Comparative Study of Neural State-Space Models for Nonlinear Pendulum Identification

Abstract

This paper presents a simulation-based comparative study of neural state-space models (NSSMs) for the identification of a damped and forced nonlinear pendulum. Three model variants are considered: a baseline data-driven NSSM, a physics-informed NSSM, and a Lyapunov-constrained NSSM. A total of 50 training runs were executed, and the bestachieved experiment under a rollout-oriented selection criterion is reported in detail. All models were trained and evaluated on the same train/validation/test split. For the selected experiment, the baseline NSSM achieved the lowest one-step and long-horizon rollout errors, while the Lyapunov-constrained model provided better long-horizon behavior than the physics-informed variant but remained less accurate than the baseline. All three models remained bounded under the adopted test protocol. The results indicate that, for the considered pendulum benchmark, a plain NSSM is sufficient when the operating region is well covered by data, whereas structured variants mainly improve qualitative properties at the cost of reduced predictive accuracy.