arXiv:2501.11937cs.LGcs.AI2025-01被引 1

MeshONet让结构化网格生成更快更通用,无需重新训练就能适配新形状。

MeshONet: A Generalizable and Efficient Operator Learning Method for Structured Mesh Generation

  • 将网格生成转为函数空间映射的算子学习问题,用双分支共享主干结构建模多变量关系。
  • 相比传统方法效率提升高达10000倍,且在不同几何形状间可直接泛化。
  • 适合需要快速生成高质量网格的工程仿真场景,如流体、结构分析等。

网格生成在科学计算中至关重要。传统方法如TFI和基于偏微分方程的方法难以兼顾效率与网格质量。近年来,物理信息智能学习方法虽显著提升了生成效率并保持高网格质量,但面对未见过的几何形状时缺乏泛化能力,仅边界形状微小变化即需大量重训练。本文提出MeshONet,首个通用化的智能网格生成方法。该方法将网格生成任务转化为具有多个输入与输出函数的算子学习问题。为克服算子学习中多变量映射的限制,提出双分支共享主干架构,基于输入-输出对逼近函数空间间的映射。实验表明,MeshONet相较传统方法生成效率最高提升四个数量级,且无需重训即可推广至不同几何形状,极大提升智能方法的实用性。

原文摘要 · Abstract (English)

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.

网格生成算子学习深度学习通用性

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