State-Space Kolmogorov Arnold Networks for Interpretable Nonlinear System Identification

TL;DR

This paper introduces State-Space Kolmogorov-Arnold Networks (SS-KAN), a novel interpretable model for nonlinear system identification that balances accuracy and interpretability by integrating Kolmogorov-Arnold Networks within a state-space framework.

Contribution

The paper presents SS-KAN, a new model that enhances interpretability in nonlinear system identification through sparsity and visualization, validated on benchmark systems.

Findings

SS-KAN offers improved interpretability via sparsity and visualization.

SS-KAN achieves competitive accuracy on benchmark systems.

The model reveals system nonlinearities effectively.

Abstract

While accurate, black-box system identification models lack interpretability of the underlying system dynamics. This paper proposes State-Space Kolmogorov-Arnold Networks (SS-KAN) to address this challenge by integrating Kolmogorov-Arnold Networks within a state-space framework. The proposed model is validated on two benchmark systems: the Silverbox and the Wiener-Hammerstein benchmarks. Results show that SS-KAN provides enhanced interpretability due to sparsity-promoting regularization and the direct visualization of its learned univariate functions, which reveal system nonlinearities at the cost of accuracy when compared to state-of-the-art black-box models, highlighting SS-KAN as a promising approach for interpretable nonlinear system identification, balancing accuracy and interpretability of nonlinear system dynamics.