Strong convergence for the dynamic mode decomposition based on the total least squares to noisy datasets

Abstract

Dynamic mode decomposition (DMD) is a popular technique for extracting important information of nonlinear dynamical systems. In this paper, we focus on the DMD based on the total least squares (TLS), which is experimentally efficient for noisy datasets for a dynamical system, while the asymptotic analysis is not given. We propose a statistical model of random noise, adapting to the Koopman operator associated with the DMD. Moreover, under reasonable assumptions, we prove strong convergence of random variables, corresponding to the eigenpairs computed by the DMD based on the TLS.