Preconditioned dynamic mode decomposition and mode selection algorithms for large datasets using incremental proper orthogonal decomposition

Yuya Ohmichi

doi:10.1063/1.4996024

Abstract

In this letter, we propose a simple and efficient framework of dynamic mode decomposition (DMD) and mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal decomposition (POD) to DMD and mode selection algorithms. By performing the preconditioning step, the DMD and mode selection can be performed with low memory consumption and therefore can be applied to large datasets. Additionally, we propose a simple mode selection algorithm based on a greedy method. The proposed framework is applied to the analysis of three-dimensional flow around a circular cylinder.

Highlights

Preconditioned dynamic mode decomposition and mode selection algorithms for large datasets using incremental proper orthogonal decomposition
Dynamic mode decomposition[1,2] (DMD) has been often used to extract important spatial and temporal structures from fluid flow data since the method was first proposed in 2008.1 DMD extracts latent dynamic behavior from input datasets by determining the linear dynamical system that best fits the input datasets
Another issue of standard DMD is that it is not easy to select physically important modes from the obtained modes.[7]. Several algorithms, such as optimized DMD8 and sparsity-promoting DMD9 have been proposed. These methods can determine the small number of DMD modes that are able to represent the input datasets with fewer errors

Summary

Introduction

Preconditioned dynamic mode decomposition and mode selection algorithms for large datasets using incremental proper orthogonal decomposition. These methods can determine the small number of DMD modes that are able to represent the input datasets with fewer errors. In the proposed framework, preprocessing steps are introduced before performing DMD and mode selection.

Results

Conclusion