# Conformal Predictions Enhanced Expert-guided Meshing with Graph Neural Networks

arXiv: https://arxiv.org/abs/2308.07358 · HTML: https://mlsanity.com/paper/2308.07358/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 47 references that are in the map.
- First posted on arXiv 14 Aug 2023.

## Builds on (most cited first, 22 of 22)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Classification with Valid and Adaptive Coverage](https://mlsanity.com/paper/2006.02544/) (2020)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [SEGCloud: Semantic Segmentation of 3D Point Clouds](https://mlsanity.com/paper/1710.07563/) (2017)
- [Generative and Discriminative Voxel Modeling with Convolutional Neural Networks](https://mlsanity.com/paper/1608.04236/) (2016)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Recurrent Slice Networks for 3D Segmentation of Point Clouds](https://mlsanity.com/paper/1802.04402/) (2018)
- [3D Shape Segmentation with Projective Convolutional Networks](https://mlsanity.com/paper/1612.02808/) (2016)
- [PcDGAN: A Continuous Conditional Diverse Generative Adversarial Network For Inverse Design](https://mlsanity.com/paper/2106.03620/) (2021)
- [MO-PaDGAN: Reparameterizing Engineering Designs for Augmented Multi-objective Optimization](https://mlsanity.com/paper/2009.07110/) (2020)
- [Machine Learning-Based Optimal Mesh Generation in Computational Fluid Dynamics](https://mlsanity.com/paper/2102.12923/) (2021)

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

- [Reducing the Sensitivity of Neural Physics Simulators to Mesh Topology via Pretraining](https://mlsanity.com/paper/2501.09597/) (2025)

## Abstract (arXiv)

Computational Fluid Dynamics (CFD) is widely used in different engineering fields, but accurate simulations are dependent upon proper meshing of the simulation domain. While highly refined meshes may ensure precision, they come with high computational costs. Similarly, adaptive remeshing techniques require multiple simulations and come at a great computational cost. This means that the meshing process is reliant upon expert knowledge and years of experience. Automating mesh generation can save significant time and effort and lead to a faster and more efficient design process. This paper presents a machine learning-based scheme that utilizes Graph Neural Networks (GNN) and expert guidance to automatically generate CFD meshes for aircraft models. In this work, we introduce a new 3D segmentation algorithm that outperforms two state-of-the-art models, PointNet++ and PointMLP, for surface classification. We also present a novel approach to project predictions from 3D mesh segmentation models to CAD surfaces using the conformal predictions method, which provides marginal statistical guarantees and robust uncertainty quantification and handling. We demonstrate that the addition of conformal predictions effectively enables the model to avoid under-refinement, hence failure, in CFD meshing even for weak and less accurate models. Finally, we demonstrate the efficacy of our approach through a real-world case study that demonstrates that our automatically generated mesh is comparable in quality to expert-generated meshes and enables the solver to converge and produce accurate results. Furthermore, we compare our approach to the alternative of adaptive remeshing in the same case study and find that our method is 5 times faster in the overall process of simulation. The code and data for this project are made publicly available at https://github.com/ahnobari/AutoSurf.