# State-Space Kolmogorov Arnold Networks for Interpretable Nonlinear System Identification

arXiv: https://arxiv.org/abs/2506.16392 · HTML: https://mlsanity.com/paper/2506.16392/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 19 Jun 2025.

## Builds on (most cited first, 11 of 11)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networks](https://mlsanity.com/paper/2406.02917/) (2024)
- [KAN-ODEs: Kolmogorov-Arnold Network Ordinary Differential Equations for Learning Dynamical Systems and Hidden Physics](https://mlsanity.com/paper/2407.04192/) (2024)
- [Deep networks for system identification: a Survey](https://mlsanity.com/paper/2301.12832/) (2023)
- [Nonlinear state-space identification using deep encoder networks](https://mlsanity.com/paper/2012.07697/) (2020)
- [Nonlinear port-Hamiltonian system identification from input-state-output data (ISO-pHNN)](https://mlsanity.com/paper/2501.06118/) (2025)
- [Physics-Informed Learning Using Hamiltonian Neural Networks with Output Error Noise Models](https://mlsanity.com/paper/2305.01338/) (2023)
- [Retrieving highly structured models starting from black-box nonlinear state-space models using polynomial decoupling](https://mlsanity.com/paper/2001.02861/) (2020)
- [Physics-Guided State-Space Model Augmentation Using Weighted Regularized Neural Networks](https://mlsanity.com/paper/2405.10429/) (2024)
- [Decoupling multivariate functions using a non-parametric Filtered CPD approach](https://mlsanity.com/paper/2105.08518/) (2021)
- [KAN/MultKAN with Physics-Informed Spline fitting (KAN-PISF) for ordinary/partial differential equation discovery of nonlinear dynamic systems](https://mlsanity.com/paper/2411.11801/) (2024)

## Built on by (most cited first, 3 of 3)

- [Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning](https://mlsanity.com/paper/2603.23854/) (2026)
- [Morephy-Net: An Evolutionary Multi-objective Optimization for Replica-Exchange-based Physics-informed Neural Operator Learning Networks](https://mlsanity.com/paper/2509.00663/) (2025)
- [PH-KAN: Port-Hamiltonian Kolmogorov-Arnold Network](https://mlsanity.com/paper/2606.14708/) (2026)

## Abstract (arXiv)

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.