Topology-Agnostic Graph U-Nets for Scalar Field Prediction on Unstructured Meshes

Machine-learned surrogate models to accelerate lengthy computer simulations are becoming increasingly important as engineers look to streamline the product design cycle. In many cases, these approaches offer the ability to predict relevant quantities throughout a geometry, but place constraints on the form of the input data. In a world of diverse data types, a preferred approach would not restrict the input to a particular structure. In this paper, we propose Topology-Agnostic Graph U-Net (TAG U-Net), a graph convolutional network that can be trained to input any mesh or graph structure and output a prediction of a target scalar field at each node. The model constructs coarsened versions of each input graph and performs a set of convolution and pooling operations to predict the node-wise outputs on the original graph. By training on a diverse set of shapes, the model can make strong predictions, even for shapes unlike those seen during training. A 3-D additive manufacturing dataset is presented, containing Laser Powder Bed Fusion simulation results for thousands of parts. The model is demonstrated on this dataset, and it performs well, predicting both 2-D and 3-D scalar fields with a median R-squared > 0.85 on test geometries. Code and datasets are available online.

Scalar Field Prediction on Meshes Using Interpolated Multi-Resolution Convolutional Neural Networks

Scalar fields, such as stress or temperature fields, are often calculated in shape optimization and design problems in engineering. For complex problems where shapes have varying topology and cannot be parametrized, data-driven scalar field prediction can be faster than traditional finite element methods. However, current data-driven techniques to predict scalar fields are limited to a fixed grid domain, instead of arbitrary mesh structures. In this work, we propose a method to predict scalar fields on arbitrary meshes. It uses a convolutional neural network whose feature maps at multiple resolutions are interpolated to node positions before being fed into a multilayer perceptron to predict solutions to partial differential equations at mesh nodes. The model is trained on finite element von Mises stress fields, and once trained it can estimate stress values at each node on any input mesh. Two shape datasets are investigated, and the model has strong performance on both, with a median R-squared value of 0.91. We also demonstrate the model on a temperature field in a heat conduction problem, where its predictions have a median R-squared value of 0.99. Our method provides a potential flexible alternative to finite element analysis in engineering design contexts. Code and datasets are available online.