In CFD, mesh smoothing methods are commonly utilized to refine the mesh quality to achieve high-precision numerical simulations. Specifically, optimization-based smoothing is used for high-quality mesh smoothing, but it incurs significant computational overhead. Pioneer works improve its smoothing efficiency by adopting supervised learning to learn smoothing methods from high-quality meshes. However, they pose difficulty in smoothing the mesh nodes with varying degrees and also need 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 GMSNet, a lightweight neural network model for intelligent mesh smoothing. GMSNet adopts graph neural networks to extract features of the node's neighbors and output 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 smoothing mesh nodes with varying degrees and remain unaffected by the order of input data. A novel loss function, MetricLoss, is also developed to eliminate the need for high-quality meshes, which provides a stable and rapid convergence during training. We compare GMSNet with commonly used mesh smoothing methods on two-dimensional triangle meshes. The experimental results show that GMSNet achieves outstanding mesh smoothing performances with 5% model parameters of the previous model, and attains 13.56 times faster than optimization-based smoothing.

翻译：在计算流体力学中，网格平滑方法通常用于提升网格质量，以实现高精度数值模拟。具体而言，基于优化的平滑方法虽能获得高质量网格平滑效果，但计算开销巨大。前期研究通过采用监督学习从高质量网格中学习平滑方法，提高了平滑效率。然而，此类方法难以处理不同变形程度的网格节点，且需通过数据增强应对节点输入顺序问题。此外，所需标注的高质量网格进一步限制了方法的适用性。本文提出GMSNet——一种用于智能网格平滑的轻量级神经网络模型。GMSNet采用图神经网络提取节点邻域特征，并输出最优节点位置。在平滑过程中，我们引入容错机制以防止GMSNet生成负体积单元。借助轻量级模型，GMSNet能有效平滑不同变形程度的网格节点，且不受输入数据顺序影响。我们还设计了新型损失函数MetricLoss，以消除对高质量网格的依赖，并在训练过程中实现稳定快速收敛。我们将GMSNet与常用网格平滑方法在二维三角形网格上进行对比。实验结果表明，GMSNet以仅占先前模型5%的参数规模实现了优异的网格平滑性能，且速度比基于优化的平滑方法快13.56倍。