Implicit geometry neural network for mesh generation

The accuracy of numerical computation heavily relies on appropriate meshing, which serves as the foundation for numerical computation. Although adaptive refinement methods are available, an adaptive numerical solution is likely to be ineffective if it originates from a poorly initial mesh. Therefore, it is crucial to generate meshes that accurately capture the geometric features. As an indispensable input in meshing methods, the Mesh Size Function (MSF) determines the quality of the generated mesh. However, the current generation of MSF involves human participation to specify numerous parameters, leading to difficulties in practical usage. Considering the capacity of machine learning to reveal the latent relationships within data, this paper proposes a novel machine learning method, Implicit Geometry Neural Network (IGNN), for automatic prediction of appropriate MSFs based on the existing mesh data, enabling the generation of unstructured meshes that align precisely with geometric features. IGNN employs the generative adversarial theory to learn the mapping between the implicit representation of the geometry (Signed Distance Function, SDF) and the corresponding MSF. Experimental results show that the proposed method is capable of automatically generating appropriate meshes and achieving comparable meshing results compared to traditional methods. This paper demonstrates the possibility of significantly decreasing the workload of mesh generation using machine learning techniques, and it is expected to increase the automation level of mesh generation.