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The paper introduces SOLIS, a novel physics-informed neural network approach for identifying nonlinear systems by learning a state-conditioned second-order surrogate model. SOLIS recovers interpretable Quasi-LPV representations (natural frequency, damping, gain) without needing a predefined global equation, addressing limitations of inverse PINNs. The method uses a cyclic curriculum and local physics hints (windowed ridge-regression anchors) to stabilize training and decouple trajectory reconstruction from parameter estimation, enabling accurate parameter recovery and coherent rollouts from sparse data.
SOLIS cracks open the black box of Neural ODEs, extracting interpretable, state-dependent physical parameters from complex nonlinear systems without requiring a pre-defined governing equation.
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.