Mesh generation plays a crucial role in scientific computing. Traditional mesh generation methods, such as TFI and PDE-based methods, often struggle to achieve a balance between efficiency and mesh quality. To address this challenge, physics-informed intelligent learning methods have recently emerged, significantly improving generation efficiency while maintaining high mesh quality. However, physics-informed methods fail to generalize when applied to previously unseen geometries, as even small changes in the boundary shape necessitate burdensome retraining to adapt to new geometric variations. In this paper, we introduce MeshONet, the first generalizable intelligent learning method for structured mesh generation. The method transforms the mesh generation task into an operator learning problem with multiple input and solution functions. To effectively overcome the multivariable mapping restriction of operator learning methods, we propose a dual-branch, shared-trunk architecture to approximate the mapping between function spaces based on input-output pairs. Experimental results show that MeshONet achieves a speedup of up to four orders of magnitude in generation efficiency over traditional methods. It also enables generalization to different geometries without retraining, greatly enhancing the practicality of intelligent methods.

翻译：网格生成在科学计算中扮演着关键角色。传统的网格生成方法，如TFI和基于偏微分方程的方法，往往难以在效率和网格质量之间取得平衡。为应对这一挑战，近年来兴起了物理信息智能学习方法，在保持高质量网格的同时显著提升了生成效率。然而，物理信息方法在处理未见过的几何形状时缺乏泛化能力，因为即使边界形状发生微小变化，也需要进行繁重的重新训练以适应新的几何变化。本文提出MeshONet，这是首个适用于结构化网格生成的通用智能学习方法。该方法将网格生成任务转化为具有多个输入函数和解函数的算子学习问题。为有效克服算子学习方法在多变量映射方面的限制，我们提出了一种双分支、共享主干架构，基于输入-输出对来逼近函数空间之间的映射关系。实验结果表明，与传统方法相比，MeshONet在生成效率上实现了高达四个数量级的加速。该方法还能在不重新训练的情况下泛化至不同几何形状，极大地提升了智能方法的实用性。