A data-free Kolmogorov–Arnold Network-based method for structured mesh generation

Mesh generation is a critical but time-consuming process for stable and accurate numerical simulations. Although multi-layer perceptron-based meshing methods can be effective, they suffer from slow training convergence and heavy reliance on prior datasets. To overcome these problems, we propose the Kolmogorov–Arnold Network-based meshing network, an efficient data-free method for structured mesh generation. The proposed method takes the meshing task as an optimization problem and embeds meshing-related differential equations into the loss function of Kolmogorov–Arnold Networks. It employs two parts to generate meshes efficiently. The Kolmogorov–Arnold Network part introduces learnable activation functions on the edges of the network, which enables the network to learn meshing rules between parametric and computational domains. The physics-informed learning part provides meshing-related information to guide the network training. Finally, the proposed method can produce high-quality structured meshes with a user-defined number of quadrilateral or hexahedral cells through feed-forward prediction. Experiments on different geometries show that the proposed method achieves up to three orders of magnitude improvement in meshing efficiency compared to traditional methods. It also outperforms state-of-the-art multi-layer perceptron-based methods, yielding high-quality meshes in both two-dimensional and three-dimensional cases without prepared data.