Modeling Non-Stationary Wind-Induced Fluid Motions With Physics-Informed Neural Networks for the Shallow Water Equations in a Polar Coordinate System
Zaiyang Zhou (East China Normal University)
Yu Kuai (TU Delft - Coastal Engineering)
Jianzhong Ge (Institute of Eco-Chongming (IEC), East China Normal University)
Bas van Maren (TU Delft - Environmental Fluid Mechanics, Deltares, East China Normal University)
Zhenwu Wang (East China Normal University)
Kailin Huang (Wuhan University)
Pingxing Ding (East China Normal University)
Zhengbing Wang (Deltares, TU Delft - Coastal Engineering)
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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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