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

• URL: http://arxiv.org/abs/2604.14879v1
• Date: Thu, 16 Apr 2026 11:12:36 GMT
• Title: SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems
• Abstract summary: textbfSOLIS models unknown dynamics via a emphstate-conditioned second-order surrogate model<n>textbfLocal Physics Hints windowed ridge-regression anchors that mitigate optimization collapse.<n>Experiments on benchmarks show accurate parameter-manifold recovery and coherent physical rollouts from sparse data, including regimes where standard inverse methods fail.
• Score: 6.5745172279769255
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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