Statistical Evaluation for Mode Selection in Sparsity-promoting Dynamic Mode Decomposition

Abstract

Sparsity-promoting dynamic mode decomposition (SP-DMD) is a data-driven method for estimating a modal representation of a nonlinear dynamical system, where the modes are selected via l1-regularization depending on the tradeoff between the quality of the representation and the number of the modes. However, the way to statistically evaluate modes selected by SP-DMD is not established. If statistical evaluation is not performed, we may not specify issues caused by different reasons such as noise and overfitting. In this paper, we propose a method to statistically evaluate modes selected by SP-DMD. We develop the method based on the combination of bootstrap and SP-DMD.