Discover governing differential equations from evolving systems
Discovering the governing equations of evolving systems from available observations is essential and challenging. In this paper, we consider a different scenario: discovering governing equations from streaming data. Current methods struggle to discover governing differential equations with consideri...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.023126 |
| _version_ | 1797210467227140096 |
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| author | Yuanyuan Li Kai Wu Jing Liu |
| author_facet | Yuanyuan Li Kai Wu Jing Liu |
| author_sort | Yuanyuan Li |
| collection | DOAJ |
| description | Discovering the governing equations of evolving systems from available observations is essential and challenging. In this paper, we consider a different scenario: discovering governing equations from streaming data. Current methods struggle to discover governing differential equations with considering measurements as a whole, leading to failure to handle this task. We propose an online modeling method capable of handling samples one by one sequentially by modeling streaming data instead of processing the entire data set. The proposed method performs well in discovering ordinary differential equations and partial differential equations from streaming data. Evolving systems are changing over time, which invariably changes with system status. Thus finding the exact change points is critical. The measurement generated from a changed system is distributed dissimilarly to before; hence the difference can be identified by the proposed method. Our proposal is competitive in identifying the change points and discovering governing differential equations in three hybrid systems and two switching linear systems. |
| first_indexed | 2024-04-24T10:11:03Z |
| format | Article |
| id | doaj.art-cda6250f186d462999f04e9865bfb04b |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:11:03Z |
| publishDate | 2023-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-cda6250f186d462999f04e9865bfb04b2024-04-12T17:31:15ZengAmerican Physical SocietyPhysical Review Research2643-15642023-05-015202312610.1103/PhysRevResearch.5.023126Discover governing differential equations from evolving systemsYuanyuan LiKai WuJing LiuDiscovering the governing equations of evolving systems from available observations is essential and challenging. In this paper, we consider a different scenario: discovering governing equations from streaming data. Current methods struggle to discover governing differential equations with considering measurements as a whole, leading to failure to handle this task. We propose an online modeling method capable of handling samples one by one sequentially by modeling streaming data instead of processing the entire data set. The proposed method performs well in discovering ordinary differential equations and partial differential equations from streaming data. Evolving systems are changing over time, which invariably changes with system status. Thus finding the exact change points is critical. The measurement generated from a changed system is distributed dissimilarly to before; hence the difference can be identified by the proposed method. Our proposal is competitive in identifying the change points and discovering governing differential equations in three hybrid systems and two switching linear systems.http://doi.org/10.1103/PhysRevResearch.5.023126 |
| spellingShingle | Yuanyuan Li Kai Wu Jing Liu Discover governing differential equations from evolving systems Physical Review Research |
| title | Discover governing differential equations from evolving systems |
| title_full | Discover governing differential equations from evolving systems |
| title_fullStr | Discover governing differential equations from evolving systems |
| title_full_unstemmed | Discover governing differential equations from evolving systems |
| title_short | Discover governing differential equations from evolving systems |
| title_sort | discover governing differential equations from evolving systems |
| url | http://doi.org/10.1103/PhysRevResearch.5.023126 |
| work_keys_str_mv | AT yuanyuanli discovergoverningdifferentialequationsfromevolvingsystems AT kaiwu discovergoverningdifferentialequationsfromevolvingsystems AT jingliu discovergoverningdifferentialequationsfromevolvingsystems |