Graph Neural Networks for Mesh Generation and Adaptation in Structural and Fluid Mechanics

The finite element discretization of computational physics problems frequently involves the manual generation of an initial mesh and the application of adaptive mesh refinement (AMR). This approach is employed to selectively enhance the accuracy of resolution in regions that encompass significant features throughout the simulation process. In this paper, we introduce Adaptnet, a Graph Neural Networks (GNNs) framework for learning mesh generation and adaptation. The model is composed of two GNNs: the first one, Meshnet, learns mesh parameters commonly used in open-source mesh generators, to generate an initial mesh from a Computer Aided Design (CAD) file; while the second one, Graphnet, learns mesh-based simulations to predict the components of an Hessian-based metric to perform anisotropic mesh adaptation. Our approach is tested on structural (Deforming plate–Linear elasticity) and fluid mechanics (Flow around cylinders–steady-state Stokes) problems. Our findings demonstrate the model’s ability to precisely predict the dynamics of the system and adapt the mesh as needed. The adaptability of the model enables learning resolution-independent mesh-based simulations during training, allowing it to scale effectively to more intricate state spaces during inference.