求解二维不可压Navier-Stokes方程的PINN算法
PINN Algorithm for Solving Two-Dimensional Incompressible Navier-Stokes Equations
摘要: 本文采用物理信息神经网络(PINN)来求解不可压缩湍流Navier-Stokes方程。本研究引入了动态权重调整策略，使得各项误差在训练过程中得到适当的平衡，从而避免了某些误差项主导整个训练过程的问题。此外，为了加速训练收敛并提高精度，本研究还对网络结构进行了优化，结合物理约束优化过程，改变了优化方法，提高了模型的训练效率。
Abstract: In this paper, physical information neural networks (PINN) are used to solve the Navier-Stokes equations of incompressible turbulence. In this study, the dynamic weighting adjustment strategy is presented to make the errors properly balanced in the training process, so as to avoid the problem that some error terms dominate the whole training process. In addition, in order to accelerate the training convergence and improve the accuracy, this study also optimized the network structure, combining with the physical constraint optimization process and changing the optimization method to improve the training efficiency of the model.
文章引用：沈旭彬, 何流利. 求解二维不可压Navier-Stokes方程的PINN算法[J]. 应用数学进展, 2025, 14(5): 348-356. https://doi.org/10.12677/aam.2025.145264

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