# Proposing an intelligent mesh smoothing method with graph neural networks

arXiv: https://arxiv.org/abs/2311.12815 · HTML: https://mlsanity.com/paper/2311.12815/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 70 references that are in the map.
- First posted on arXiv 24 Sep 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Instance Normalization: The Missing Ingredient for Fast Stylization](https://mlsanity.com/paper/1607.08022/) (2016)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Tune: A Research Platform for Distributed Model Selection and Training](https://mlsanity.com/paper/1807.05118/) (2018)
- [GraphNorm: A Principled Approach to Accelerating Graph Neural Network Training](https://mlsanity.com/paper/2009.03294/) (2020)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks](https://mlsanity.com/paper/2106.04900/) (2021)
- [MeshingNet: A New Mesh Generation Method based on Deep Learning](https://mlsanity.com/paper/2004.07016/) (2020)
- [M2N: Mesh Movement Networks for PDE Solvers](https://mlsanity.com/paper/2204.11188/) (2022)
- [E2N: Error Estimation Networks for Goal-Oriented Mesh Adaptation](https://mlsanity.com/paper/2207.11233/) (2022)
- [HLO: Half-kernel Laplacian Operator for Surface Smoothing](https://mlsanity.com/paper/1905.04678/) (2019)

## Built on by (most cited first, 1 of 1)

- [GNNRL-Smoothing: A Prior-Free Reinforcement Learning Model for Mesh Smoothing](https://mlsanity.com/paper/2410.19834/) (2024)

## Abstract (arXiv)

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.