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

2026-04-16

AI Summary

This work addresses the longstanding challenge in nonlinear system identification of balancing physical interpretability with model flexibility: conventional approaches are constrained by fixed parametric forms, while neural ordinary differential equations (Neural ODEs) often lack physical grounding. To overcome this, we propose a state-dependent second-order quasi-linear parameter-varying (quasi-LPV) neural surrogate model that leverages state-conditioned modeling and a local physics-informed prompting mechanism. This framework reformulates system identification as a parameter manifold learning problem without requiring a predefined global dynamical equation, effectively decoupling trajectory reconstruction from physical parameter estimation to prevent optimization collapse. By integrating recurrent curriculum learning with a windowed ridge regression anchoring strategy, our method accurately recovers key physical parameters—such as natural frequencies, damping ratios, and gains—from sparse data and generates dynamics-consistent predictions, outperforming existing inverse modeling techniques across multiple benchmarks.

Technology Category

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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.

Problem

• nonlinear system identification
• physical interpretability
• unknown dynamics
• parameter identifiability
• state-dependent systems

Innovation

• Physics-Informed Learning
• Neural Surrogates
• Quasi-LPV
• Local Physics Hints
• Nonlinear System Identification