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

2026-03-19

AI Summary

This work addresses the lack of sparsity and interpretability in Kolmogorov–Arnold Networks (KANs) when modeling nonlinear dynamical systems by proposing a novel integration of the Sparse Identification of Nonlinear Dynamics (SINDy) framework directly into the activation function layer of KANs. During training, the method simultaneously optimizes both the network architecture and a sparse set of governing equations, achieving, for the first time, a deep fusion of SINDy and KAN at the activation level. This approach preserves KANs’ powerful function approximation capabilities while substantially enhancing global sparsity and physical interpretability. Experimental results demonstrate that the proposed method accurately recovers the true governing equations across multiple symbolic regression and dynamical system tasks, outperforming existing baselines.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Neuro-Symbolic Learning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

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.

Problem

• interpretability
• sparsity
• nonlinear dynamics
• symbolic regression
• Kolmogorov-Arnold networks

Innovation

• SINDy-KANs
• Kolmogorov-Arnold networks
• sparse identification
• symbolic regression
• interpretable machine learning