用可解释的物理模型，从稀疏数据中学习非线性系统的动态规律。
SOLIS: Physics-Informed Learning of Interpretable Neural Surrogates for Nonlinear Systems
- 构建状态依赖的二阶代理模型，将系统识别转为可解释的Quasi-LPV形式。
- 在稀疏数据下准确恢复自然频率、阻尼和增益的参数流形，且能稳定预测物理轨迹。
- 适合需要可解释性与高精度的工程建模场景，如机械振动或控制系统设计。
非线性系统辨识需兼顾物理可解释性与模型灵活性。传统方法生成结构化、控制相关模型，但依赖固定参数形式，常忽略复杂非线性；神经微分方程表达力强却多为黑箱。物理信息神经网络（PINNs）处于两者之间，但逆PINNs通常假设已知的控制方程与固定系数，当真实动力学未知或状态依赖时易出现可辨识性失败。本文提出SOLIS，通过状态条件化的二阶代理模型建模未知动力学，将辨识重构为学习准线性参数变化（Quasi-LPV）表示，无需预设全局方程即可恢复可解释的自然频率、阻尼和增益。SOLIS解耦轨迹重建与参数估计，并采用循环式训练策略与局部物理提示窗口岭回归锚点，有效缓解优化崩溃。基准测试表明，即使在稀疏数据下，SOLIS仍能准确恢复参数流形并生成一致的物理演化轨迹，包括标准逆方法失效的区域。
原文摘要 · Abstract (English)
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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