Combining Off-White and Sparse Black Models in Multi-step Physics-based Systems Identification -- EXTENDED VERSION

Abstract: In this paper, we propose a unified framework for identifying interpretable nonlinear dynamical models that preserve physical properties. The proposed approach integrates physical principles with black-box basis functions to compensate for unmodeled dynamics, ensuring accuracy over long prediction horizons and computational efficiency. 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 gradient stability and 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 demonstrated on a nonlinear system identification benchmark.