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...
Saved in:
| Main Authors: | , |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846119480389795840 |
|---|---|
| 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 |
| id | doaj-art-701b1318896c4c7a87ed4aa35e294b2c |
| institution | Kabale University |
| issn | 2095-0349 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Elsevier |
| record_format | Article |
| 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 |