Visualization and selection of Dynamic Mode Decomposition components for unsteady flow
Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a low-dimensional spectral decomposition of the data into the following com...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-09-01
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| Series: | Visual Informatics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2468502X21000309 |
| _version_ | 1818649059370467328 |
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| author | T. Krake S. Reinhardt M. Hlawatsch B. Eberhardt D. Weiskopf |
| author_facet | T. Krake S. Reinhardt M. Hlawatsch B. Eberhardt D. Weiskopf |
| author_sort | T. Krake |
| collection | DOAJ |
| description | Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a low-dimensional spectral decomposition of the data into the following components: the modes, called DMD modes, encode the spatial contribution of the decomposition, whereas the DMD amplitudes specify their impact. Each associated eigenvalue, referred to as DMD eigenvalue, characterizes the frequency and growth rate of the DMD mode. In this paper, we demonstrate how the components of DMD can be utilized to obtain temporal and spatial information from time-dependent flow fields. We begin with the theoretical background of DMD and its application to unsteady flow. Next, we examine the conventional process with DMD mathematically and put it in relationship to the discrete Fourier transform. Our analysis shows that the current use of DMD components has several drawbacks. To resolve these problems we adjust the components and provide new and meaningful insights into the decomposition: we show that our improved components capture the spatio-temporal patterns of the flow better. Moreover, we remove redundancies in the decomposition and clarify the interplay between components, allowing users to understand the impact of components. These new representations, which respect the spatio-temporal character of DMD, enable two clustering methods that segment the flow into physically relevant sections and can therefore be used for the selection of DMD components. With a number of typical examples, we demonstrate that the combination of these techniques allows new insights with DMD for unsteady flow. |
| first_indexed | 2024-12-17T01:28:18Z |
| format | Article |
| id | doaj.art-00e09be24667418badca484281ad91d5 |
| institution | Directory Open Access Journal |
| issn | 2468-502X |
| language | English |
| last_indexed | 2024-12-17T01:28:18Z |
| publishDate | 2021-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Visual Informatics |
| spelling | doaj.art-00e09be24667418badca484281ad91d52022-12-21T22:08:39ZengElsevierVisual Informatics2468-502X2021-09-01531527Visualization and selection of Dynamic Mode Decomposition components for unsteady flowT. Krake0S. Reinhardt1M. Hlawatsch2B. Eberhardt3D. Weiskopf4Visualization Research Center (VISUS), Allmandring 19, 70569 Stuttgart, Germany; Hochschule der Medien, Nobelstraße 10, 70569 Stuttgart, Germany; Corresponding author.Visualization Research Center (VISUS), Allmandring 19, 70569 Stuttgart, Germany; Hochschule der Medien, Nobelstraße 10, 70569 Stuttgart, GermanyVisualization Research Center (VISUS), Allmandring 19, 70569 Stuttgart, GermanyHochschule der Medien, Nobelstraße 10, 70569 Stuttgart, GermanyVisualization Research Center (VISUS), Allmandring 19, 70569 Stuttgart, GermanyDynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a low-dimensional spectral decomposition of the data into the following components: the modes, called DMD modes, encode the spatial contribution of the decomposition, whereas the DMD amplitudes specify their impact. Each associated eigenvalue, referred to as DMD eigenvalue, characterizes the frequency and growth rate of the DMD mode. In this paper, we demonstrate how the components of DMD can be utilized to obtain temporal and spatial information from time-dependent flow fields. We begin with the theoretical background of DMD and its application to unsteady flow. Next, we examine the conventional process with DMD mathematically and put it in relationship to the discrete Fourier transform. Our analysis shows that the current use of DMD components has several drawbacks. To resolve these problems we adjust the components and provide new and meaningful insights into the decomposition: we show that our improved components capture the spatio-temporal patterns of the flow better. Moreover, we remove redundancies in the decomposition and clarify the interplay between components, allowing users to understand the impact of components. These new representations, which respect the spatio-temporal character of DMD, enable two clustering methods that segment the flow into physically relevant sections and can therefore be used for the selection of DMD components. With a number of typical examples, we demonstrate that the combination of these techniques allows new insights with DMD for unsteady flow.http://www.sciencedirect.com/science/article/pii/S2468502X21000309Dynamic Mode DecompositionSpectral decomposition |
| spellingShingle | T. Krake S. Reinhardt M. Hlawatsch B. Eberhardt D. Weiskopf Visualization and selection of Dynamic Mode Decomposition components for unsteady flow Visual Informatics Dynamic Mode Decomposition Spectral decomposition |
| title | Visualization and selection of Dynamic Mode Decomposition components for unsteady flow |
| title_full | Visualization and selection of Dynamic Mode Decomposition components for unsteady flow |
| title_fullStr | Visualization and selection of Dynamic Mode Decomposition components for unsteady flow |
| title_full_unstemmed | Visualization and selection of Dynamic Mode Decomposition components for unsteady flow |
| title_short | Visualization and selection of Dynamic Mode Decomposition components for unsteady flow |
| title_sort | visualization and selection of dynamic mode decomposition components for unsteady flow |
| topic | Dynamic Mode Decomposition Spectral decomposition |
| url | http://www.sciencedirect.com/science/article/pii/S2468502X21000309 |
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