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Cited by 1,528

The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.

On dynamic mode decomposition: Theory and applications

Open access
Tu, Jonathan H., Rowley, Clarence W., Luchtenburg, Dirk M., Brunton, Steven L., Kutz, J. Nathan·2014·Journal of Computational Dynamics
DOI 10.3934/jcd.2014.1.391
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Abstract

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time series for which the measurement dimension is much larger than the number of measurements taken. We present a theoretical framework in which we define DMD as the eigendecomposition of an approximating linear operator. This generalizes DMD to a larger class of datasets, including nonsequential time series. We demonstrate the utility of this approach by presenting novel sampling strategies that increase computational efficiency and mitigate the effects of noise, respectively. We also introduce the concept of linear consistency, which helps explain the potential pitfalls of applying DMD to rank-deficient datasets, illustrating with examples. Such computations are not considered in the existing literature but can be understood using our more general framework. In addition, we show that our theory strengthens the connections between DMD and Koopman operator theory. It also establishes connections between DMD and other techniques, including the eigensystem realization algorithm (ERA), a system identification method, and linear inverse modeling (LIM), a method from climate science. We show that under certain conditions, DMD is equivalent to LIM.

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Metadata

Authors
Tu, J. H., Rowley, C. W., Luchtenburg, D. M., Brunton, S. L., & Kutz, J. N.
Venue
Journal of Computational Dynamics
Publisher
American Institute of Mathematical Sciences (AIMS)
Published
2014
Volume
1
Issue
2
Pages
391-421
ISSN
  • 2158-2491 (ISSN-L)
  • 2158-2505
DOI
10.3934/jcd.2014.1.391
OpenAlex
W2078898317
Cited by
1,528
References
27
FWCI
23.07
Type
journal article
Language
en
Open access
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CoChat. (2026). Citation check: On dynamic mode decomposition: Theory and applications. https://app.cochat.ai/papers/10.3934/jcd.2014.1.391
The paper
Tu, J. H., Rowley, C. W., Luchtenburg, D. M., Brunton, S. L., & Kutz, J. N. (2014). On dynamic mode decomposition: Theory and applications. Journal of Computational Dynamics. https://doi.org/10.3934/jcd.2014.1.391

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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.