An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD

What is it about?

1. We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) to derive reduced-order models of the shallow water equations. 2. We clarify the connection between Koopman modes and POD dynamic modes by a quantitative comparison of the spatial modes computed from the two decompositions discussed here using the Modal Assurance Criterion (MAC), as a measure of the degree of linearity between Koopman and POD modes. 3. We prove the benefit of employing the improved DMD method in the case of modal decomposition of 2D flows described by shallow water equations model.

Featured Image

Why is it important?

1. An improved framework for dynamic mode decomposition of 2D flows, for problems originating from meteorology is presented. 2. Based on the classical DMD method, we propose an improved DMD algorithm. 3. Key innovation for the DMD-based ROM introduced in this paper are the use of the Moore-Penrose pseudo-inverse in the DMD computation that produce an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values.

Perspectives