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Delay-Embedding Spatio-Temporal Dynamic Mode Decomposition

Author

Listed:
  • Gyurhan Nedzhibov

    (Faculty of Mathematics and Informatics, Konstantin Preslavsky University of Shumen, 9700 Shumen, Bulgaria)

Abstract

Spatio-temporal dynamic mode decomposition (STDMD) is an extension of dynamic mode decomposition (DMD) designed to handle spatio-temporal datasets. It extends the framework so that it can analyze data that have both spatial and temporal variations. This facilitates the extraction of spatial structures along with their temporal evolution. The STDMD method extracts temporal and spatial development information simultaneously, including wavenumber, frequencies, and growth rates, which are essential in complex dynamic systems. We provide a comprehensive mathematical framework for sequential and parallel STDMD approaches. To increase the range of applications of the presented techniques, we also introduce a generalization of delay coordinates. The extension, labeled delay-embedding STDMD allows the use of delayed data, which can be both time-delayed and space-delayed. An explicit expression of the presented algorithms in matrix form is also provided, making theoretical analysis easier and providing a solid foundation for further research and development. The novel approach is demonstrated using some illustrative model dynamics.

Suggested Citation

  • Gyurhan Nedzhibov, 2024. "Delay-Embedding Spatio-Temporal Dynamic Mode Decomposition," Mathematics, MDPI, vol. 12(5), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:762-:d:1350819
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    References listed on IDEAS

    as
    1. Steven L. Brunton & Bingni W. Brunton & Joshua L. Proctor & Eurika Kaiser & J. Nathan Kutz, 2017. "Chaos as an intermittently forced linear system," Nature Communications, Nature, vol. 8(1), pages 1-9, December.
    2. Jordan Mann & J. Nathan Kutz, 2016. "Dynamic mode decomposition for financial trading strategies," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1643-1655, November.
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