Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods
This article presents a review on two methods based on dynamic mode decomposition and its multiple applications, focusing on higher order dynamic mode decomposition (which provides a purely temporal Fourier-like decomposition) and spatiotemporal Koopman decomposition (which gives a spatiotemporal Fo...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/6920783 |
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| author | Soledad Le Clainche José M. Vega |
| author_facet | Soledad Le Clainche José M. Vega |
| author_sort | Soledad Le Clainche |
| collection | DOAJ |
| description | This article presents a review on two methods based on dynamic mode decomposition and its multiple applications, focusing on higher order dynamic mode decomposition (which provides a purely temporal Fourier-like decomposition) and spatiotemporal Koopman decomposition (which gives a spatiotemporal Fourier-like decomposition). These methods are purely data-driven, using either numerical or experimental data, and permit reconstructing the given data and identifying the temporal growth rates and frequencies involved in the dynamics and the spatial growth rates and wavenumbers in the case of the spatiotemporal Koopman decomposition. Thus, they may be used to either identify and extrapolate the dynamics from transient behavior to permanent dynamics or construct efficient, purely data-driven reduced order models. |
| format | Article |
| id | doaj-art-2f274696865c420c982a390b116fb96d |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-2f274696865c420c982a390b116fb96d2025-02-03T01:24:15ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/69207836920783Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like MethodsSoledad Le Clainche0José M. Vega1E.T.S.I. Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 Madrid, SpainE.T.S.I. Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 Madrid, SpainThis article presents a review on two methods based on dynamic mode decomposition and its multiple applications, focusing on higher order dynamic mode decomposition (which provides a purely temporal Fourier-like decomposition) and spatiotemporal Koopman decomposition (which gives a spatiotemporal Fourier-like decomposition). These methods are purely data-driven, using either numerical or experimental data, and permit reconstructing the given data and identifying the temporal growth rates and frequencies involved in the dynamics and the spatial growth rates and wavenumbers in the case of the spatiotemporal Koopman decomposition. Thus, they may be used to either identify and extrapolate the dynamics from transient behavior to permanent dynamics or construct efficient, purely data-driven reduced order models.http://dx.doi.org/10.1155/2018/6920783 |
| spellingShingle | Soledad Le Clainche José M. Vega Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods Complexity |
| title | Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods |
| title_full | Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods |
| title_fullStr | Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods |
| title_full_unstemmed | Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods |
| title_short | Analyzing Nonlinear Dynamics via Data-Driven Dynamic Mode Decomposition-Like Methods |
| title_sort | analyzing nonlinear dynamics via data driven dynamic mode decomposition like methods |
| url | http://dx.doi.org/10.1155/2018/6920783 |
| work_keys_str_mv | AT soledadleclainche analyzingnonlineardynamicsviadatadrivendynamicmodedecompositionlikemethods AT josemvega analyzingnonlineardynamicsviadatadrivendynamicmodedecompositionlikemethods |