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Delay Embedding Spatio-Temporal Dynamic Mode Decomposition
Version 1
: Received: 18 February 2024 / Approved: 19 February 2024 / Online: 19 February 2024 (11:19:30 CET)
A peer-reviewed article of this Preprint also exists.
Nedzhibov, G. Delay-Embedding Spatio-Temporal Dynamic Mode Decomposition. Mathematics 2024, 12, 762. Nedzhibov, G. Delay-Embedding Spatio-Temporal Dynamic Mode Decomposition. Mathematics 2024, 12, 762.
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 has both spatial and temporal variations, allowing for the extraction of spatial structures and their temporal evolution. The STDMD method extracts temporal and spatial development information simultaneously, including wavenumber, frequencies and growth rates, which is essential in complex dynamic systems. We provide a comprehensive mathematical framework for sequential and parallel STDMD approaches. We also introduce delay coordinates generalization to the presented algorithms to extend the scope of their application. 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, which facilitates theoretical analysis and provides a solid foundation for further research and development. The novel approach is demonstrated using some illustrative model dynamics.
Keywords
DMDmethod; Spatio-Temporal Dynamicmode decomposition; Koopman operator; Delay embedding
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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