Search papers, labs, and topics across Lattice.
This paper introduces SINDy-KANs, a method that combines Kolmogorov-Arnold Networks (KANs) with Sparse Identification of Nonlinear Dynamics (SINDy) to learn sparse and interpretable representations of dynamical systems. SINDy is applied to the activation functions within the KAN architecture, enabling the discovery of governing equations. The method demonstrates accurate equation discovery on symbolic regression tasks and dynamical systems, improving the interpretability of KANs.
Unlock the power of interpretable AI: SINDy-KANs distills complex neural networks into sparse equations, revealing the underlying dynamics of systems.
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.
