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

## TL;DR

This paper introduces a preconditioned dynamic mode decomposition framework using incremental proper orthogonal decomposition, enabling efficient analysis of large datasets with low memory and computational costs.

## Contribution

It presents a novel preconditioning approach for DMD and mode selection algorithms that is suitable for large datasets, improving efficiency and scalability.

## Key findings

- Effective analysis of 3D flow around a cylinder
- Low memory and computational complexity achieved
- Applicable to large datasets in fluid dynamics

## Abstract

This note proposes a simple and general framework of dynamic mode decomposition (DMD) and a mode selection for large datasets. The proposed framework explicitly introduces a preconditioning step using an incremental proper orthogonal decomposition to DMD and mode selection algorithms. By performing the preconditioning step, the DMD and the mode selection can be performed with low memory consumption and small computational complexity and can be applied to large datasets. In addition, a simple mode selection algorithm based on a greedy method is proposed. The proposed framework is applied to the analysis of a three-dimensional flows around a circular cylinder.