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StruMNet: 一种融合神经网络和偏微分方程的结构网格生成方法

StruMNet: A Structural Mesh Generation Method Integrating Neural Networks and Partial Differential Equations

  • 摘要: 网格生成是计算流体力学前处理环节的关键, 在整个计算流体力学数值模拟中扮演着十分重要的角色. 为了进一步提升网格生成效率及智能化水平, 提出了一种融合神经网络和偏微分方程的结构网格生成方法StruMNet. 所提出的方法以计算域的边界以及内部的采样点为输入, 建立结合偏微分方程的神经网络模型用于网格生成, 控制方程和几何边界约束嵌入在损失函数中作为模型的优化目标; 所提出的方法引入了损失函数自适应权重策略和点加权机制来提升网格质量及在复杂边界处的拟合能力; 训练后的StruMNet能够根据给定的边界形状预测网格点; 实验结果表明, StruMNet在不同几何上的网格生成质量优于物理信息神经网络方法和MGNet方法, 在网格生成效率方面相较于传统方法提高3个数量级, 最终实现结构网格的快速生成.

     

    Abstract: Mesh generation is a crucial step in the preprocessing phase of computational fluid dynamics (CFD) and plays a vital role in the overall CFD numerical simulation process. To further enhance the efficiency and intelligence of mesh generation, we propose StruMNet, a structured mesh generation method that integrates neural networks with partial differential equations. This method takes the boundaries of the computational domain and internal sampling points as inputs to establish a neural network model combined with partial differential equations for mesh generation. The loss function incorporates both control equation loss and geometric boundary constraint loss as optimization objectives. Additionally, the method introduces an adaptive weighting strategy for the loss function and a point-weighting mechanism to enhance mesh quality and fitting capabilities, especially at complex boundaries. Once trained, StruMNet can predict mesh points based on given boundary shapes. Experimental results show that StruMNet outperforms the physics-informed neural networks method and the MGNet method in terms of mesh quality across various geometries and improves mesh generation efficiency by three orders of magnitude compared to traditional methods, ultimately enabling the rapid generation of structured meshes.

     

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