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: Zaiyang Zhou, Yu Kuai, Jianzhong Ge, Bas vanMaren, Zhenwu Wang, Kailin Huang, Pingxing Ding, Zhengbing Wang
Format: Article
Language:English
Published: Wiley 2025-01-01
Series:Water Resources Research
Subjects:
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.
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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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