Dynamic Mode Decomposition for Large and Streaming Datasets

TL;DR

This paper introduces a low-storage, efficient dynamic mode decomposition method suitable for large-scale and streaming datasets, enabling real-time extraction of dominant fluid dynamics from noisy measurements.

Contribution

It presents two algorithms for dynamic mode decomposition that are computationally efficient and effective for large and streaming data, with one incorporating data compression.

Findings

Both algorithms accurately capture key fluid dynamic behaviors.

The methods work reliably on simulated and experimental data.

Enhanced noise robustness with the compression-based algorithm.

Abstract

We formulate a low-storage method for performing dynamic mode decomposition that can be updated inexpensively as new data become available; this formulation allows dynamical information to be extracted from large datasets and data streams. We present two algorithms: the first is mathematically equivalent to a standard "batch-processed" formulation; the second introduces a compression step that maintains computational efficiency, while enhancing the ability to isolate pertinent dynamical information from noisy measurements. Both algorithms reliably capture dominant fluid dynamic behaviors, as demonstrated on cylinder wake data collected from both direct numerical simulations and particle image velocimetry experiments