Sinc Kolmogorov-Arnold Network

This repository contains companion code for "Sinc Kolmogorov-Arnold Network and Its Applications on Physics-informed Neural Networks". We provide instructions for reproducing our experiments and plots.

Requirements

To install requirements:

anaconda:

conda install -r environment.yml

docker:

docker pull ghcr.io/nvidia/jax:equinox

Data

To generate data, you can use the current dataset in data.py or you can add new data.

Training

To train the model(s) in the paper, change the directory to the specific directory,

for example, run command for approximation:

cd ./approximation/
python approximation_1d.py --mode train

Evaluation

To evaluate the model(s) in the paper, change the directory to the specific directory,

for example, run command for approximation:

cd ./approximation/
python approximation_1d.py --mode eval

Results ($L^2$ Relative errors)

We demostrate partial results of our paper:

Model name	MLP	KAN	SincKAN
pbl	2.89e-2 ± 3.09e-2	4.48e-3 ± 4.20e-3	1.88e-3 ± 8.55e-4
bl_1000	9.87 ± 8.70	11.3 ± 8.79	5.48e-3 ± 3.45e-3