Modeling Non‐Stationary Wind‐Induced Fluid Motions With Physics‐Informed Neural Networks for the Shallow Water Equations in a Polar Coordinate System
Abstract Physics‐informed neural networks (PINNs) are increasingly being used in various scientific disciplines. However, dealing with non‐stationary physical processes remains a significant challenge in such models, whereas fluid motions are typically non‐stationary. In this study, a PINN‐based met...
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| Main Authors: | , , , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2025-01-01
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| Series: | Water Resources Research |
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| Online Access: | https://doi.org/10.1029/2024WR037490 |
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| author | Zaiyang Zhou Yu Kuai Jianzhong Ge Bas vanMaren Zhenwu Wang Kailin Huang Pingxing Ding Zhengbing Wang |
| author_facet | Zaiyang Zhou Yu Kuai Jianzhong Ge Bas vanMaren Zhenwu Wang Kailin Huang Pingxing Ding Zhengbing Wang |
| author_sort | Zaiyang Zhou |
| collection | DOAJ |
| description | Abstract Physics‐informed neural networks (PINNs) are increasingly being used in various scientific disciplines. However, dealing with non‐stationary physical processes remains a significant challenge in such models, whereas fluid motions are typically non‐stationary. In this study, a PINN‐based method was designed and optimized to solve non‐stationary fluid dynamics with shallow water equations in a polar coordinate system (PINN‐SWEP). It was developed and validated with a classic circular basin case that is well‐documented in scientific literature. In the validation case, the wind‐induced water surface fluctuations are less than 1 cm, posing challenges in modeling. However, our PINN‐SWEP model can accurately simulate such tiny water surface fluctuations and resolve complex fluid motions based on limited and sparse data. A boundary discontinuity problem associated with the use of a polar coordinate system is further discussed and improved, thereby enhancing the applicability of PINN in water research. The methodology can provide an alternative solution for numerical or analytical solutions with high accuracy. |
| format | Article |
| id | doaj-art-98c0c47ed1b344f78e84b09cbe04e7b5 |
| institution | OA Journals |
| issn | 0043-1397 1944-7973 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Water Resources Research |
| spelling | doaj-art-98c0c47ed1b344f78e84b09cbe04e7b52025-08-20T02:09:28ZengWileyWater Resources Research0043-13971944-79732025-01-01611n/an/a10.1029/2024WR037490Modeling Non‐Stationary Wind‐Induced Fluid Motions With Physics‐Informed Neural Networks for the Shallow Water Equations in a Polar Coordinate SystemZaiyang Zhou0Yu Kuai1Jianzhong Ge2Bas vanMaren3Zhenwu Wang4Kailin Huang5Pingxing Ding6Zhengbing Wang7State Key Laboratory of Estuarine and Coastal Research East China Normal University Shanghai ChinaFaculty of Civil Engineering and Geosciences Delft University of Technology Delft The NetherlandsState Key Laboratory of Estuarine and Coastal Research East China Normal University Shanghai ChinaState Key Laboratory of Estuarine and Coastal Research East China Normal University Shanghai ChinaState Key Laboratory of Estuarine and Coastal Research East China Normal University Shanghai ChinaState Key Laboratory of Water Resources Engineering and Management Wuhan University Wuhan ChinaState Key Laboratory of Estuarine and Coastal Research East China Normal University Shanghai ChinaFaculty of Civil Engineering and Geosciences Delft University of Technology Delft The NetherlandsAbstract Physics‐informed neural networks (PINNs) are increasingly being used in various scientific disciplines. However, dealing with non‐stationary physical processes remains a significant challenge in such models, whereas fluid motions are typically non‐stationary. In this study, a PINN‐based method was designed and optimized to solve non‐stationary fluid dynamics with shallow water equations in a polar coordinate system (PINN‐SWEP). It was developed and validated with a classic circular basin case that is well‐documented in scientific literature. In the validation case, the wind‐induced water surface fluctuations are less than 1 cm, posing challenges in modeling. However, our PINN‐SWEP model can accurately simulate such tiny water surface fluctuations and resolve complex fluid motions based on limited and sparse data. A boundary discontinuity problem associated with the use of a polar coordinate system is further discussed and improved, thereby enhancing the applicability of PINN in water research. The methodology can provide an alternative solution for numerical or analytical solutions with high accuracy.https://doi.org/10.1029/2024WR037490PINNshallow water equationpolar coordinatenon‐stationaryboundary discontinuityhybrid model |
| spellingShingle | Zaiyang Zhou Yu Kuai Jianzhong Ge Bas vanMaren Zhenwu Wang Kailin Huang Pingxing Ding Zhengbing Wang Modeling Non‐Stationary Wind‐Induced Fluid Motions With Physics‐Informed Neural Networks for the Shallow Water Equations in a Polar Coordinate System Water Resources Research PINN shallow water equation polar coordinate non‐stationary boundary discontinuity hybrid model |
| title | Modeling Non‐Stationary Wind‐Induced Fluid Motions With Physics‐Informed Neural Networks for the Shallow Water Equations in a Polar Coordinate System |
| title_full | Modeling Non‐Stationary Wind‐Induced Fluid Motions With Physics‐Informed Neural Networks for the Shallow Water Equations in a Polar Coordinate System |
| title_fullStr | Modeling Non‐Stationary Wind‐Induced Fluid Motions With Physics‐Informed Neural Networks for the Shallow Water Equations in a Polar Coordinate System |
| title_full_unstemmed | Modeling Non‐Stationary Wind‐Induced Fluid Motions With Physics‐Informed Neural Networks for the Shallow Water Equations in a Polar Coordinate System |
| title_short | Modeling Non‐Stationary Wind‐Induced Fluid Motions With Physics‐Informed Neural Networks for the Shallow Water Equations in a Polar Coordinate System |
| title_sort | modeling non stationary wind induced fluid motions with physics informed neural networks for the shallow water equations in a polar coordinate system |
| topic | PINN shallow water equation polar coordinate non‐stationary boundary discontinuity hybrid model |
| url | https://doi.org/10.1029/2024WR037490 |
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