基于图神经网络的网格平滑方法研究

王志超; 陈新海; 颜君峻; 刘杰

doi:10.1631/FITEE.2300878

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基于图神经网络的网格平滑方法研究

常规文章 | Updated：2025-04-03

- 基于图神经网络的网格平滑方法研究
  Enhanced Publication
- An intelligent mesh-smoothing method with graph neural networks
- 信息与电子工程前沿（英文） 2025年26卷第3期页码：367-384
- Affiliations：
  
  1.Science and Technology on Parallel and Distributed Processing Laboratory, National University of Defense Technology, Changsha 410073, China
  2.Laboratory of Digitizing Software for Frontier Equipment, National University of Defense Technology, Changsha 410073, China
- Author bio：
  
  E-mail: wangzhichao@nudt.edu.cn
  ‡Corresponding author
- Funds：
  
  National Key Research and Development Program of China(2021YFB0300101);Youth Foundation of National University of Defense Technology, China(ZK2023-11);National Natural Science Foundation of China(12102467)
- DOI：10.1631/FITEE.2300878
  中图分类号： TP391.4
- 收稿：2023-12-29，
  
  修回：2024-04-16，
  
  纸质出版：2025-03
- Accepted：
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王志超, 陈新海, 颜君峻, 等. 基于图神经网络的网格平滑方法研究[J]. 信息与电子工程前沿（英文）, 2025,26(3):367-384.

Zhichao WANG, Xinhai CHEN, Junjun YAN, et al. An intelligent mesh-smoothing method with graph neural networks[J]. Frontiers of Information Technology & Electronic Engineering, 2025, 26(3): 367-384.
王志超, 陈新海, 颜君峻, 等. 基于图神经网络的网格平滑方法研究[J]. 信息与电子工程前沿（英文）, 2025,26(3):367-384. DOI： 10.1631/FITEE.2300878.

Zhichao WANG, Xinhai CHEN, Junjun YAN, et al. An intelligent mesh-smoothing method with graph neural networks[J]. Frontiers of Information Technology & Electronic Engineering, 2025, 26(3): 367-384. DOI： 10.1631/FITEE.2300878.

摘要

在计算流体力学中，网格平滑方法通常被应用于优化网格质量，以实现高精度的数值模拟。其中，基于优化的平滑方法广泛用于高质量网格平滑，但其计算成本相对较高。一些先驱性研究工作尝试采用监督学习的方法，从高质量网格样本中学习平滑方法，以提高其平滑效率。然而，该方法存在一些限制，例如难以处理不同度节点的问题，并且需要数据增强来解决网格节点输入顺序的问题。此外，对于高质量网格数据的依赖也限制了该方法的适用性。为解决这些问题，本文提出一种轻量级神经网络模型GMSNet，以实现智能化的网格平滑。GMSNet采用图神经网络来提取节点邻居的特征，并输出最优的节点位置。在平滑过程中，本文还引入了一种容错机制，以防止GMSNet生成负体积元素。通过轻量级的模型架构，GMSNet能够有效地平滑不同度的网格节点，并且不受输入数据顺序的影响。此外，本文还提出一种新颖的损失函数MetricLoss，用于消除对高质量网格数据的依赖，并促进训练的稳定、快速收敛。本文在二维非结构网格上将GMSNet与常用的网格平滑方法进行对比。实验结果表明，相较于之前的模型，GMSNet在具有出色的网格平滑性能的同时，仅需要其5%的参数，并且平滑速度是基于优化的方法的13.56倍。

Abstract

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.

关键词

Keywords

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