SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems
For nonlinear system identification, SOLIS bridges the gap between interpretability and flexibility, enabling control-relevant model learning from sparse data.
SOLIS introduces a physics-informed neural surrogate that learns interpretable Quasi-LPV models from sparse data, recovering natural frequency, damping, and gain without assuming a known governing equation. It achieves accurate parameter-manifold recovery and coherent rollouts where standard inverse PINNs fail.
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.