MeshAFN: An efficient attention-based Fourier network for self-supervised mesh generation

Mesh generation is a necessary pre-processing step in computational fluid dynamics. Recent advancements in deep learning have enhanced mesh generation capabilities. However, most existing methods rely on data-driven training, which is constrained by the high cost of acquiring high-quality mesh datasets. Data-free methods effectively address the cost issue of dataset construction but have difficulty fitting boundary conditions properly, making the generated meshes unacceptable for practical engineering scenarios. To overcome this limitation, this paper presents MeshAFN, a self-supervised approach for structured mesh generation. MeshAFN introduces an attention-based Fourier network to enhance feature extraction while optimizing mesh quality. By incorporating attention mechanisms and Fourier series into the feature extraction layer, MeshAFN effectively captures critical geometric characteristics. Furthermore, a novel loss function is designed based on the Navier–Lamé and Laplace equations to learn mapping between the computational domain and the physical domain, ensuring that the generated meshes strictly meet physical constraints and boundary conditions. Experimental results demonstrate that MeshAFN achieves superior mesh quality and fewer model parameters in mesh generation tasks.