  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.
