</td>
+          <td>3</td>
         </tr>
 
         <tr id="Unsupervised domain adaptation (UDA) provides a strategy for improving machine learning performance in data-rich (target) domains where ground truth labels are inaccessible but can be found in related (source) domains. In cases where meta-domain information such as label distributions is available, weak supervision can further boost performance. We propose a novel framework, CALDA, to tackle these two problems. CALDA synergistically combines the principles of contrastive learning and adversarial learning to robustly support multi-source UDA (MS-UDA) for time series data. Similar to prior methods, CALDA utilizes adversarial learning to align source and target feature representations. Unlike prior approaches, CALDA additionally leverages cross-source label information across domains. CALDA pulls examples with the same label close to each other, while pushing apart examples with different labels, reshaping the space through contrastive learning. Unlike prior contrastive adaptation methods, CALDA requires neither data augmentation nor pseudo labeling, which may be more challenging for time series. We empirically validate our proposed approach. Based on results from human activity recognition, electromyography, and synthetic datasets, we find utilizing cross-source information improves performance over prior time series and contrastive methods. Weak supervision further improves performance, even in the presence of noise, allowing CALDA to offer generalizable strategies for MS-UDA.">
@@ -545,7 +545,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2021-09-30</td>
           <td>IEEE Transactions on Pattern Analysis and Machine Intelligence</td>
           <td>14</td>
-          <td>72</td>
+          <td>71</td>
         </tr>
 
         <tr id="To improve the accuracy of clinical multivariate time series (MTS) classification (such as EEG and ECG) by a novel self-supervised paradigm that directly captures the dynamics between the different time series learned together to optimize the classification task. Labels in clinical datasets are very often insufficient. One way to address this challenge is leveraging self-supervision. This paradigm attempts to identify a supervisory signal inherent within a dataset to serve as a surrogate label. We present a novel form of self-supervision: dynamics of clinical MTS. Unlike other self-supervision methods, such as masking, that are intuitive but still heuristic, we suggest to learn a representation justified by Koopman theory. The latter was shown useful for representing clinical time series and can be used as a form of surrogate task to improve the clinical MTS classification. In the ECG task, we show that our proposed framework achieved higher sensitivity and specificity than the state-of-the-art (SOTA) baseline over numerous common diagnoses. For EEG abnormality classification, our proposed framework also achieved higher sensitivity and specificity than the SOTA baseline. All results are statistically significant. Our technique yields reliable clinical diagnosis in an empirical study employing signals from thousands of patients in multiple clinical tasks employing two types of clinical-grade sensors (ECG and EEG) as compared to the state-of-the-art machine learning. Leveraging time-series-dynamics self-supervision can help mitigate the lack of labels in clinical datasets used for training machine learning algorithms and significantly improve their performance. Specifically, the ECG system presented in this work is being trialed in hospitals, used by top cardiologists for patient diagnosis and treatment. We believe that the deployment of such cutting-edge technology will significantly improve the accuracy and speed of cardiac assessments.">
@@ -579,7 +579,7 @@ <h3 data-intro='Recommendations for the article'>
             Konstantinos Kallidromitis, Denis A. Gudovskiy, Kozuka Kazuki, Ohama Iku, Luca Rigazio
           </td>
           <td>2021-10-24</td>
-          <td>DBLP, ArXiv</td>
+          <td>ArXiv, DBLP</td>
           <td>10</td>
           <td>13</td>
         </tr>
@@ -593,7 +593,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-04-24</td>
           <td>IEEE transactions on neural networks and learning systems</td>
           <td>4</td>
-          <td>5</td>
+          <td>6</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/73dd9c49f205280991826b2ea4b50344203916b4/index.html b/site/recommendations/73dd9c49f205280991826b2ea4b50344203916b4/index.html
index 8e99bea3..f9570a62 100644
--- a/site/recommendations/73dd9c49f205280991826b2ea4b50344203916b4/index.html
+++ b/site/recommendations/73dd9c49f205280991826b2ea4b50344203916b4/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:09 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:33 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -508,7 +508,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-01</td>
           <td>ArXiv</td>
-          <td>0</td>
+          <td>1</td>
           <td>1</td>
         </tr>
 
@@ -536,6 +536,18 @@ <h3 data-intro='Recommendations for the article'>
           <td>5</td>
         </tr>
 
+        <tr id="Data-driven discovery of dynamics via machine learning is pushing the frontiers of modelling and control efforts, providing a tremendous opportunity to extend the reach of model predictive control (MPC). However, many leading methods in machine learning, such as neural networks (NN), require large volumes of training data, may not be interpretable, do not easily include known constraints and symmetries, and may not generalize beyond the attractor where models are trained. These factors limit their use for the online identification of a model in the low-data limit, for example following an abrupt change to the system dynamics. In this work, we extend the recent sparse identification of nonlinear dynamics (SINDY) modelling procedure to include the effects of actuation and demonstrate the ability of these models to enhance the performance of MPC, based on limited, noisy data. SINDY models are parsimonious, identifying the fewest terms in the model needed to explain the data, making them interpretable and generalizable. We show that the resulting SINDY-MPC framework has higher performance, requires significantly less data, and is more computationally efficient and robust to noise than NN models, making it viable for online training and execution in response to rapid system changes. SINDY-MPC also shows improved performance over linear data-driven models, although linear models may provide a stopgap until enough data is available for SINDY. SINDY-MPC is demonstrated on a variety of dynamical systems with different challenges, including the chaotic Lorenz system, a simple model for flight control of an F8 aircraft, and an HIV model incorporating drug treatment.">
+          <td id="tag"><i class="material-icons">visibility_off</i></td>
+          <td><a href="https://www.semanticscholar.org/paper/b2eb064f432557c59ce99834d7dc7817e4687271" target='_blank'>Sparse identification of nonlinear dynamics for model predictive control in the low-data limit</a></td>
+          <td>
+            E. Kaiser, J. Kutz, S. Brunton
+          </td>
+          <td>2017-11-15</td>
+          <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
+          <td>428</td>
+          <td>65</td>
+        </tr>
+
         <tr id="None">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/acd85b948087067938680356a0cb7597de12a25d" target='_blank'>Data-based modeling and control of nonlinear process systems using sparse identification: An overview of recent results</a></td>
@@ -556,8 +568,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>190</td>
-          <td>63</td>
+          <td>194</td>
+          <td>65</td>
         </tr>
 
         <tr id="We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide finite sample error bounds of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems, such as upper bounds on noise levels and model difference, is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.">
@@ -572,18 +584,6 @@ <h3 data-intro='Recommendations for the article'>
           <td>36</td>
         </tr>
 
-        <tr id="Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations often result in discrepancies between the model and sensor-based measurements of the system, revealing the approximate nature of the equations and/or the signal-to-noise ratio of the sensor itself. In modern dynamical systems, such discrepancies between model and measurement can lead to poor quantification, often undermining the ability to produce accurate and precise control algorithms. We introduce a discrepancy modeling framework to identify the missing physics and resolve the model-measurement mismatch with two distinct approaches: (i) by learning a model for the evolution of systematic state-space residual, and (ii) by discovering a model for the deterministic dynamical error. Regardless of approach, a common suite of data-driven model discovery methods can be used. The choice of method depends on one's intent (e.g., mechanistic interpretability) for discrepancy modeling, sensor measurement characteristics (e.g., quantity, quality, resolution), and constraints imposed by practical applications (e.g., modeling approaches using the suite of data-driven modeling methods on three continuous dynamical systems under varying signal-to-noise ratios. Finally, we emphasize structural shortcomings of each discrepancy modeling approach depending on error type. In summary, if the true dynamics are unknown (i.e., an imperfect model), one should learn a discrepancy model of the missing physics in the dynamical space. Yet, if the true dynamics are known yet model-measurement mismatch still exists, one should learn a discrepancy model in the state space.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/c4a38c94d23389326f5043d63b9f5f6f0d8c0c50" target='_blank'>Discrepancy Modeling Framework: Learning Missing Physics, Modeling Systematic Residuals, and Disambiguating between Deterministic and Random Effects</a></td>
-          <td>
-            Megan R. Ebers, K. Steele, J. Kutz
-          </td>
-          <td>2022-03-10</td>
-          <td>SIAM J. Appl. Dyn. Syst.</td>
-          <td>5</td>
-          <td>31</td>
-        </tr>
-
   </tbody>
   <tfoot>
     <tr>
diff --git a/site/recommendations/883547fdbd88552328a6615ec620f96e39c57018/index.html b/site/recommendations/883547fdbd88552328a6615ec620f96e39c57018/index.html
index 3f48920e..5c3030a5 100644
--- a/site/recommendations/883547fdbd88552328a6615ec620f96e39c57018/index.html
+++ b/site/recommendations/883547fdbd88552328a6615ec620f96e39c57018/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:11 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:38 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-07-05</td>
           <td>Royal Society Open Science</td>
-          <td>52</td>
+          <td>54</td>
           <td>31</td>
         </tr>
 
@@ -497,7 +497,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-01-30</td>
           <td>ArXiv</td>
           <td>11</td>
-          <td>63</td>
+          <td>65</td>
         </tr>
 
         <tr id="None">
@@ -520,8 +520,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>190</td>
-          <td>63</td>
+          <td>194</td>
+          <td>65</td>
         </tr>
 
         <tr id="We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to speed up computation. The resulting method, Bayesian-SINDy, not only quantifies uncertainty in the parameters estimated but also is more robust when learning the correct model from limited and noisy data. Using both synthetic and real-life examples such as Lynx-Hare population dynamics, we demonstrate the effectiveness of the new framework in learning correct model equations and compare its computational and data efficiency with existing methods. Because Bayesian-SINDy can quickly assimilate data and is robust against noise, it is particularly suitable for biological data and real-time system identification in control. Its probabilistic framework also enables the calculation of information entropy, laying the foundation for an active learning strategy.">
@@ -532,8 +532,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-23</td>
           <td>ArXiv</td>
-          <td>0</td>
-          <td>37</td>
+          <td>1</td>
+          <td>38</td>
         </tr>
 
         <tr id="Significance Understanding dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled technology, including aircraft, combustion engines, satellites, and electrical power. This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. There are many critical data-driven problems, such as understanding cognition from neural recordings, inferring climate patterns, determining stability of financial markets, predicting and suppressing the spread of disease, and controlling turbulence for greener transportation and energy. With abundant data and elusive laws, data-driven discovery of dynamics will continue to play an important role in these efforts. Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.">
@@ -544,8 +544,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3159</td>
-          <td>63</td>
+          <td>3190</td>
+          <td>65</td>
         </tr>
 
         <tr id="The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that can act as a basis for the system. In this paper, we demonstrate on real world data how the Augmented SINDy algorithm outperforms SINDy in the presence of system variable uncertainty. We then show SINDy can be further augmented to perform robustly when both kinds of uncertainty are present.">
diff --git a/site/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/index.html b/site/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/index.html
index 36892e4f..85aa7bd5 100644
--- a/site/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/index.html
+++ b/site/recommendations/b2eb064f432557c59ce99834d7dc7817e4687271/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:06 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:26 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -476,18 +476,6 @@ <h3 data-intro='Recommendations for the article'>
   </thead>
   <tbody>
 
-        <tr id="Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based optimization technique that enables the control of such nonlinear systems with constraints. However, modern systems often lack computationally tractable models, motivating the use of system identification techniques to learn accurate and efficient models for real-time control. In this tutorial article, we review emerging data-driven methods for model discovery and how they are used for nonlinear MPC. In particular, we focus on the sparse identification of nonlinear dynamics (SINDy) algorithm and show how it may be used with MPC on an infectious disease control example. We compare the performance against MPC based on a linear dynamic mode decomposition (DMD) model. Code is provided to run the tutorial examples and may be modified to extend this data-driven control framework to arbitrary nonlinear systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/700552dde778bd1f6b76f7237e9b561597b859ba" target='_blank'>SINDy with Control: A Tutorial</a></td>
-          <td>
-            Urban Fasel, E. Kaiser, J. Kutz, Bingni W. Brunton, S. Brunton
-          </td>
-          <td>2021-08-30</td>
-          <td>2021 60th IEEE Conference on Decision and Control (CDC)</td>
-          <td>45</td>
-          <td>63</td>
-        </tr>
-
         <tr id="In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real dynamical systems. While SINDy can be an appealing strategy for pursuing physics-based learning, our analysis highlights difficulties in dealing with unobserved states and non-smooth dynamics. Due to the ubiquity of these features in real systems in general, and control applications in particular, we complement our analysis with hands-on approaches to tackle these issues in order to exploit SINDy also in these challenging contexts.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/99877062e70fae24c531d58aa880fa443ec10c9b" target='_blank'>SINDy vs Hard Nonlinearities and Hidden Dynamics: a Benchmarking Study</a></td>
@@ -496,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-01</td>
           <td>ArXiv</td>
-          <td>0</td>
+          <td>1</td>
           <td>1</td>
         </tr>
 
@@ -520,8 +508,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-04-05</td>
           <td>Proceedings. Mathematical, Physical, and Engineering Sciences</td>
-          <td>190</td>
-          <td>63</td>
+          <td>194</td>
+          <td>65</td>
         </tr>
 
         <tr id="Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that violate basic physical laws. This work proposes a novel method for the Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI). SINDy-SI is an iterative method that uses Sum-of-Squares (SOS) programming to learn optimally fitted models while guaranteeing that the learned model satisfies side information, such as symmetry's and physical laws. Guided by the principle of Occam's razor, that the simplest or most regularized best fitted model is typically the superior choice, during each iteration SINDy-SI prunes the basis functions associated with small coefficients, yielding a sparse dynamical model upon termination. Through several numerical experiments we will show how the combination of side information constraints and sparse polynomial representation cultivates dynamical models that obey known physical laws while displaying impressive generalized performance beyond the training set.">
@@ -556,8 +544,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3159</td>
-          <td>63</td>
+          <td>3190</td>
+          <td>65</td>
         </tr>
 
         <tr id="Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers.">
@@ -568,8 +556,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-11-12</td>
           <td>J. Open Source Softw.</td>
-          <td>108</td>
-          <td>63</td>
+          <td>109</td>
+          <td>65</td>
         </tr>
 
         <tr id="We develop a principled mathematical framework for controlling nonlinear, networked dynamical systems. Our method integrates dimensionality reduction, bifurcation theory, and emerging model discovery tools to find low-dimensional subspaces where feed-forward control can be used to manipulate a system to a desired outcome. The method leverages the fact that many high-dimensional networked systems have many fixed points, allowing for the computation of control signals that will move the system between any pair of fixed points. The sparse identification of nonlinear dynamics (SINDy) algorithm is used to fit a nonlinear dynamical system to the evolution on the dominant, low-rank subspace. This then allows us to use bifurcation theory to find collections of constant control signals that will produce the desired objective path for a prescribed outcome. Specifically, we can destabilize a given fixed point while making the target fixed point an attractor. The discovered control signals can be easily projected back to the original high-dimensional state and control space. We illustrate our nonlinear control procedure on established bistable, low-dimensional biological systems, showing how control signals are found that generate switches between the fixed points. We then demonstrate our control procedure for high-dimensional systems on random high-dimensional networks and Hopfield memory networks.">
diff --git a/site/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/index.html b/site/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/index.html
index b8a00b10..4169ed58 100644
--- a/site/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/index.html
+++ b/site/recommendations/c0fc3882a9976f6a9cdc3a724bce184b786503da/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:13 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:42 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -485,7 +485,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2018-07-14</td>
           <td>ArXiv</td>
           <td>9</td>
-          <td>63</td>
+          <td>65</td>
         </tr>
 
         <tr id="Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the estimators is a challenging (\NP-hard) non-convex optimization problem. In this paper, we derive new strong convex relaxations for sparse regression. These relaxations are based on the ideal (convex-hull) formulations for rank-one quadratic terms with indicator variables. The new relaxations can be formulated as semidefinite optimization problems in an extended space and are stronger and more general than the state-of-the-art formulations, including the perspective reformulation and formulations with the reverse Huber penalty and the minimax concave penalty functions. Furthermore, the proposed rank-one strengthening can be interpreted as a \textit{non-separable, non-convex, unbiased} sparsity-inducing regularizer, which dynamically adjusts its penalty according to the shape of the error function without inducing bias for the sparse solutions. In our computational experiments with benchmark datasets, the proposed conic formulations are solved within seconds and result in near-optimal solutions (with 0.4\% optimality gap) for non-convex $\ell_0$-problems. Moreover, the resulting estimators also outperform alternative convex approaches from a statistical perspective, achieving high prediction accuracy and good interpretability.">
@@ -521,7 +521,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2014-01-03</td>
           <td></td>
           <td>58</td>
-          <td>94</td>
+          <td>95</td>
         </tr>
 
         <tr id="High-dimensional sparse linear regression is a basic problem in machine learning and statistics. Consider a linear model $y = X\theta^\star + w$, where $y \in \mathbb{R}^n$ is the vector of observations, $X \in \mathbb{R}^{n \times d}$ is the covariate matrix and $w \in \mathbb{R}^n$ is an unknown noise vector. In many applications, the linear regression model is high-dimensional in nature, meaning that the number of observations $n$ may be substantially smaller than the number of covariates $d$. In these cases, it is common to assume that $\theta^\star$ is sparse, and the goal in sparse linear regression is to estimate this sparse $\theta^\star$, given $(X,y)$. 
@@ -535,7 +535,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2017-07-25</td>
           <td>ArXiv</td>
           <td>1</td>
-          <td>29</td>
+          <td>30</td>
         </tr>
 
         <tr id="Reconstruction of signals from undersampled and noisy measurements is a topic of considerable interest. Sharpness conditions directly control the recovery performance of restart schemes for first-order methods without the need for restrictive assumptions such as strong convexity. However, they are challenging to apply in the presence of noise or approximate model classes (e.g., approximate sparsity). We provide a first-order method: Weighted, Accelerated and Restarted Primal-dual (WARPd), based on primal-dual iterations and a novel restart-reweight scheme. Under a generic approximate sharpness condition, WARPd achieves stable linear convergence to the desired vector. Many problems of interest fit into this framework. For example, we analyze sparse recovery in compressed sensing, low-rank matrix recovery, matrix completion, TV regularization, minimization of $\|Bx\|_{l^1}$ under constraints ($l^1$-analysis problems for general $B$), and mixed regularization problems. We show how several quantities controlling recovery performance also provide explicit approximate sharpness constants. Numerical experiments show that WARPd compares favorably with specialized state-of-the-art methods and is ideally suited for solving large-scale problems. We also present a noise-blind variant based on the Square-Root LASSO decoder. Finally, we show how to unroll WARPd as neural networks. This approximation theory result provides lower bounds for stable and accurate neural networks for inverse problems and sheds light on architecture choices. Code and a gallery of examples are made available online as a MATLAB package.">
@@ -558,7 +558,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2017-03-23</td>
           <td>IEEE Transactions on Computational Imaging</td>
-          <td>83</td>
+          <td>84</td>
           <td>30</td>
         </tr>
 
@@ -570,7 +570,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2010-10-04</td>
           <td>Advances in Computational Mathematics</td>
-          <td>79</td>
+          <td>80</td>
           <td>70</td>
         </tr>
 
@@ -582,7 +582,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2010-10-04</td>
           <td>Advances in Computational Mathematics</td>
-          <td>79</td>
+          <td>80</td>
           <td>70</td>
         </tr>
 
diff --git a/site/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/index.html b/site/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/index.html
index 791e9ee0..4f634880 100644
--- a/site/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/index.html
+++ b/site/recommendations/c3c94ccc094dcf546e8e31c9a42506302e837524/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:53 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:08 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -485,7 +485,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-04-23</td>
           <td>ArXiv</td>
           <td>5</td>
-          <td>49</td>
+          <td>50</td>
         </tr>
 
         <tr id="Time series are the primary data type used to record dynamic system measurements and generated in great volume by both physical sensors and online processes (virtual sensors). Time series analytics is therefore crucial to unlocking the wealth of information implicit in available data. With the recent advancements in graph neural networks (GNNs), there has been a surge in GNN-based approaches for time series analysis. These approaches can explicitly model inter-temporal and inter-variable relationships, which traditional and other deep neural network-based methods struggle to do. In this survey, we provide a comprehensive review of graph neural networks for time series analysis (GNN4TS), encompassing four fundamental dimensions: forecasting, classification, anomaly detection, and imputation. Our aim is to guide designers and practitioners to understand, build applications, and advance research of GNN4TS. At first, we provide a comprehensive task-oriented taxonomy of GNN4TS. Then, we present and discuss representative research works and introduce mainstream applications of GNN4TS. A comprehensive discussion of potential future research directions completes the survey. This survey, for the first time, brings together a vast array of knowledge on GNN-based time series research, highlighting foundations, practical applications, and opportunities of graph neural networks for time series analysis.">
@@ -495,9 +495,9 @@ <h3 data-intro='Recommendations for the article'>
             Ming Jin, Huan Yee Koh, Qingsong Wen, Daniele Zambon, C. Alippi, G. I. Webb, Irwin King, Shirui Pan
           </td>
           <td>2023-07-07</td>
-          <td>ArXiv</td>
-          <td>59</td>
-          <td>49</td>
+          <td>IEEE transactions on pattern analysis and machine intelligence</td>
+          <td>61</td>
+          <td>50</td>
         </tr>
 
         <tr id="Spatio-temporal forecasting of future values of spatially correlated time series is important across many cyber-physical systems (CPS). Recent studies offer evidence that the use of graph neural networks to capture latent correlations between time series holds a potential for enhanced forecasting. However, most existing methods rely on predefined or self-learning graphs, which are either static or unintentionally dynamic, and thus cannot model the time-varying correlations that exhibit trends and periodicities caused by the regularity of the underlying processes in CPS. To tackle such limitation, we propose Time-aware Graph Structure Learning (TagSL), which extracts time-aware correlations among time series by measuring the interaction of node and time representations in high-dimensional spaces. Notably, we introduce time discrepancy learning that utilizes contrastive learning with distance-based regularization terms to constrain learned spatial correlations to a trend sequence. Additionally, we propose a periodic discriminant function to enable the capture of periodic changes from the state of nodes. Next, we present a Graph Convolution-based Gated Recurrent Unit (GCGRU) that jointly captures spatial and temporal dependencies while learning time-aware and node-specific patterns. Finally, we introduce a unified framework named Time-aware Graph Convolutional Recurrent Network (TGCRN), combining TagSL, and GCGRU in an encoder-decoder architecture for multi-step spatiotemporal forecasting. We report on experiments with TGCRN and popular existing approaches on five real-world datasets, thus providing evidence that TGCRN is capable of advancing the state-of-the-art. We also cover a detailed ablation study and visualization analysis, offering detailed insight into the effectiveness of time-aware structure learning.">
@@ -532,7 +532,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-02-22</td>
           <td>ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</td>
-          <td>4</td>
+          <td>5</td>
           <td>42</td>
         </tr>
 
@@ -556,8 +556,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-02-17</td>
           <td>IEEE Transactions on Knowledge and Data Engineering</td>
-          <td>54</td>
-          <td>42</td>
+          <td>58</td>
+          <td>43</td>
         </tr>
 
         <tr id="Existing multivariate time series anomaly detection methods utilize graph neural networks to model inter-sensor dependencies and achieve satisfactory results. However, these methods often employ a predefined or self-learning static adjacency matrix for graph information aggregation, disregarding the dynamic characteristics of inter-sensor dependencies in the real world, which change over time and are observable at different time scales as dynamic changing graph structure information. Furthermore, existing techniques struggle to capture long-term temporal contextual relationships. To address these issues, we propose a Dynamic Graph Learning with Long and Short-term time model (DGL-LS) for multivariate time series anomaly detection. The network integrates a dynamic graph structure learning method among sensors in multi-time mode and long- and short-term temporal context information to enhance the prediction of multivariate time series anomalies. We propose a strategy for learning dynamic graphs that aggregates sensor node representations at various time intervals, and then uses an attention-based gating unit to evolve the node dynamic characterization and construct a series of adjacency matrices that describe the dynamic changes in graph structure over time. Moreover, we formulate a long-short time convolution to capture the long-term and short-term temporal dependencies within the time series. We demonstrate the superiority of our approach over other state-of-the-art methods by conducting extensive experiments on three publicly available datasets.">
@@ -569,7 +569,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-09-07</td>
           <td>2023 IEEE 12th International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS)</td>
           <td>0</td>
-          <td>3</td>
+          <td>4</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/index.html b/site/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/index.html
index 0de40a3b..eadf0816 100644
--- a/site/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/index.html
+++ b/site/recommendations/ccea298edb788edf821aef58f0952c3e8debc25a/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:45 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:04:58 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -509,7 +509,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-05-26</td>
           <td>J. Mach. Learn. Res.</td>
           <td>11</td>
-          <td>49</td>
+          <td>50</td>
         </tr>
 
         <tr id="The challenge of effectively learning inter-series correlations for multivariate time series forecasting remains a substantial and unresolved problem. Traditional deep learning models, which are largely dependent on the Transformer paradigm for modeling long sequences, often fail to integrate information from multiple time series into a coherent and universally applicable model. To bridge this gap, our paper presents ForecastGrapher, a framework reconceptualizes multivariate time series forecasting as a node regression task, providing a unique avenue for capturing the intricate temporal dynamics and inter-series correlations. Our approach is underpinned by three pivotal steps: firstly, generating custom node embeddings to reflect the temporal variations within each series; secondly, constructing an adaptive adjacency matrix to encode the inter-series correlations; and thirdly, augmenting the GNNs' expressive power by diversifying the node feature distribution. To enhance this expressive power, we introduce the Group Feature Convolution GNN (GFC-GNN). This model employs a learnable scaler to segment node features into multiple groups and applies one-dimensional convolutions with different kernel lengths to each group prior to the aggregation phase. Consequently, the GFC-GNN method enriches the diversity of node feature distribution in a fully end-to-end fashion. Through extensive experiments and ablation studies, we show that ForecastGrapher surpasses strong baselines and leading published techniques in the domain of multivariate time series forecasting.">
@@ -532,8 +532,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-24</td>
           <td>Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining</td>
-          <td>934</td>
-          <td>54</td>
+          <td>950</td>
+          <td>55</td>
         </tr>
 
         <tr id="Graph Neural Networks (GNN) have gained significant traction in the forecasting domain, especially for their capacity to simultaneously account for intra-series temporal correlations and inter-series relationships. This paper introduces a novel Hierarchical GNN (DeepHGNN) framework, explicitly designed for forecasting in complex hierarchical structures. The uniqueness of DeepHGNN lies in its innovative graph-based hierarchical interpolation and an end-to-end reconciliation mechanism. This approach ensures forecast accuracy and coherence across various hierarchical levels while sharing signals across them, addressing a key challenge in hierarchical forecasting. A critical insight in hierarchical time series is the variance in forecastability across levels, with upper levels typically presenting more predictable components. DeepHGNN capitalizes on this insight by pooling and leveraging knowledge from all hierarchy levels, thereby enhancing the overall forecast accuracy. Our comprehensive evaluation set against several state-of-the-art models confirm the superior performance of DeepHGNN. This research not only demonstrates DeepHGNN's effectiveness in achieving significantly improved forecast accuracy but also contributes to the understanding of graph-based methods in hierarchical time series forecasting.">
@@ -556,8 +556,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-11-10</td>
           <td>ArXiv</td>
-          <td>24</td>
-          <td>4</td>
+          <td>30</td>
+          <td>5</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/index.html b/site/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/index.html
index f11b5312..da4b9cff 100644
--- a/site/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/index.html
+++ b/site/recommendations/d3dbbd0f0de51b421a6220bd6480b8d2e99a88e9/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:41 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:04:55 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -509,7 +509,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-10-24</td>
           <td>ArXiv</td>
           <td>4</td>
-          <td>49</td>
+          <td>50</td>
         </tr>
 
         <tr id="With the recent advances in technology, a wide range of systems continue to collect a large amount of data over time and thus generate time series. Time-Series Anomaly Detection (TSAD) is an important task in various time-series applications such as e-commerce, cybersecurity, vehicle maintenance, and healthcare monitoring. However, this task is very challenging as it requires considering both the intra-variable dependency and the inter-variable dependency, where a variable can be defined as an observation in time-series data. Recent graph-based approaches have made impressive progress in tackling the challenges of this field. In this survey, we conduct a comprehensive and up-to-date review of TSAD using graphs, referred to as G-TSAD. First, we explore the significant potential of graph representation learning for time-series data. Then, we review state-of-the-art graph anomaly detection techniques in the context of time series and discuss their strengths and drawbacks. Finally, we discuss the technical challenges and potential future directions for possible improvements in this research field.">
@@ -520,7 +520,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-01-31</td>
           <td>ArXiv</td>
-          <td>6</td>
+          <td>4</td>
           <td>15</td>
         </tr>
 
@@ -532,8 +532,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-11-10</td>
           <td>ArXiv</td>
-          <td>24</td>
-          <td>4</td>
+          <td>30</td>
+          <td>5</td>
         </tr>
 
         <tr id="Anomaly detection of time series, especially multivariate time series(time series with multiple sensors), has been focused on for several years. Though existing method has achieved great progress, there are several challenging problems to be solved. Firstly, existing method including neural network only concentrate on the relationship in terms of timestamp. To be exact, they only want to know how does the data in the past influence which in the future. However, one sensor sometimes intervenes in other sensor such as the speed of wind may cause decrease of temperature. Secondly, there exist two categories of model for time series anomaly detection: prediction model and reconstruction model. Prediction model is adept at learning timely representation while short of capability when faced with sparse anomaly. Conversely, reconstruction model is opposite. Therefore, how can we efficiently get the relationship both in terms of both timestamp and sensors becomes our main topic. Our approach uses GAT, which is originated from graph neural network, to obtain connection between sensors. And LSTM is used to obtain relationships timely. Our approach is also designed to be double headed to calculate both prediction loss and reconstruction loss via VAE(Variational Auto-Encoder). In order to take advantage of two sorts of model, multi-task optimization algorithm is used in this model.">
@@ -556,7 +556,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-02-04</td>
           <td>ArXiv</td>
-          <td>3</td>
+          <td>4</td>
           <td>22</td>
         </tr>
 
@@ -593,7 +593,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-07-17</td>
           <td>IEEE transactions on neural networks and learning systems</td>
           <td>8</td>
-          <td>18</td>
+          <td>19</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/index.html b/site/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/index.html
index 0f851a55..c0ff51f0 100644
--- a/site/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/index.html
+++ b/site/recommendations/e2a83369383aff37224170c1ae3d3870d5d9e419/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:43 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:04:57 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -485,7 +485,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2023-10-24</td>
           <td>ArXiv</td>
           <td>4</td>
-          <td>49</td>
+          <td>50</td>
         </tr>
 
         <tr id="Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in most spatiotemporal GNNs, the computational complexity scales up to a quadratic factor with the length of the sequence times the number of links in the graph, hence hindering the application of these models to large graphs and long temporal sequences. While methods to improve scalability have been proposed in the context of static graphs, few research efforts have been devoted to the spatiotemporal case. To fill this gap, we propose a scalable architecture that exploits an efficient encoding of both temporal and spatial dynamics. In particular, we use a randomized recurrent neural network to embed the history of the input time series into high-dimensional state representations encompassing multi-scale temporal dynamics. Such representations are then propagated along the spatial dimension using different powers of the graph adjacency matrix to generate node embeddings characterized by a rich pool of spatiotemporal features. The resulting node embeddings can be efficiently pre-computed in an unsupervised manner, before being fed to a feed-forward decoder that learns to map the multi-scale spatiotemporal representations to predictions. The training procedure can then be parallelized node-wise by sampling the node embeddings without breaking any dependency, thus enabling scalability to large networks. Empirical results on relevant datasets show that our approach achieves results competitive with the state of the art, while dramatically reducing the computational burden.">
@@ -496,8 +496,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2022-09-14</td>
           <td>ArXiv</td>
-          <td>27</td>
-          <td>49</td>
+          <td>29</td>
+          <td>50</td>
         </tr>
 
         <tr id="Outstanding achievements of graph neural networks for spatiotemporal time series analysis show that relational constraints introduce an effective inductive bias into neural forecasting architectures. Often, however, the relational information characterizing the underlying data-generating process is unavailable and the practitioner is left with the problem of inferring from data which relational graph to use in the subsequent processing stages. We propose novel, principled - yet practical - probabilistic score-based methods that learn the relational dependencies as distributions over graphs while maximizing end-to-end the performance at task. The proposed graph learning framework is based on consolidated variance reduction techniques for Monte Carlo score-based gradient estimation, is theoretically grounded, and, as we show, effective in practice. In this paper, we focus on the time series forecasting problem and show that, by tailoring the gradient estimators to the graph learning problem, we are able to achieve state-of-the-art performance while controlling the sparsity of the learned graph and the computational scalability. We empirically assess the effectiveness of the proposed method on synthetic and real-world benchmarks, showing that the proposed solution can be used as a stand-alone graph identification procedure as well as a graph learning component of an end-to-end forecasting architecture.">
@@ -509,7 +509,7 @@ <h3 data-intro='Recommendations for the article'>
           <td>2022-05-26</td>
           <td>J. Mach. Learn. Res.</td>
           <td>11</td>
-          <td>49</td>
+          <td>50</td>
         </tr>
 
         <tr id="Time series forecasting with additional spatial de-pendencies has attracted a tremendous amount of research interest in social sciences, due to its importance in modern real-world applications. The Graph Neural Networks (GNN) is one of the most exciting deep learning techniques among these spatio-temporal modeling approaches. Most existing spatio-temporal GNN frameworks are based on a two-step modeling process. In such scenario, spatial and temporal dependencies are modeled in separate steps, which lead to problems such as complex architecture design, hard to scale, etc. Targeting the shortcomings of existing studies, we take both spatial and temporal dependencies from another perspective, and consider them as two heterogeneous types of edges in the graph. We propose a unified spatio-temporal GNN framework that captures both dependencies in a single step. More specifically, for each node in the graph, a unified neural network component is designed to simultaneously extract information from its sur-rounding neighbors (spatial) and its past records (temporal), which enables much easier dependency aggregation with faster execution. Experiment results demonstrate the superiority of the proposed framework over state-of-the-art (SOTA) baselines on various applications, including modeling smart cities and data-driven political science research.">
@@ -544,8 +544,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-11-10</td>
           <td>ArXiv</td>
-          <td>24</td>
-          <td>4</td>
+          <td>30</td>
+          <td>5</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/index.html b/site/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/index.html
index 1d1f3084..e04ea48b 100644
--- a/site/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/index.html
+++ b/site/recommendations/e2e1f1b8e6c1b7f4f166e15b7c674945856a51b6/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:50 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:03 UTC</i>
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   <div class="note info" onclick="startIntro()">
@@ -492,12 +492,12 @@ <h3 data-intro='Recommendations for the article'>
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/818793961396bbe4c744932676f0ff9cc8385bed" target='_blank'>Generative Pre-Trained Diffusion Paradigm for Zero-Shot Time Series Forecasting</a></td>
           <td>
-            Jiarui Yang, Tao Dai, Naiqi Li, Junxi Wu, Peiyuan Liu, Jinmin Li, Jigang Bao, Haigang Zhang, Shutao Xia
+            Jiarui Yang, Tao Dai, Naiqi Li, Junxi Wu, Peiyuan Liu, Jinmin Li, Jigang Bao, Haigang Zhang, Shu-Tao Xia
           </td>
           <td>2024-06-04</td>
           <td>ArXiv</td>
           <td>0</td>
-          <td>3</td>
+          <td>4</td>
         </tr>
 
         <tr id="We introduce Chronos, a simple yet effective framework for pretrained probabilistic time series models. Chronos tokenizes time series values using scaling and quantization into a fixed vocabulary and trains existing transformer-based language model architectures on these tokenized time series via the cross-entropy loss. We pretrained Chronos models based on the T5 family (ranging from 20M to 710M parameters) on a large collection of publicly available datasets, complemented by a synthetic dataset that we generated via Gaussian processes to improve generalization. In a comprehensive benchmark consisting of 42 datasets, and comprising both classical local models and deep learning methods, we show that Chronos models: (a) significantly outperform other methods on datasets that were part of the training corpus; and (b) have comparable and occasionally superior zero-shot performance on new datasets, relative to methods that were trained specifically on them. Our results demonstrate that Chronos models can leverage time series data from diverse domains to improve zero-shot accuracy on unseen forecasting tasks, positioning pretrained models as a viable tool to greatly simplify forecasting pipelines.">
@@ -508,7 +508,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>23</td>
+          <td>27</td>
           <td>18</td>
         </tr>
 
@@ -520,7 +520,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-12</td>
           <td>ArXiv</td>
-          <td>13</td>
+          <td>14</td>
           <td>40</td>
         </tr>
 
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-07</td>
           <td>ArXiv</td>
-          <td>4</td>
+          <td>5</td>
           <td>5</td>
         </tr>
 
diff --git a/site/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/index.html b/site/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/index.html
index 812e1450..9b031606 100644
--- a/site/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/index.html
+++ b/site/recommendations/e6f0a85009481dcfd93aaa43ed3f980e5033b0d8/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 09:00:12 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:40 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -496,8 +496,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2015-09-11</td>
           <td>Proceedings of the National Academy of Sciences</td>
-          <td>3159</td>
-          <td>63</td>
+          <td>3190</td>
+          <td>65</td>
         </tr>
 
         <tr id="Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that violate basic physical laws. This work proposes a novel method for the Sparse Identification of Nonlinear Dynamics with Side Information (SINDy-SI). SINDy-SI is an iterative method that uses Sum-of-Squares (SOS) programming to learn optimally fitted models while guaranteeing that the learned model satisfies side information, such as symmetry's and physical laws. Guided by the principle of Occam's razor, that the simplest or most regularized best fitted model is typically the superior choice, during each iteration SINDy-SI prunes the basis functions associated with small coefficients, yielding a sparse dynamical model upon termination. Through several numerical experiments we will show how the combination of side information constraints and sparse polynomial representation cultivates dynamical models that obey known physical laws while displaying impressive generalized performance beyond the training set.">
@@ -520,8 +520,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2021-11-12</td>
           <td>J. Open Source Softw.</td>
-          <td>108</td>
-          <td>63</td>
+          <td>109</td>
+          <td>65</td>
         </tr>
 
         <tr id="Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the uncertainty inherent in differential equations learned from data remains an open problem, thus we propose leveraging recent advances in statistical inference for sparse regression to address this issue. Focusing on systems of ordinary differential equations (ODEs), SINDy assumes that each equation is a parsimonious linear combination of a few candidate functions, such as polynomials, and uses methods such as sequentially-thresholded least squares or the Lasso to identify a small subset of these functions that govern the system's dynamics. We instead employ bias-corrected versions of the Lasso and ridge regression estimators, as well as an empirical Bayes variable selection technique known as SEMMS, to estimate each ODE as a linear combination of terms that are statistically significant. We demonstrate through simulations that this approach allows us to recover the functional terms that correctly describe the dynamics more often than existing methods that do not account for uncertainty.">
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-05-05</td>
           <td>Nature Communications</td>
-          <td>234</td>
+          <td>238</td>
           <td>12</td>
         </tr>
 
@@ -556,8 +556,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2020-04-17</td>
           <td>arXiv: Dynamical Systems</td>
-          <td>46</td>
-          <td>63</td>
+          <td>47</td>
+          <td>65</td>
         </tr>
 
         <tr id="Data-driven modeling frameworks that adopt sparse regression techniques, such as sparse identification of nonlinear dynamics (SINDy) and its modifications, are developed to resolve difficulties in extracting underlying dynamics from experimental data. In contrast to neural-network-based methods, these methods are designed to obtain white-box analytical models. In this work, we incorporate the concept of SINDy and knowledge in the field of classical mechanics to identify interpretable and sparse expressions of total energy and the Lagrangian that shelters the hidden dynamics. Moreover, our method (hereafter referred as Lagrangian-SINDy) is developed to use knowledge of simple systems that form the system being analyzed to ensure the likelihood of correct results and to improve the learning pace. Lagrangian-SINDy is highly accurate in discovering interpretable dynamics via energy-related physical quantities. Its performance is validated with three popular multi-DOF nonlinear dynamical systems, namely the spherical pendulum, double pendulum and cart-pendulum system. Comparisons with other SINDy-based methods are made and Lagrangian-SINDy is found to provide the most compact analytical models.">
@@ -572,18 +572,6 @@ <h3 data-intro='Recommendations for the article'>
           <td>23</td>
         </tr>
 
-        <tr id="Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based optimization technique that enables the control of such nonlinear systems with constraints. However, modern systems often lack computationally tractable models, motivating the use of system identification techniques to learn accurate and efficient models for real-time control. In this tutorial article, we review emerging data-driven methods for model discovery and how they are used for nonlinear MPC. In particular, we focus on the sparse identification of nonlinear dynamics (SINDy) algorithm and show how it may be used with MPC on an infectious disease control example. We compare the performance against MPC based on a linear dynamic mode decomposition (DMD) model. Code is provided to run the tutorial examples and may be modified to extend this data-driven control framework to arbitrary nonlinear systems.">
-          <td id="tag"><i class="material-icons">visibility_off</i></td>
-          <td><a href="https://www.semanticscholar.org/paper/700552dde778bd1f6b76f7237e9b561597b859ba" target='_blank'>SINDy with Control: A Tutorial</a></td>
-          <td>
-            Urban Fasel, E. Kaiser, J. Kutz, Bingni W. Brunton, S. Brunton
-          </td>
-          <td>2021-08-30</td>
-          <td>2021 60th IEEE Conference on Decision and Control (CDC)</td>
-          <td>45</td>
-          <td>63</td>
-        </tr>
-
         <tr id="With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics (SINDy) has been introduced to identify the governing equations of dynamical systems from simulation data. In this study, we extend SINDy to stochastic dynamical systems which are frequently used to model biophysical processes. We prove the asymptotic correctness of stochastic SINDy in the infinite data limit, both in the original and projected variables. We discuss algorithms to solve the sparse regression problem arising from the practical implementation of SINDy and show that cross validation is an essential tool to determine the right level of sparsity. We demonstrate the proposed methodology on two test systems, namely, the diffusion in a one-dimensional potential and the projected dynamics of a two-dimensional diffusion process.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/8787d66296c0337aeb54d87885d29a63af17711b" target='_blank'>Sparse learning of stochastic dynamical equations.</a></td>
@@ -592,8 +580,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2017-12-06</td>
           <td>The Journal of chemical physics</td>
-          <td>189</td>
-          <td>44</td>
+          <td>191</td>
+          <td>45</td>
         </tr>
 
   </tbody>
diff --git a/site/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/index.html b/site/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/index.html
index 30d4b39e..1df9551e 100644
--- a/site/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/index.html
+++ b/site/recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:48 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:01 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,7 +484,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-12</td>
           <td>ArXiv</td>
-          <td>13</td>
+          <td>14</td>
           <td>40</td>
         </tr>
 
@@ -508,7 +508,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2023-10-03</td>
           <td>ArXiv</td>
-          <td>109</td>
+          <td>120</td>
           <td>9</td>
         </tr>
 
diff --git a/site/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/index.html b/site/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/index.html
index 63e453c9..d65bfb41 100644
--- a/site/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/index.html
+++ b/site/recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/index.html
@@ -445,7 +445,7 @@ <h1 id="_1"></h1>
 
 <body>
   <p>
-  <i class="footer">This page was last updated on 2024-08-05 08:59:54 UTC</i>
+  <i class="footer">This page was last updated on 2024-08-19 06:05:12 UTC</i>
   </p>
 
   <div class="note info" onclick="startIntro()">
@@ -484,8 +484,8 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-04</td>
           <td>ArXiv</td>
-          <td>6</td>
-          <td>65</td>
+          <td>5</td>
+          <td>66</td>
         </tr>
 
         <tr id="Large pre-trained models have been vital in recent advancements in domains like language and vision, making model training for individual downstream tasks more efficient and provide superior performance. However, tackling time-series analysis tasks usually involves designing and training a separate model from scratch leveraging training data and domain expertise specific to the task. We tackle a significant challenge for pre-training a foundational time-series model from multi-domain time-series datasets: extracting semantically useful tokenized inputs to the model across heterogenous time-series from different domains. We propose Large Pre-trained Time-series Models (LPTM) that introduces a novel method of \textit{adaptive segmentation} that automatically identifies optimal dataset-specific segmentation strategy during pre-training. This enables LPTM to perform similar to or better than domain-specific state-of-art model when fine-tuned to different downstream time-series analysis tasks and under zero-shot settings. LPTM achieves superior forecasting and time-series classification results taking up to 40% less data and 50% less training time compared to state-of-art baselines.">
@@ -508,7 +508,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-26</td>
           <td>ArXiv</td>
-          <td>3</td>
+          <td>4</td>
           <td>3</td>
         </tr>
 
@@ -544,7 +544,7 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-03-12</td>
           <td>ArXiv</td>
-          <td>23</td>
+          <td>27</td>
           <td>18</td>
         </tr>
 
@@ -556,11 +556,11 @@ <h3 data-intro='Recommendations for the article'>
           </td>
           <td>2024-02-04</td>
           <td>ArXiv</td>
-          <td>26</td>
+          <td>28</td>
           <td>22</td>
         </tr>
 
-        <tr id="Learning time-series representations for discriminative tasks has been a long-standing challenge. Current pre-training methods are limited in either unidirectional next-token prediction or randomly masked token prediction. We propose a novel architecture called Bidirectional Timely Generative Pre-trained Transformer (BiTimelyGPT), which pre-trains on time-series data by both next-token and previous-token predictions in alternating transformer layers. This pre-training task preserves original distribution and data shapes of the time-series. Additionally, the full-rank forward and backward attention matrices exhibit more expressive representation capabilities. Using biosignal data, BiTimelyGPT demonstrates superior performance in predicting neurological functionality, disease diagnosis, and physiological signs. By visualizing the attention heatmap, we observe that the pre-trained BiTimelyGPT can identify discriminative segments from time-series sequences, even more so after fine-tuning on the task.">
+        <tr id="Learning time-series representations for discriminative tasks, such as classification and regression, has been a long-standing challenge in the healthcare domain. Current pre-training methods are limited in either unidirectional next-token prediction or randomly masked token prediction. We propose a novel architecture called Bidirectional Timely Generative Pre-trained Transformer (BiTimelyGPT), which pre-trains on biosignals and longitudinal clinical records by both next-token and previous-token prediction in alternating transformer layers. This pre-training task preserves original distribution and data shapes of the time-series. Additionally, the full-rank forward and backward attention matrices exhibit more expressive representation capabilities. Using biosignals and longitudinal clinical records, BiTimelyGPT demonstrates superior performance in predicting neurological functionality, disease diagnosis, and physiological signs. By visualizing the attention heatmap, we observe that the pre-trained BiTimelyGPT can identify discriminative segments from biosignal time-series sequences, even more so after fine-tuning on the task.">
           <td id="tag"><i class="material-icons">visibility_off</i></td>
           <td><a href="https://www.semanticscholar.org/paper/1d0328153f4136635b7df336fb958c92d066ac29" target='_blank'>Bidirectional Generative Pre-training for Improving Time Series Representation Learning</a></td>
           <td>
diff --git a/site/search/search_index.json b/site/search/search_index.json
index 0a17a87d..86e569f6 100644
--- a/site/search/search_index.json
+++ b/site/search/search_index.json
@@ -1 +1 @@
-{"config":{"lang":["en"],"separator":"[\\s\\-]+","pipeline":["stopWordFilter"]},"docs":[{"location":"","title":"Home","text":"Introduction <p>Welcome to Team VPE's Literature Survey System! This project leverages the powerful Semantic Scholar's Recommendation API to provide you with highly relevant research article recommendations based on your curated lists of articles.</p> <p>Moreover, this website contains curated collection of references on differentiable and learned simulator algorithms for developing digital twins with applications in drug discovery and development.</p> Features <ul> <li>List-based recommendations: For each topic, we use a manually curated list of positive articles. We then select an equal number of negative articles from other topics. Semantics Scholar's recommendation system uses the set of positive and negative to provide up to 300 recommendations per topic.</li> <li>Single-paper recommendations: For each article in our curated lists, Semantics Scholar's recommendation system returns up to 10 related articles.</li> </ul> How it works? <ul> <li>Scroll to the top of this page and click one of the tabs to open the relevant section.</li> <li>Each topic contains two tables. The first table lists the manually curated articles, and the second table lists the articles recommended for that topic by the recommendation system. The last column of the first table contains a hyperlink that opens a new tab with articles recommended for that specific article.</li> <li>Click on the help icon at the top of the page to learn more about that section.</li> </ul>         Check out our GitHub open_in_new repository to learn how to build one for yourself."},{"location":"Symbolic%20regression/","title":"Symbolic regression","text":"<p> This page was last updated on 2024-08-05 09:00:19 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p> </p> <p> </p>"},{"location":"Symbolic%20regression/#manually_curated_articles","title":"Manually curated articles on Symbolic regression","text":"Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index                View recommendations                visibility_off                  Discovering governing equations from data by sparse identification of nonlinear dynamical systems                               S. Brunton, J. Proctor, J. Kutz            2015-09-11 Proceedings of the National Academy of Sciences of the United States of America, Proceedings of the National Academy of Sciences 3159 63 open_in_new visibility_off                  Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression                               Patrick A. K. Reinbold, Logan Kageorge, M. Schatz, R. Grigoriev            2021-02-24 Nature Communications 84 23 open_in_new visibility_off                  Data-driven discovery of coordinates and governing equations                               Kathleen P. Champion, Bethany Lusch, J. Kutz, S. Brunton            2019-03-29 Proceedings of the National Academy of Sciences of the United States of America 595 63 open_in_new visibility_off                  Chaos as an intermittently forced linear system                               S. Brunton, Bingni W. Brunton, J. Proctor, E. Kaiser, J. Kutz            2016-08-18 Nature Communications 446 63 open_in_new visibility_off                  Sparse identification of nonlinear dynamics for model predictive control in the low-data limit                               E. Kaiser, J. Kutz, S. Brunton            2017-11-15 Proceedings of the Royal Society A, Proceedings. Mathematical, Physical, and Engineering Sciences 425 63 open_in_new visibility_off                  Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics                               N. Mangan, S. Brunton, J. Proctor, J. Kutz            2016-05-26 IEEE Transactions on Molecular Biological and Multi-Scale Communications, IEEE Transactions on Molecular, Biological and Multi-Scale Communications 314 63 open_in_new visibility_off                  SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics                               Kadierdan Kaheman, J. Kutz, S. Brunton            2020-04-05 Proceedings of the Royal Society A, Proceedings. Mathematical, Physical, and Engineering Sciences 190 63 open_in_new visibility_off                  Multidimensional Approximation of Nonlinear Dynamical Systems                               Patrick Gel\u00df, Stefan Klus, J. Eisert, Christof Schutte            2018-09-07 Journal of Computational and Nonlinear Dynamics 61 76 open_in_new visibility_off                  Learning Discrepancy Models From Experimental Data                               Kadierdan Kaheman, E. Kaiser, B. Strom, J. Kutz, S. Brunton            2019-09-18 ArXiv, arXiv.org 31 63 open_in_new visibility_off                  Discovery of Physics From Data: Universal Laws and Discrepancies                               Brian M. de Silva, D. Higdon, S. Brunton, J. Kutz            2019-06-19 Frontiers in Artificial Intelligence 66 63 open_in_new visibility_off                  Data-driven discovery of partial differential equations                               S. Rudy, S. Brunton, J. Proctor, J. Kutz            2016-09-21 Science Advances 1164 63 open_in_new visibility_off                  Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control                               Urban Fasel, J. Kutz, Bingni W. Brunton, S. Brunton            2021-11-22 Proceedings of the Royal Society A, Proceedings. Mathematical, Physical, and Engineering Sciences 154 63 open_in_new visibility_off                  Learning sparse nonlinear dynamics via mixed-integer optimization                               D. Bertsimas, Wes Gurnee            2022-06-01 Nonlinear Dynamics 27 90 open_in_new visibility_off                  A Unified Framework for Sparse Relaxed Regularized Regression: SR3                               P. Zheng, T. Askham, S. Brunton, J. Kutz, A. Aravkin            2018-07-14 IEEE Access 114 63 open_in_new Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index View recommendations"},{"location":"Symbolic%20regression/#recommended_articles","title":"Recommended articles on Symbolic regression","text":"Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index visibility_off                Discovering governing equation in structural dynamics from acceleration-only measurements                             Calvin Alvares, Souvik Chakraborty            2024-07-18 ArXiv 0 0 visibility_off                Discovery of differential equations using sparse state and parameter regression                             Teddy Meissner, Karl Glasner            2024-06-10 ArXiv 0 0 visibility_off                Minimum Reduced-Order Models via Causal Inference                             Nan Chen, Honghu Liu            2024-06-29 ArXiv 0 0 visibility_off                Data-driven system identification of unknown systems utilising sparse identification of nonlinear dynamics (SINDy)                             P. Pandey, H. Haddad Khodaparast, M. Friswell, T. Chatterjee, N. Jamia, T. Deighan            2024-06-01 Journal of Physics: Conference Series 0 1 visibility_off                Data-driven Discovery of Delay Differential Equations with Discrete Delays                             Alessandro Pecile, N. Demo, M. Tezzele, G. Rozza, Dimitri Breda            2024-07-29 ArXiv 0 49 visibility_off                Learning dynamical systems from data: An introduction to physics-guided deep learning                             Rose Yu, Rui Wang            2024-06-24 Proceedings of the National Academy of Sciences of the United States of America 1 1 visibility_off                Principal Component Flow Map Learning of PDEs from Incomplete, Limited, and Noisy Data                             Victor Churchill            2024-07-15 ArXiv 0 0 visibility_off                Sparse identification of quasipotentials via a combined data-driven method                             Bo Lin, P. Belardinelli            2024-07-06 ArXiv 0 12 visibility_off                KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics                             Benjamin C. Koenig, Suyong Kim, Sili Deng            2024-07-05 ArXiv 2 22 visibility_off                Physics-informed active learning with simultaneous weak-form latent space dynamics identification                             Xiaolong He, April Tran, David M. Bortz, Youngsoo Choi            2024-06-29 ArXiv 0 3 visibility_off                Data-Driven Linearization of Dynamical Systems                             George Haller, B. Kasz'as            2024-07-11 ArXiv 1 0 visibility_off                Learning Networked Dynamical System Models with Weak Form and Graph Neural Networks                             Yin Yu, Daning Huang, Seho Park, H. Pangborn            2024-07-23 ArXiv 0 11 visibility_off                Modeling Nonlinear Dynamics from Videos                             Antony Yang, Joar Axaas, Fanni K'ad'ar, G'abor St'ep'an, George Haller            2024-06-13 ArXiv 1 0 visibility_off                How more data can hurt: Instability and regularization in next-generation reservoir computing                             Yuanzhao Zhang, Sean P. Cornelius            2024-07-11 ArXiv 0 1 visibility_off                MBD-NODE: physics-informed data-driven modeling and simulation of constrained multibody systems                             Jingquan Wang, Shu Wang, H. Unjhawala, Jinlong Wu, D. Negrut            2024-07-11 Multibody System Dynamics 0 28 visibility_off                Data-Driven Computing Methods for Nonlinear Physics Systems with Geometric Constraints                             Yunjin Tong            2024-06-20 ArXiv 0 0 visibility_off                Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systems                             James H. Adler, Samuel Hocking, Xiaozhe Hu, Shafiqul Islam            2024-07-25 ArXiv 0 2 visibility_off                Identifying Ordinary Differential Equations for Data-efficient Model-based Reinforcement Learning                             Tobias Nagel, Marco F. Huber            2024-06-28 ArXiv 0 2 visibility_off                Development of data-driven modeling method for nonlinear coupling components                             Taesan Ryu, Seunghun Baek            2024-06-27 Scientific Reports 0 0 visibility_off                Tangent and Normal Space-Based Method for Dynamics Identification in Microgrids                             Hanyang He, John Harlim, Daning Huang, Yan Li            2024-06-19 2024 IEEE Transportation Electrification Conference and Expo (ITEC) 0 0 visibility_off                Stable Sparse Operator Inference for Nonlinear Structural Dynamics                             P. D. Boef, Diana Manvelyan, Jos Maubach, W. Schilders, N. Wouw            2024-07-31 ArXiv 0 47 visibility_off                Extended Lagrangian-Informed Deep Learning and Control for Electro-mechanical Systems                             Nikhil Pagar, Pegah Ghaf-Ghanbari, Atul G. Kelkar, Javad Mohammadpour            2024-06-25 2024 European Control Conference (ECC) 0 4 visibility_off                Tensor-Based Data-Driven Identification of Partial Differential Equations                             Wanting Lin, Xiaofan Lu, Linan Zhang            2024-06-10 Journal of Computational and Nonlinear Dynamics 0 1 visibility_off                Physics-constrained learning for PDE systems with uncertainty quantified port-Hamiltonian models                             Kaiyuan Tan, Peilun Li, Thomas Beckers            2024-06-17 DBLP, ArXiv 0 1 visibility_off                Promising directions of machine learning for partial differential equations.                             Steve Brunton, J. 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Kopp, Lisa Fuchs, Christoph Ament            2024-06-11 2024 32nd Mediterranean Conference on Control and Automation (MED) 0 0 visibility_off                Estimation of Carleman operator from a univariate time series.                             Sherehe Semba, Huijie Yang, Xiaolu Chen, Huiyun Wan, C. Gu            2024-08-01 Chaos 0 17 visibility_off                Model Predictive Control of the Neural Manifold                             Christof Fehrman, C. D. 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Phys. 50 11 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/ae42c0cff384495683192b06bd985cdd7a54632a/","title":"Ae42c0cff384495683192b06bd985cdd7a54632a","text":""},{"location":"recommendations/ae42c0cff384495683192b06bd985cdd7a54632a/#_1","title":"Ae42c0cff384495683192b06bd985cdd7a54632a","text":"<p> This page was last updated on 2024-07-22 06:06:19 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Interaction Networks for Learning about Objects, Relations and Physics Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Flexible Neural Representation for Physics Prediction              Damian Mrowca, Chengxu Zhuang, E. Wang, Nick Haber, Li Fei-Fei, J. 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Clementi            2017-12-06 The Journal of chemical physics 189 44 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/","title":"F45f85fa1beaa795c24c4ff86f1f2deece72252f","text":""},{"location":"recommendations/f45f85fa1beaa795c24c4ff86f1f2deece72252f/#_1","title":"F45f85fa1beaa795c24c4ff86f1f2deece72252f","text":"<p> This page was last updated on 2024-08-05 08:59:48 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article A decoder-only foundation model for time-series forecasting Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Lag-Llama: Towards Foundation Models for Probabilistic Time Series Forecasting              Kashif Rasul, Arjun Ashok, Andrew Robert Williams, Arian Khorasani, George Adamopoulos, Rishika Bhagwatkar, Marin Bilovs, Hena Ghonia, N. Hassen, Anderson Schneider, Sahil Garg, Alexandre Drouin, Nicolas Chapados, Yuriy Nevmyvaka, I. Rish            2023-10-12 ArXiv 13 40 visibility_off Are Language Models Actually Useful for Time Series Forecasting?              Mingtian Tan, Mike A. Merrill, Vinayak Gupta, Tim Althoff, Tom Hartvigsen            2024-06-22 ArXiv 0 3 visibility_off Time-LLM: Time Series Forecasting by Reprogramming Large Language Models              Ming Jin, Shiyu Wang, Lintao Ma, Zhixuan Chu, James Y. Zhang, X. 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Choudhry, Wonmin Byeon            2022-02-24 ArXiv 4 91 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/","title":"Ff1f1cf9df8c413ec7345da7604ba28597da5b90","text":""},{"location":"recommendations/ff1f1cf9df8c413ec7345da7604ba28597da5b90/#_1","title":"Ff1f1cf9df8c413ec7345da7604ba28597da5b90","text":"<p> This page was last updated on 2024-08-05 08:59:54 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article UNITS: A Unified Multi-Task Time Series Model Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Timer: Generative Pre-trained Transformers Are Large Time Series Models              Yong Liu, Haoran Zhang, Chenyu Li, Xiangdong Huang, Jianmin Wang, Mingsheng Long            2024-02-04 ArXiv 6 65 visibility_off Large Pre-trained time series models for cross-domain Time series analysis tasks              Harshavardhan Kamarthi, B. 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+{"config":{"lang":["en"],"separator":"[\\s\\-]+","pipeline":["stopWordFilter"]},"docs":[{"location":"","title":"Home","text":"Introduction <p>Welcome to Team VPE's Literature Survey System! This project leverages the powerful Semantic Scholar's Recommendation API to provide you with highly relevant research article recommendations based on your curated lists of articles.</p> <p>Moreover, this website contains curated collection of references on differentiable and learned simulator algorithms for developing digital twins with applications in drug discovery and development.</p> Features <ul> <li>List-based recommendations: For each topic, we use a manually curated list of positive articles. We then select an equal number of negative articles from other topics. Semantics Scholar's recommendation system uses the set of positive and negative to provide up to 300 recommendations per topic.</li> <li>Single-paper recommendations: For each article in our curated lists, Semantics Scholar's recommendation system returns up to 10 related articles.</li> </ul> How it works? <ul> <li>Scroll to the top of this page and click one of the tabs to open the relevant section.</li> <li>Each topic contains two tables. The first table lists the manually curated articles, and the second table lists the articles recommended for that topic by the recommendation system. The last column of the first table contains a hyperlink that opens a new tab with articles recommended for that specific article.</li> <li>Click on the help icon at the top of the page to learn more about that section.</li> </ul>         Check out our GitHub open_in_new repository to learn how to build one for yourself."},{"location":"Symbolic%20regression/","title":"Symbolic regression","text":"<p> This page was last updated on 2024-08-19 06:05:48 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p> </p> <p> </p>"},{"location":"Symbolic%20regression/#manually_curated_articles","title":"Manually curated articles on Symbolic regression","text":"Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index                View recommendations                visibility_off                  Discovering governing equations from data by sparse identification of nonlinear dynamical systems                               S. Brunton, J. Proctor, J. Kutz            2015-09-11 Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences of the United States of America 3190 65 open_in_new visibility_off                  Robust learning from noisy, incomplete, high-dimensional experimental data via physically constrained symbolic regression                               Patrick A. K. Reinbold, Logan Kageorge, M. Schatz, R. Grigoriev            2021-02-24 Nature Communications 85 23 open_in_new visibility_off                  Data-driven discovery of coordinates and governing equations                               Kathleen P. Champion, Bethany Lusch, J. Kutz, S. Brunton            2019-03-29 Proceedings of the National Academy of Sciences of the United States of America 603 65 open_in_new visibility_off                  Chaos as an intermittently forced linear system                               S. Brunton, Bingni W. Brunton, J. Proctor, E. Kaiser, J. Kutz            2016-08-18 Nature Communications 448 65 open_in_new visibility_off                  Sparse identification of nonlinear dynamics for model predictive control in the low-data limit                               E. Kaiser, J. Kutz, S. Brunton            2017-11-15 Proceedings of the Royal Society A, Proceedings. Mathematical, Physical, and Engineering Sciences 428 65 open_in_new visibility_off                  Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics                               N. Mangan, S. Brunton, J. Proctor, J. Kutz            2016-05-26 IEEE Transactions on Molecular, Biological and Multi-Scale Communications, IEEE Transactions on Molecular Biological and Multi-Scale Communications 317 65 open_in_new visibility_off                  SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics                               Kadierdan Kaheman, J. Kutz, S. Brunton            2020-04-05 Proceedings of the Royal Society A, Proceedings. Mathematical, Physical, and Engineering Sciences 194 65 open_in_new visibility_off                  Multidimensional Approximation of Nonlinear Dynamical Systems                               Patrick Gel\u00df, Stefan Klus, J. Eisert, Christof Schutte            2018-09-07 Journal of Computational and Nonlinear Dynamics 61 76 open_in_new visibility_off                  Learning Discrepancy Models From Experimental Data                               Kadierdan Kaheman, E. Kaiser, B. Strom, J. Kutz, S. Brunton            2019-09-18 arXiv.org, ArXiv 32 65 open_in_new visibility_off                  Discovery of Physics From Data: Universal Laws and Discrepancies                               Brian M. de Silva, D. Higdon, S. Brunton, J. Kutz            2019-06-19 Frontiers in Artificial Intelligence 67 65 open_in_new visibility_off                  Data-driven discovery of partial differential equations                               S. Rudy, S. Brunton, J. Proctor, J. Kutz            2016-09-21 Science Advances 1172 65 open_in_new visibility_off                  Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control                               Urban Fasel, J. Kutz, Bingni W. Brunton, S. Brunton            2021-11-22 Proceedings of the Royal Society A, Proceedings. Mathematical, Physical, and Engineering Sciences 158 65 open_in_new visibility_off                  Learning sparse nonlinear dynamics via mixed-integer optimization                               D. Bertsimas, Wes Gurnee            2022-06-01 Nonlinear Dynamics 28 91 open_in_new visibility_off                  A Unified Framework for Sparse Relaxed Regularized Regression: SR3                               P. Zheng, T. Askham, S. Brunton, J. Kutz, A. Aravkin            2018-07-14 IEEE Access 115 65 open_in_new Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index View recommendations"},{"location":"Symbolic%20regression/#recommended_articles","title":"Recommended articles on Symbolic regression","text":"Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index visibility_off                Discovering governing equation in structural dynamics from acceleration-only measurements                             Calvin Alvares, Souvik Chakraborty            2024-07-18 ArXiv 0 0 visibility_off                Data-driven system identification of unknown systems utilising sparse identification of nonlinear dynamics (SINDy)                             P. Pandey, H. Haddad Khodaparast, M. Friswell, T. Chatterjee, N. Jamia, T. Deighan            2024-06-01 Journal of Physics: Conference Series 0 2 visibility_off                Learning dynamical systems from data: An introduction to physics-guided deep learning                             Rose Yu, Rui Wang            2024-06-24 Proceedings of the National Academy of Sciences of the United States of America 1 1 visibility_off                Data-driven Discovery of Delay Differential Equations with Discrete Delays                             Alessandro Pecile, N. Demo, M. Tezzele, G. Rozza, Dimitri Breda            2024-07-29 ArXiv 1 49 visibility_off                Principal Component Flow Map Learning of PDEs from Incomplete, Limited, and Noisy Data                             Victor Churchill            2024-07-15 ArXiv 0 0 visibility_off                Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems                             Shane A. 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Sundaram            2023-02-08 ArXiv 7 36 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/80744010d90c8ede052c7ac6ba8c38c9de959c6e/","title":"80744010d90c8ede052c7ac6ba8c38c9de959c6e","text":""},{"location":"recommendations/80744010d90c8ede052c7ac6ba8c38c9de959c6e/#_1","title":"80744010d90c8ede052c7ac6ba8c38c9de959c6e","text":"<p> This page was last updated on 2024-07-22 06:06:35 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator. Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Two methods to approximate the Koopman operator with a reservoir computer.              Marvyn Gulina, A. 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Johnson, Shara Balakrishnan, Enoch Yeung            2022-12-14 ArXiv 1 17 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/8540780e6b9422f7a1264edb70f39d3ff79bb8c1/","title":"8540780e6b9422f7a1264edb70f39d3ff79bb8c1","text":""},{"location":"recommendations/8540780e6b9422f7a1264edb70f39d3ff79bb8c1/#_1","title":"8540780e6b9422f7a1264edb70f39d3ff79bb8c1","text":"<p> This page was last updated on 2024-07-22 06:05:55 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Graph Neural Ordinary Differential Equations Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Continuous-Depth Neural Models for Dynamic Graph Prediction              Michael Poli, Stefano Massaroli, Clayton M. Rabideau, Junyoung Park, A. Yamashita, H. 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Sterck, Omer Ege Kara            2024-04-03 ArXiv 0 25 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/883547fdbd88552328a6615ec620f96e39c57018/","title":"883547fdbd88552328a6615ec620f96e39c57018","text":""},{"location":"recommendations/883547fdbd88552328a6615ec620f96e39c57018/#_1","title":"883547fdbd88552328a6615ec620f96e39c57018","text":"<p> This page was last updated on 2024-08-19 06:05:38 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Sparsifying priors for Bayesian uncertainty quantification in model discovery              Seth M. Hirsh, D. Barajas-Solano, J. 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The enabling modules in the toolkit are combined into a single method, but the individual modules can be tactically applied in other equation discovery methods (SINDy or not) to improve results on high-noise data. Second, we propose a technique, applicable to any model discovery method based on  $\\dot { \\boldsymbol x} = { \\boldsymbol f} ({ \\boldsymbol x})$ , to assess the accuracy of a discovered model in the context of non-unique solutions due to noisy data. Currently, this non-uniqueness can obscure a discovered model\u2019s accuracy and thus a discovery method\u2019s effectiveness. We describe a technique that uses linear dependencies among functionals to transform a discovered model into an equivalent form that is closest to the true model, enabling more accurate assessment of a discovered model\u2019s correctness.\"&gt;           visibility_off A Toolkit for Data-Driven Discovery of Governing Equations in High-Noise Regimes              Charles B. Delahunt, J. 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Syed, Vuong Van Pham            2022-12-05 Artificial Intelligence Review 17 16 Abstract Title Authors Publication Date Journal/Conference Citation count Highest h-index </p>"},{"location":"recommendations/90cc86274f947b15ec3cc8c1dcfe1fc8db608e03/","title":"90cc86274f947b15ec3cc8c1dcfe1fc8db608e03","text":""},{"location":"recommendations/90cc86274f947b15ec3cc8c1dcfe1fc8db608e03/#_1","title":"90cc86274f947b15ec3cc8c1dcfe1fc8db608e03","text":"<p> This page was last updated on 2024-07-22 06:06:14 UTC </p> <p>          Click here for a quick intro of the page! help </p> <p>      Recommendations for the article Physical Design using Differentiable Learned Simulators Abstract Title Authors Publication Date Journal/ Conference Citation count Highest h-index visibility_off Neural Fluidic System Design and Control with Differentiable Simulation              Yifei Li, Yuchen Sun, Pingchuan Ma, Eftychios Sifakis, Tao Du, Bo Zhu, Wojciech Matusik            2024-05-22 ArXiv 0 33 visibility_off Accelerating Particle and Fluid Simulations with Differentiable Graph Networks for Solving Forward and Inverse Problems              Krishna Kumar, Yonjin Choi            2023-09-23 Proceedings of the SC '23 Workshops of The International Conference on High Performance Computing, Network, Storage, and Analysis 3 1 visibility_off FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulation              Zhou Xian, Bo Zhu, Zhenjia Xu, H. 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