Decoding microstructure-property relationships in polycrystals: an explainable GNN surrogate for crystal plasticity

Abstract

In this work, a surrogate modeling approach based on graph neural networks (GNNs) is presented to rapidly predict the homogenized stress-strain response of polycrystalline microstructure volume elements (MVEs). Each grain is represented as a node in a graph, with features such as crystallographic orientation, grain size, and aspect ratio, while grain boundaries are encoded as edges. This graph-based representation enables the GNN to capture both local and long-range interactions that govern the macroscopic mechanical response. A synthetic dataset of MVEs was generated using DREAM.3D, covering a wide range of microstructural variations in grain size distributions, morphological anisotropy, and four crystallographic texture classes. Full-field crystal plasticity (CP) simulations performed on these MVEs provided the ground-truth stress-strain data used to train and validate the GNN model. The results demonstrate high correlation between GNN predictions and CP simulations, with strong agreement across different loading conditions and an inference-time speedup of approximately 55,000×\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\times $$\end{document} relative to full-field CP, achieved up to the reported accuracies and excluding the one-time training and data-generation overhead. The trained surrogate is then subjected to a comprehensive explainability analysis using integrated gradients, providing grain-level attribution maps that identify the microstructural features most influential to the predicted stress response. Population-level attribution statistics, together with cross-validation against GradientShap, trace the dominant attribution to the statistical representativity of each volume element, whose response dispersion scales inversely with the square root of its grain count. Overall, the proposed framework offers an accurate, efficient, and interpretable tool for microstructure-informed mechanical property prediction in heterogeneous polycrystalline materials.