A Kernel-Based Approach to Physics-Informed Nonlinear System Identification

This paper presents a kernel-based framework for physics-informed nonlinear system identification that extends kernel-based techniques, accounting for unmodeled dynamics, to seamlessly embed partially known physics-based models, improving parameter estimation and overall model accuracy. The two models' components are identified from data simultaneously, thereby minimizing a suitable cost that balances the relative importance of the physical and the black-box parts of the model. Additionally, nonlinear state smoothing is employed to address scenarios involving state-space models with not-fully measurable states. Numerical simulations on an experimental benchmark system demonstrate the effectiveness of the proposed approach, achieving up to 51% reduction in simulation root mean square error compared to physics-only models and 31% performance improvement over state-of-the-art identification techniques.