Adaptive integral alternating minimization method for robust learning of nonlinear dynamical systems from highly corrupted data

This paper proposes an adaptive integral alternating minimization method (AIAMM) for learning nonlinear dynamical systems using highly corrupted measured data. This approach selects and identifies the system directly from noisy data using the integral model, encompassing unknown sparse coefficients, initial values, and outlier noisy data within the learning problem. It is defined as a sparse robust linear regression problem. An adaptive threshold parameter selection method is proposed to constrain model fitting errors and select appropriate threshold parameters for sparsity. The robustness and accuracy of the proposed AIAMM are demonstrated through several numerical experiments on typical nonlinear dynamical systems, including the van der Pol oscillator, Mathieu oscillator, Lorenz system, and 5D self-exciting homopolar disc dynamo. The proposed method is also compared to several advanced methods for sparse recovery, with the results indicating that the AIAMM demonstrates superior performance in processing highly corrupted data.