A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study

Abstract In recent years, identification of nonlinear dynamical systems from data has become increasingly popular. Sparse regression approaches, such as Identification Nonlinear Dynamics (SINDy), fostered the development novel governing equation algorithms assuming state variables are known {\it a priori} and equations lend themselves to sparse, linear expansions in (nonlinear) basis variables. context systems, one faces problem identifiability model parameters when measurements corrupted by noise. Measurement noise affects stability recovery process yielding incorrect sparsity patterns inaccurate estimation coefficients equations. this work, we investigate compare performance several local global smoothing techniques denoise numerically estimate time-derivatives improve accuracy robustness two sparse methods recover equations: Sequentially Thresholded Least Squares (STLS) Weighted Basis Pursuit Denoising (WBPDN) algorithms. We empirically show that, general, methods, which use entire measurement set, outperform employ neighboring subset around point. additionally Generalized Cross Validation (GCV) Pareto curve criteria selection automatically near optimal tuning parameters, conclude that curves yield better results. The denoising strategies is evaluated through well-known benchmark problems systems.