Regularized dynamic mode decomposition algorithm for time sequence predictions

Dynamic mode decomposition (DMD) aims at extracting intrinsic mechanisms in a time sequence via linear recurrence relation of its observables, thereby predicting later terms in the sequence. Stability is a major concern in DMD predictions. We adopt a regularized form and propose a Regularized DMD (R...

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Main Authors: Xiaoyang Xie, Shaoqiang Tang
Format: Article
Language:English
Published: Elsevier 2024-09-01
Series:Theoretical and Applied Mechanics Letters
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S2095034924000667
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author Xiaoyang Xie
Shaoqiang Tang
author_facet Xiaoyang Xie
Shaoqiang Tang
author_sort Xiaoyang Xie
collection DOAJ
description Dynamic mode decomposition (DMD) aims at extracting intrinsic mechanisms in a time sequence via linear recurrence relation of its observables, thereby predicting later terms in the sequence. Stability is a major concern in DMD predictions. We adopt a regularized form and propose a Regularized DMD (ReDMD) algorithm to determine the regularization parameter. This leverages stability and accuracy. Numerical tests for Burgers’ equation demonstrate that ReDMD effectively stabilizes the DMD prediction while maintaining accuracy. Comparisons are made with the truncated DMD algorithm.
format Article
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institution Kabale University
issn 2095-0349
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publishDate 2024-09-01
publisher Elsevier
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series Theoretical and Applied Mechanics Letters
spelling doaj-art-701b1318896c4c7a87ed4aa35e294b2c2024-12-17T04:59:32ZengElsevierTheoretical and Applied Mechanics Letters2095-03492024-09-01145100555Regularized dynamic mode decomposition algorithm for time sequence predictionsXiaoyang Xie0Shaoqiang Tang1Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, ChinaCorresponding author.; Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, ChinaDynamic mode decomposition (DMD) aims at extracting intrinsic mechanisms in a time sequence via linear recurrence relation of its observables, thereby predicting later terms in the sequence. Stability is a major concern in DMD predictions. We adopt a regularized form and propose a Regularized DMD (ReDMD) algorithm to determine the regularization parameter. This leverages stability and accuracy. Numerical tests for Burgers’ equation demonstrate that ReDMD effectively stabilizes the DMD prediction while maintaining accuracy. Comparisons are made with the truncated DMD algorithm.http://www.sciencedirect.com/science/article/pii/S2095034924000667Dynamic mode decompositionReduced order modellingStabilityRegularization
spellingShingle Xiaoyang Xie
Shaoqiang Tang
Regularized dynamic mode decomposition algorithm for time sequence predictions
Theoretical and Applied Mechanics Letters
Dynamic mode decomposition
Reduced order modelling
Stability
Regularization
title Regularized dynamic mode decomposition algorithm for time sequence predictions
title_full Regularized dynamic mode decomposition algorithm for time sequence predictions
title_fullStr Regularized dynamic mode decomposition algorithm for time sequence predictions
title_full_unstemmed Regularized dynamic mode decomposition algorithm for time sequence predictions
title_short Regularized dynamic mode decomposition algorithm for time sequence predictions
title_sort regularized dynamic mode decomposition algorithm for time sequence predictions
topic Dynamic mode decomposition
Reduced order modelling
Stability
Regularization
url http://www.sciencedirect.com/science/article/pii/S2095034924000667
work_keys_str_mv AT xiaoyangxie regularizeddynamicmodedecompositionalgorithmfortimesequencepredictions
AT shaoqiangtang regularizeddynamicmodedecompositionalgorithmfortimesequencepredictions