Data-driven model discovery with Kolmogorov-Arnold networks
<|reference_start|>Data-driven model discovery with Kolmogorov-Arnold networks: Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical terms. Examples where sparse optimization fails abound, such as the classic Ikeda or optical-cavity map in nonlinear dynamics and a large variety of ecosystems. Exploiting the recently articulated Kolmogorov-Arnold networks, we develop a general model-discovery framework for any dynamical systems including those that do not satisfy the sparsity condition. In particular, we demonstrate non-uniqueness in that a large number of approximate models of the system can be found which generate the same invariant set with the correct statistics such as the Lyapunov exponents and Kullback-Leibler divergence. An analogy to shadowing of numerical trajectories in chaotic systems is pointed out.<|reference_end|>
@article{moradi2024data-driven,
    title={Data-driven model discovery with Kolmogorov-Arnold networks},
    author={Mohammadamin Moradi, Shirin Panahi, Erik M. Bollt, and Ying-Cheng Lai},
    journal={arXiv preprint arXiv:2409.15167},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.15167},
    primaryClass={cs.LG math.DS nlin.CD physics.data-an}
}