Learning state-space models with Kolmogorov-Arnold networks: an autonomous underwater engineering perspective.

Abstract

This paper investigates Kolmogorov-Arnold Networks (KANs) as parametrisations of learned nonlinear state-space models in control-relevant settings. We ask whether replacing standard MLP maps with KAN-based ones yields a useful trade-off between predictive accuracy and deployability-oriented properties such as compactness, smoothness, and post hoc inspectability, with particular focus on underwater robotics. To study this question, we use a common autoencoder-based identification backbone and instantiate two KAN-based identification realisations, comparing their performance with their MLP-parametrised counterparts under the same training pipeline. The evaluation covers maritime robotics benchmarks of increasing difficulty, including autonomous underwater vehicles and a disturbance-driven underwater glider, as well as standard nonlinear system-identification datasets. Across these case studies, KAN-based models remain competitive in predictive performance while often using fewer parameters and, in several settings, supporting symbolic extraction of learned nonlinear features.