Graph convolutional network for predicting abnormal grain growth in Monte Carlo simulations of microstructural evolution

TL;DR

This work tackles predicting abnormal grain growth (AGG) from the initial microstructure using two approaches: a computer-vision pipeline and a graph-based Simple Graph Convolution (SGC) on a grain-graph representation. A large Monte Carlo Potts dataset (27,588 simulations, $512\times512$ grids, $CGR$ threshold of 10) enables a direct comparison, with SGC achieving about 73% test accuracy—outperforming the CV baseline (~69–70%) and showing less overfitting. Feature analysis indicates grain type and local connectivity near the candidate grain carry the predictive signal, reflecting the physical mechanism of AGG, where high-mobility boundaries propagate growth through the grain network. The study also reveals substantial intrinsic uncertainty due to stochasticity in the simulations, suggesting that future work should emphasize predictive distributions and robustness through repeated sampling and richer feature sets.

Abstract

Recent developments in graph neural networks show promise for predicting the occurrence of abnormal grain growth, which has been a particularly challenging area of research due to its apparent stochastic nature. In this study, we generate a large dataset of Monte Carlo simulations of abnormal grain growth. We train simple graph convolution networks to predict which initial microstructures will exhibit abnormal grain growth, and compare the results to a standard computer vision approach for the same task. The graph neural network outperformed the computer vision method and achieved 73% prediction accuracy and fewer false positives. It also provided some physical insight into feature importance and the relevant length scale required to maximize predictive performance. Analysis of the uncertainty in the Monte Carlo simulations provides additional insights for ongoing work in this area.

Figures (10)

• Figure 1: Evolution of sample SPPARKS grain growth simulations with CGR values of 5 (top), representing normal growth, and 20 (bottom), representing abnormal growth. Snapshots of the microstructure are shown after of 0 (left), 2,000,000 (middle), and 4,000,000 (right) iterations. The candidate grain is shown in white. In both simulations, the candidate grain "wraps around" the edges of the images due to the use of periodic boundary conditions.
• Figure 2: Grayscale image representations of the initial microstructure. Left: Resized image contains full initial state of the system. Right: Cropped image includes the local neighborhood of the candidate grain.
• Figure 3: Schematic of graph extraction process. a) Output from SPPARKS. Pixel color corresponds to arbitrary grain id. b) Graph structure overlaid on image from a). Nodes, shown in white circles, correspond to individual grains. Edges, shown in black lines, correspond to boundaries between neighboring grains. c) Graph feature extraction. The color and radius of the circle for each node indicate grain "type" and area.
• Figure 4: Training, validation, and test accuracy for SVM models trained with and without image cropping. Each result represents the model with the best validation performance after parameter tuning.
• Figure 5: Confusion matrices for computer vision model trained without cropping images.