KANDy: Kolmogorov-Arnold Networks and Dynamical System Discovery

TL;DR

KANDy introduces a neural network architecture that effectively discovers governing equations of complex dynamical systems, including chaotic PDEs, by combining Kolmogorov-Arnold Networks with sparse regression, enhancing interpretability and accuracy.

Contribution

The paper presents KANDy, a novel zero-depth neural network that explicitly learns governing equations, overcoming limitations of sparse regression in dynamical system discovery.

Findings

Successfully recovers topological structures in the Hopf Fibration

Applies to both discrete and continuous systems, including chaotic PDEs

Provides an interpretable alternative for data-driven modeling

Abstract

We introduce the Kolmogorov-Arnold Network for Dynamics (KANDy) as a zero-depth, wide neural architecture capable of discovering governing equations in chaotic and complex dynamical systems. Building on the foundation of Kolmogorov-Arnold Networks (KANs), KANDy explicitly learns governing equations by replacing sparse regression with a KAN. The synthesis of KANs and sparse regression addresses the limitations of equation discovery for KANs applied to dynamical systems and overcomes cases where sparse regression is hindered by sparsity constraints. Additionally, we show that our model, applied to the Hopf Fibration, recovers topological structure, thereby improving coherence with attractor properties. We apply our model to discrete and continuous dynamical systems, as well as to chaotic partial differential equations (PDEs). These results position KANDy as an interpretable and effective alternative for data-driven modeling of nonlinear dynamical systems.