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

Abstract

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.