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

Kevin Ferguson, Yu-hsuan Chen, Yiming Chen, Andrew Gillman, James Hardin, Levent Burak Kara

TL;DR

Topology-Agnostic Graph U-Net is proposed, 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.

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.

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

TL;DR

Topology-Agnostic Graph U-Net is proposed, 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.

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.
Paper Structure (19 sections, 3 equations, 10 figures, 2 tables)

This paper contains 19 sections, 3 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methods
  4. Datasets
  5. 2-D Dataset: von Mises Stress of a Compressed Part
  6. 3-D Dataset: Simulated Additive Manufacturing Displacement Fields
  7. Topology-Agnostic Graph U-Net
  8. Convolution
  9. Pooling
  10. Training Information
  11. Model details: 2-D problem
  12. Model details: 3-D problem
  13. Results and Discussion
  14. R-Squared Analysis
  15. Visualizations
  16. ...and 4 more sections

Figures (10)

  • Figure 1: 2-D dataset generation process: shapes are inputted into a PDE solver; loads, boundary conditions, and material properties are assigned as in the problem definition shown; von Mises stress fields are outputted as mesh data
  • Figure 2: 3-D dataset generation process: shapes are inputted into Netfabb; material properties, and process parameters are assigned via input files; z-displacement fields are outputted as mesh data
  • Figure 3: Topology-Agnostic Graph U-Net (TAG U-Net) Architecture
  • Figure 4: $k$-d tree pooling, demonstrated for a 2-D mesh
  • Figure 5: $R^2$ distributions for test shapes in the 2-D stress prediction and 3-D displacement prediction tasks.
  • ...and 5 more figures