SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks

TL;DR

This paper introduces SINDy-KANs, a novel method combining Kolmogorov-Arnold networks and sparse identification techniques to improve the interpretability and accuracy of nonlinear dynamical system representations.

Contribution

The paper presents a new approach that trains KANs with embedded SINDy-like sparse representations, enhancing interpretability without sacrificing the expressive power of deep networks.

Findings

Accurately discovers equations for various dynamical systems.

Maintains deep KAN function compositions while increasing sparsity.

Demonstrates effectiveness on symbolic regression tasks.

Abstract

Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpretable, in the sense of being sparse or parsimonious. Sparse identification of nonlinear dynamics (SINDy) is a complementary approach that allows for learning sparse equations for dynamical systems from data; however, learned equations are limited by the library. In this work, we present SINDy-KANs, which simultaneously train a KAN and a SINDy-like representation to increase interpretability of KAN representations with SINDy applied at the level of each activation function, while maintaining the function compositions possible through deep KANs. We apply our method to a number of symbolic regression tasks, including dynamical systems, to show accurate equation discovery across a range of systems.