The code is associated with the paper entitled "KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics" (CMAME, Arxiv).

Please find the sources codes in the folder "Lotka-Volterra".

Please find the source codes in the folder "PDE examples".

The results in the corresponding manuscript are generated exclusively in Julia. We strongly recommend using the Julia code for speed, convergence, and robustness. However, we provide Pytorch code as well for users who may be interested in experimenting with KAN-ODEs in Python. Please find these in the folder "Lotka-Volterra-Pytorch".

Please see the following paper and GitHub repository for LeanKAN, our optimized KAN layer structure that includes multiplication: Neural Networks paper, Github.

If you use the code in your research or if you find our paper useful, please cite this paper:

@article{koenig2024kanodes,
title = {KAN-ODEs: Kolmogorov–Arnold network ordinary differential equations for learning dynamical systems and hidden physics},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {432},
pages = {117397},
year = {2024},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2024.117397},
url = {https://www.sciencedirect.com/science/article/pii/S0045782524006522},
author = {Benjamin C. Koenig and Suyong Kim and Sili Deng},
}