Comparative study of modal decomposition and dynamic equation reconstruction in data-driven modeling
Due to the increasing complexity of dynamic systems, it is increasingly difficult for traditional mathematical methods to meet the modeling requirements of complex dynamic systems. With the continuous innovation of computer and big data technologies, massive data can be easily obtained and stored. T...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIP Publishing LLC
2021-08-01
|
| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/5.0060489 |
| _version_ | 1819119173917212672 |
|---|---|
| author | Zhenglong Yin Bo Fan Zijing Ding Zongyu Wu Yong Chen |
| author_facet | Zhenglong Yin Bo Fan Zijing Ding Zongyu Wu Yong Chen |
| author_sort | Zhenglong Yin |
| collection | DOAJ |
| description | Due to the increasing complexity of dynamic systems, it is increasingly difficult for traditional mathematical methods to meet the modeling requirements of complex dynamic systems. With the continuous innovation of computer and big data technologies, massive data can be easily obtained and stored. Therefore, studies of dynamic system modeling through data-driven approaches have attracted more and more researchers’ attention. This paper compares the dynamic mode decomposition method and dynamic equation reconstruction. Taking Lorenz and nonlinear Helmholtz resonant systems as examples, the two methods show the ability to reconstruct and describe the evolution characteristics of the dynamic system. Specifically, the dynamic mode decomposition method can describe the characteristics of the dynamic system more intuitively; however, it cannot provide physical insights. On the other hand, the discovery of dynamic equations from data can more accurately express the physical evolution characteristics of the dynamic system; however, it is easily affected by random noise. Because the dynamic mode decomposition method can obtain a reduced-order model, which can not only retain useful information of the original data but also reduce the noise disturbances, it can effectively improve the noise attenuation and finally reconstructions of differential dynamical equations. |
| first_indexed | 2024-12-22T06:00:34Z |
| format | Article |
| id | doaj.art-d7ff0c0ff88f4f8faddc1d83a6d96338 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-12-22T06:00:34Z |
| publishDate | 2021-08-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-d7ff0c0ff88f4f8faddc1d83a6d963382022-12-21T18:36:34ZengAIP Publishing LLCAIP Advances2158-32262021-08-01118085022085022-1410.1063/5.0060489Comparative study of modal decomposition and dynamic equation reconstruction in data-driven modelingZhenglong Yin0Bo Fan1Zijing Ding2Zongyu Wu3Yong Chen4College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, ChinaNational Innovation Institute of Defense Technology, Academy of Military Sciences, Beijing 100071, ChinaSchool of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, ChinaCollege of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, ChinaCollege of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, ChinaDue to the increasing complexity of dynamic systems, it is increasingly difficult for traditional mathematical methods to meet the modeling requirements of complex dynamic systems. With the continuous innovation of computer and big data technologies, massive data can be easily obtained and stored. Therefore, studies of dynamic system modeling through data-driven approaches have attracted more and more researchers’ attention. This paper compares the dynamic mode decomposition method and dynamic equation reconstruction. Taking Lorenz and nonlinear Helmholtz resonant systems as examples, the two methods show the ability to reconstruct and describe the evolution characteristics of the dynamic system. Specifically, the dynamic mode decomposition method can describe the characteristics of the dynamic system more intuitively; however, it cannot provide physical insights. On the other hand, the discovery of dynamic equations from data can more accurately express the physical evolution characteristics of the dynamic system; however, it is easily affected by random noise. Because the dynamic mode decomposition method can obtain a reduced-order model, which can not only retain useful information of the original data but also reduce the noise disturbances, it can effectively improve the noise attenuation and finally reconstructions of differential dynamical equations.http://dx.doi.org/10.1063/5.0060489 |
| spellingShingle | Zhenglong Yin Bo Fan Zijing Ding Zongyu Wu Yong Chen Comparative study of modal decomposition and dynamic equation reconstruction in data-driven modeling AIP Advances |
| title | Comparative study of modal decomposition and dynamic equation reconstruction in data-driven modeling |
| title_full | Comparative study of modal decomposition and dynamic equation reconstruction in data-driven modeling |
| title_fullStr | Comparative study of modal decomposition and dynamic equation reconstruction in data-driven modeling |
| title_full_unstemmed | Comparative study of modal decomposition and dynamic equation reconstruction in data-driven modeling |
| title_short | Comparative study of modal decomposition and dynamic equation reconstruction in data-driven modeling |
| title_sort | comparative study of modal decomposition and dynamic equation reconstruction in data driven modeling |
| url | http://dx.doi.org/10.1063/5.0060489 |
| work_keys_str_mv | AT zhenglongyin comparativestudyofmodaldecompositionanddynamicequationreconstructionindatadrivenmodeling AT bofan comparativestudyofmodaldecompositionanddynamicequationreconstructionindatadrivenmodeling AT zijingding comparativestudyofmodaldecompositionanddynamicequationreconstructionindatadrivenmodeling AT zongyuwu comparativestudyofmodaldecompositionanddynamicequationreconstructionindatadrivenmodeling AT yongchen comparativestudyofmodaldecompositionanddynamicequationreconstructionindatadrivenmodeling |