SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems

TL;DR

SOLIS introduces a physics-informed neural surrogate model for nonlinear systems that achieves interpretable parameter recovery and stable training without assuming known global equations.

Contribution

It models unknown dynamics with a state-conditioned surrogate and recasts identification as learning a Quasi-LPV representation, enhancing interpretability and robustness.

Findings

Accurately recovers physical parameters from sparse data.

Achieves coherent physical rollouts in challenging regimes.

Outperforms standard inverse methods in benchmark tests.

Abstract

Nonlinear system identification must balance physical interpretability with model flexibility. Classical methods yield structured, control-relevant models but rely on rigid parametric forms that often miss complex nonlinearities, whereas Neural ODEs are expressive yet largely black-box. Physics-Informed Neural Networks (PINNs) sit between these extremes, but inverse PINNs typically assume a known governing equation with fixed coefficients, leading to identifiability failures when the true dynamics are unknown or state-dependent. We propose \textbf{SOLIS}, which models unknown dynamics via a \emph{state-conditioned second-order surrogate model} and recasts identification as learning a Quasi-Linear Parameter-Varying (Quasi-LPV) representation, recovering interpretable natural frequency, damping, and gain without presupposing a global equation. SOLIS decouples trajectory reconstruction from parameter estimation and stabilizes training with a cyclic curriculum and \textbf{Local Physics Hints} windowed ridge-regression anchors that mitigate optimization collapse. Experiments on benchmarks show accurate parameter-manifold recovery and coherent physical rollouts from sparse data, including regimes where standard inverse methods fail.