Data-driven dynamics reconstruction using RBF network
Constructing the governing dynamical equations of complex systems from observational data is of great interest for both theory and applications. However, it is a difficult inverse problem to explicitly construct the dynamical equations for many real complex systems based on observational data. Here,...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2023-01-01
|
| Series: | Machine Learning: Science and Technology |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-2153/acec31 |
| _version_ | 1797649167573581824 |
|---|---|
| author | Cong-Cong Du Xuan Wang Zhangsen Wang Da-Hui Wang |
| author_facet | Cong-Cong Du Xuan Wang Zhangsen Wang Da-Hui Wang |
| author_sort | Cong-Cong Du |
| collection | DOAJ |
| description | Constructing the governing dynamical equations of complex systems from observational data is of great interest for both theory and applications. However, it is a difficult inverse problem to explicitly construct the dynamical equations for many real complex systems based on observational data. Here, we propose to implicitly represent the dynamical equations of a complex system using a radial basis function (RBF) network trained on the observed data of the system. We show that the RBF network trained on trajectory data of the classical Lorenz and Chen system can faithfully reproduce the orbits, fixed points, and local bifurcations of the original dynamical equations. We also apply this method to electrocardiogram (ECG) data and show that the fixed points of the RBF network trained using ECG can discriminate healthy people from patients with heart disease, indicating that the method can be applied to real complex systems. |
| first_indexed | 2024-03-11T15:42:21Z |
| format | Article |
| id | doaj.art-9dc65b51641842ada350bb7d826010ce |
| institution | Directory Open Access Journal |
| issn | 2632-2153 |
| language | English |
| last_indexed | 2024-03-11T15:42:21Z |
| publishDate | 2023-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Machine Learning: Science and Technology |
| spelling | doaj.art-9dc65b51641842ada350bb7d826010ce2023-10-26T10:44:52ZengIOP PublishingMachine Learning: Science and Technology2632-21532023-01-014404501610.1088/2632-2153/acec31Data-driven dynamics reconstruction using RBF networkCong-Cong Du0Xuan Wang1Zhangsen Wang2Da-Hui Wang3https://orcid.org/0000-0002-6447-7516School of Systems Science, Beijing Normal University , Beijing 100875, People’s Republic of ChinaSchool of Systems Science, Beijing Normal University , Beijing 100875, People’s Republic of ChinaSchool of Systems Science, Beijing Normal University , Beijing 100875, People’s Republic of ChinaSchool of Systems Science, Beijing Normal University , Beijing 100875, People’s Republic of ChinaConstructing the governing dynamical equations of complex systems from observational data is of great interest for both theory and applications. However, it is a difficult inverse problem to explicitly construct the dynamical equations for many real complex systems based on observational data. Here, we propose to implicitly represent the dynamical equations of a complex system using a radial basis function (RBF) network trained on the observed data of the system. We show that the RBF network trained on trajectory data of the classical Lorenz and Chen system can faithfully reproduce the orbits, fixed points, and local bifurcations of the original dynamical equations. We also apply this method to electrocardiogram (ECG) data and show that the fixed points of the RBF network trained using ECG can discriminate healthy people from patients with heart disease, indicating that the method can be applied to real complex systems.https://doi.org/10.1088/2632-2153/acec31RBF networkdynamics reconstructionfixed pointgoverning equations |
| spellingShingle | Cong-Cong Du Xuan Wang Zhangsen Wang Da-Hui Wang Data-driven dynamics reconstruction using RBF network Machine Learning: Science and Technology RBF network dynamics reconstruction fixed point governing equations |
| title | Data-driven dynamics reconstruction using RBF network |
| title_full | Data-driven dynamics reconstruction using RBF network |
| title_fullStr | Data-driven dynamics reconstruction using RBF network |
| title_full_unstemmed | Data-driven dynamics reconstruction using RBF network |
| title_short | Data-driven dynamics reconstruction using RBF network |
| title_sort | data driven dynamics reconstruction using rbf network |
| topic | RBF network dynamics reconstruction fixed point governing equations |
| url | https://doi.org/10.1088/2632-2153/acec31 |
| work_keys_str_mv | AT congcongdu datadrivendynamicsreconstructionusingrbfnetwork AT xuanwang datadrivendynamicsreconstructionusingrbfnetwork AT zhangsenwang datadrivendynamicsreconstructionusingrbfnetwork AT dahuiwang datadrivendynamicsreconstructionusingrbfnetwork |