Journal of Guangxi Normal University(Natural Science Edition) ›› 2025, Vol. 43 ›› Issue (4): 58-68.doi: 10.16088/j.issn.1001-6600.2024061802

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Attention-based PINNs Method for Solving Saint-Venant Equations

HAN Shuo, JIANG Linfeng, YANG Jianbin*   

  1. School of Mathematics, Hohai University, Nanjing Jiangsu 210000, China
  • Received:2024-06-18 Revised:2024-07-28 Online:2025-07-05 Published:2025-07-14

Abstract: A method for simulating flood dynamics using Physics-Informed Neural Networks with Attention Mechanism (PINNsFormer) is proposed to address the shortcomings of Physics-Informed Neural Networks (PINNs) in handling time-dependent problems. The PINNsFormer model is applied to solve the Saint-Venant equations. The model effectively captures spatiotemporal dependencies, thus improving accuracy and generalization. Experimental results show that this method performs excellently in simulating flood propagation and capturing water surface profile details. Compared with PINNs and neural network models FLS and QRes, which handle time features, PINNsFormer demonstrates higher stability and accuracy. Numerical experiments on a horizontal plane and a uniform adverse slope indicate that the PINNsFormer method achieves the lowest loss values and test errors, reaching an accuracy of 10-4 magnitude, accurately reproducing the shape of flood inundation boundaries.

Key words: Saint-Venant equations, PINNs, transformer, attention mechanism

CLC Number:  TP183;O241.8
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