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

TL;DR

This paper introduces a topology-agnostic graph neural network, TAG U-Net, capable of predicting scalar fields on unstructured meshes regardless of their structure, demonstrated on additive manufacturing data with high accuracy.

Contribution

The paper presents a novel topology-agnostic graph U-Net that can handle diverse mesh structures for scalar field prediction, extending the applicability of graph neural networks.

Findings

Achieves median R-squared > 0.85 on test geometries

Performs well on both 2-D and 3-D scalar fields

Generalizes to unseen shapes with diverse training data

Abstract

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.