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

TL;DR

MeshONet introduces a novel operator learning approach for structured mesh generation, achieving high efficiency and strong generalization to unseen geometries without retraining, surpassing traditional methods significantly.

Contribution

The paper presents MeshONet, the first generalizable operator learning method for structured mesh generation, overcoming limitations of physics-informed approaches.

Findings

Achieves up to 10,000x speedup over traditional methods.

Generalizes to new geometries without retraining.

Maintains high mesh quality across diverse shapes.

Abstract

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.