Source-linked AI summary
Dynamic Mode Decomposition for Large and Streaming Datasets
Maziar S. Hemati, Matthew O. Williams, Clarence W. Rowley
TL;DR
DMD traditionally requires the full dataset before analysis, limiting its use for large datasets and data streams. This paper develops two incremental algorithms, showing batch-equivalent results for low-rank data and relevant dominant dynamics with POD compression on noisy experimental data.
Problem
DMD has traditionally required the entire experimental or computational dataset before analysis, creating a need for online, incrementally updatable computation for streams and large datasets.
Method
The paper introduces a direct incremental DMD algorithm and a POD-compressed extension that updates computations as new snapshots arrive without storing previous snapshots.
Results
The direct algorithm matches batch-processed DMD on cylinder-flow simulation data, while POD-compressed incremental DMD extracts dominant frequencies and modes from experimental PIV data.
Takeaways & Limitations
Incremental DMD supports low-storage and potential real-time analysis of large datasets and data streams while retaining dominant dynamical information.
Takeaways & Limitations
POD compression makes the incremental algorithm no longer mathematically equivalent to standard DMD, although it produces comparable dynamically relevant results.
Abstract
from arXiv · showhide
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