An intelligent mesh-smoothing method with graph neural networks

In computational fluid dynamics (CFD), mesh-smoothing methods are widely used to refine the mesh quality for achieving high-precision numerical simulations. Specifically, optimization-based smoothing is used for high-quality mesh smoothing, but it incurs significant computational overhead. Pioneer works have improved its smoothing efficiency by adopting supervised learning to learn smoothing methods from high-quality meshes. However, they pose difficulties in smoothing the mesh nodes with varying degrees and require data augmentation to address the node input sequence problem. Additionally, the required labeled high-quality meshes further limit the applicability of the proposed method. In this paper, we present graph-based smoothing mesh net (GMSNet), a lightweight neural network model for intelligent mesh smoothing. GMSNet adopts graph neural networks (GNNs) to extract features of the node’s neighbors and outputs the optimal node position. During smoothing, we also introduce a fault-tolerance mechanism to prevent GMSNet from generating negative volume elements. With a lightweight model, GMSNet can effectively smooth mesh nodes with varying degrees and remain unaffected by the order of input data. A novel loss function, MetricLoss, is developed to eliminate the need for high-quality meshes, which provides stable and rapid convergence during training. We compare GMSNet with commonly used mesh-smoothing methods on two-dimensional (2D) triangle meshes. Experimental results show that GMSNet achieves outstanding mesh-smoothing performances with 5% of the model parameters compared to the previous model, but offers a speedup of 13.56 times over the optimization-based smoothing.