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.

翻译：在工程设计中，代理模型被广泛用于替代计算成本高昂的仿真过程，其通过利用计算机辅助设计（CAD）模型中的设计变量和几何参数来实现这一目标。然而，这些模型在简化至低维时往往会丢失关键信息，并且在参数定义方面面临挑战，尤其是在处理工业数据集中常见的复杂三维形状时。为应对这些局限性，我们提出了一种基于贝叶斯图神经网络（GNN）的三维深度学习代理模型框架，该框架通过网格表示直接从CAD数据中学习几何特征，以预测工程性能。我们的框架通过贝叶斯优化确定网格单元的最优尺寸，从而构建出高精度的代理模型。此外，该框架能有效处理三维CAD模型不规则且复杂的结构特征，这与深度学习通常使用的二维图像中规则均匀的像素结构存在显著差异。实验结果表明，网格质量对代理模型的预测精度具有重要影响，优化尺寸的网格能够实现更优越的性能。我们比较了基于不同三维表示（如体素、点云和图结构）的模型性能，并评估了蒙特卡洛模拟与贝叶斯优化方法在寻找最优网格尺寸时的计算成本。我们预期，所提出的框架有望应用于各工程领域的基于网格的仿真分析，并充分利用计算机辅助工程中常见的基于物理的信息。