Physics-informed deep sparse regression network for nonlinear dynamical system identification

This paper presents a novel physics-informed deep sparse regression network for nonlinear dynamical system identification. The fundamental concept is to employ implicit governing equations to guide neural network training, thereby constraining the solution space and inducing an interpretable model. Firstly, inspired by sparse regression methods, a portable sparse regression layer with a function library is developed to characterize system nonlinearity. Secondly, three Hybrid-LSTM networks are connected in parallel with state dependency constraints to construct the Hybrid-LSTM³ network. This configuration enables accurate full-state predictions even from partial measurements. Finally, the sparse regression layer and the Hybrid-LSTM³ network are synthesized to constitute the physics-informed deep sparse regression network, yielding full-state outputs and explicit closed-form dynamical formulations simultaneously. An alternate optimization method is developed to sequentially optimize the two components. The term “physics-informed” herein denotes the incorporation of state dependency constraints and residual loss from learned governing equations via the sparse regression layer. Through this fusion strategy, the proposed framework holds promise to deliver a physically interpretable model for nonlinear dynamical systems from partial noisy measurements. The effectiveness, robustness, and applicability of the proposed method are demonstrated through numerical simulations and experimental studies.