# Bayesian Mesh Optimization for Graph Neural Networks to Enhance Engineering Performance Prediction

arXiv: https://arxiv.org/abs/2406.01996 · HTML: https://mlsanity.com/paper/2406.01996/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 4 Jun 2024.

## Builds on (most cited first, 9 of 9)

- [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)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [MeshNet: Mesh Neural Network for 3D Shape Representation](https://mlsanity.com/paper/1811.11424/) (2018)
- [Integrating Deep Learning into CAD/CAE System: Generative Design and Evaluation of 3D Conceptual Wheel](https://mlsanity.com/paper/2006.02138/) (2020)
- [Explainable Artificial Intelligence for Manufacturing Cost Estimation and Machining Feature Visualization](https://mlsanity.com/paper/2010.14824/) (2020)
- [Wheel Impact Test by Deep Learning: Prediction of Location and Magnitude of Maximum Stress](https://mlsanity.com/paper/2210.01126/) (2022)

## Built on by (most cited first, 3 of 3)

- [Point-DeepONet: Predicting Nonlinear Fields on Non-Parametric Geometries under Variable Load Conditions](https://mlsanity.com/paper/2412.18362/) (2024)
- [DeepWheel: Generating a 3D Synthetic Wheel Dataset for Design and Performance Evaluation](https://mlsanity.com/paper/2504.11347/) (2025)
- [Robust and Explainable 3D Mode Shape Recognition Using Region-Aware Graph Neural Networks](https://mlsanity.com/paper/2607.01522/) (2026)

## Abstract (arXiv)

In engineering design, surrogate models are widely employed to replace computationally expensive simulations by leveraging design variables and geometric parameters from computer-aided design (CAD) models. However, these models often lose critical information when simplified to lower dimensions and face challenges in parameter definition, especially with the complex 3D shapes commonly found in industrial datasets. To address these limitations, we propose a Bayesian graph neural network (GNN) framework for a 3D deep-learning-based surrogate model that predicts engineering performance by directly learning geometric features from CAD using mesh representation. Our framework determines the optimal size of mesh elements through Bayesian optimization, resulting in a high-accuracy surrogate model. Additionally, it effectively handles the irregular and complex structures of 3D CADs, which differ significantly from the regular and uniform pixel structures of 2D images typically used in deep learning. Experimental results demonstrate that the quality of the mesh significantly impacts the prediction accuracy of the surrogate model, with an optimally sized mesh achieving superior performance. We compare the performance of models based on various 3D representations such as voxel, point cloud, and graph, and evaluate the computational costs of Monte Carlo simulation and Bayesian optimization methods to find the optimal mesh size. We anticipate that our proposed framework has the potential to be applied to mesh-based simulations across various engineering fields, leveraging physics-based information commonly used in computer-aided engineering.