On-the-fly algorithm for Dynamic Mode Decomposition using Incremental Singular Value Decomposition and Total Least Squares

Abstract

Dynamic Mode Decomposition (DMD) is a useful tool to effectively extract the dominant dynamic flow structure from a unsteady flow field. However, DMD requires massive computational resources with respect to memory consumption and the usage of storage. In this paper, an alternative incremental algorithm of Total DMD (Incremental TDMD) is proposed which is based on Incremental Singular Value Decomposition (SVD). The advantage of Incremental TDMD compared to the existing on-the-fly algorithms of DMD is that Sparsity-Promoting DMD (SPDMD) can be performed after the incremental process without saving huge datasets on the disk space. SPDMD combined with Incremental TDMD enable the effective identification of dominant modes which are relevant to the results from conventional TDMD combined with SPDMD.