Three-Dimensional Hyperbolic Mesh Generation Method Based on the Neural Network

Aiming at the limitations of the traditional hyperbolic mesh generation method, specifically the limited types of boundary control strategy along the advancing direction and the inability to control the outer boundary, this paper employs physics-informed neural networks with output range constraints to approximate the solutions of the governing equations that are used to generate the hyperbolic mesh. After transforming the form of the governing equations, the solution was fitted using the neural network driven solely by boundary data. By incorporating the governing equations and the boundary conditions into the loss function, the neural network method can directly control the boundaries along the advancing direction. For the outer boundary, a novel variance constraint strategy was proposed. Based on the proposed method, meshes were generated for three-dimensional surfaces and three-dimensional solids derived from the terrain surface. The quality of these meshes was compared with the traditional method. The results demonstrate that this method can effectively achieve boundary control during the hyperbolic mesh generation process and consistently produces high-quality hyperbolic meshes. Therefore, neural network-based hyperbolic mesh generation is an effective approach to achieving boundary control, which can further enhance the applicability of hyperbolic mesh generation methods.