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

arXiv cs.LG / 4/17/2026

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Key Points

The paper addresses nonlinear system identification by aiming to combine physical interpretability with the flexibility of neural approaches.
It argues that existing inverse PINN methods often fail when the governing dynamics are unknown or state-dependent due to identifiability issues.
SOLIS is proposed as a state-conditioned second-order surrogate that reformulates identification as learning a Quasi-Linear Parameter-Varying (Quasi-LPV) representation to recover interpretable physical quantities.
The method improves training stability by decoupling trajectory reconstruction from parameter estimation and using a cyclic curriculum plus Local Physics Hints with windowed ridge regression.
Experiments on benchmarks indicate SOLIS can accurately recover parameter manifolds and produce physically coherent rollouts from sparse data, outperforming standard inverse approaches in difficult regimes.

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.