Physics-Guided Feature Extraction for Interpretable Nonlinear System Identification from Data
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Abstract
The identification of nonlinear dynamical systems from measurement data is a foundational problem across various scientific and engineering disciplines. While traditional data-driven methodologies, particularly deep learning models, have demonstrated exceptional predictive capabilities, they often lack interpretability and fail to respect the underlying physical laws governing the system. This paper presents a comprehensive framework for physics-guided feature extraction aimed at interpretable nonlinear system identification. By embedding established physical principles into the feature engineering process, the proposed methodology constructs a specialized library of basis functions that inherently captures the phenomenological characteristics of the target dynamics. We leverage sparse regression techniques to select the most relevant physics-informed features, yielding a parsimonious model that maintains high predictive accuracy while offering explicit analytical expressions. The integration of domain knowledge not only mitigates the black-box nature of modern machine learning approaches but also significantly enhances model robustness against observational noise and limited training data. Through extensive theoretical analysis and empirical validation on canonical nonlinear systems, we demonstrate that physics-guided feature extraction bridges the gap between purely empirical data fitting and rigid first-principles modeling. This research provides a robust pathway for discovering governing equations directly from time-series data, ensuring that the resulting mathematical representations remain physically consistent, mathematically tractable, and highly generalizable across varying operational conditions.
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