Combining off-white and sparse black models in multi-step physics-based systems identification

In this paper, we propose a unified framework for identifying interpretable nonlinear dynamical models that preserve physical properties. The proposed approach integrates a model, based on physical principles, with black-box basis functions to compensate for unmodeled dynamics, thus ensuring accuracy over multi-step horizons. Additionally, we introduce penalty terms to enforce physical consistency and stability during training. We provide a comprehensive analysis of theoretical properties related to multi-step nonlinear system identification, establishing bounds on parameter estimation errors and conditions for sparsity recovery. The proposed framework demonstrates significant potential for improving model accuracy and reliability in various engineering applications, making a substantial step towards the effective use of combined off-white and sparse black models in system identification. The effectiveness of the proposed approach is proven on a nonlinear system identification benchmark.