Structured Kolmogorov-Arnold Neural ODEs (SKANODE)

This repository contains the code and data for the following work:

• Wei Liu, Kiran Bacsa, Loon Ching Tang, and Eleni Chatzi (2025). Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics.

Repository Overview

• saved_models - Trained models used for comparative analysis.
  • anode - Trained models for Augmented Neural ODE.
  • sonode - Trained models for Second-Order Neural ODE.
  • s3node - Trained models for Structured State-Space Neural ODE.
  • skanode -Trained models for Structured Kolmogorov-Arnold Neural ODE.
  • kan - Fitted Kolmogorov-Arnold Network within SKANODE.
• duffing_data.mat - Simulated data for the Duffing oscillator example.
• duffing_skanode.py - SKANODE model.
• plot_figures.py - Visualizes results as in the paper.

Citation

Please cite the following paper if you find the work relevant and useful in your research:

@article{liu2025structured,
  title={Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics},
  author={Liu, Wei and Bacsa, Kiran and Tang, Loon Ching and Chatzi, Eleni},
  journal={arXiv preprint arXiv:2506.18339},
  year={2025}
}