Polycrystalline materials, ubiquitous in daily life and industry, have properties governed by both the atomic lattice structure within each grain and their microstructure (grain size, shape, orientation, and adjacency). Predicting these properties is computationally expensive and challenging using physics-based models, especially for complex materials or conditions. Existing machine learning models, such as statistical-descriptor-based and image-based (using CNNs), often fall short because they don't directly account for the critical physical interactions between neighboring grains. This research introduces a novel approach using graph neural networks (GNNs) to address this limitation. The GNN model represents the polycrystalline microstructure as a graph, where each grain is a node and the features of each grain (orientation, size, number of neighbors) form the feature matrix. The adjacency relationships between grains are stored in an adjacency matrix. This graph representation allows the model to directly incorporate the interactions between neighboring grains, leading to more accurate and interpretable predictions of material properties.

Previous machine learning approaches to predicting polycrystalline material properties have primarily focused on two types of models: statistical-descriptor-based and image-based. Statistical-descriptor-based models rely on extracting statistical correlations between microstructures and properties using functions like two-point correlation functions. These functions capture relationships between physical features at different spatial locations but ignore direct interactions between neighboring grains. Image-based models, often using convolutional neural networks (CNNs), process raw microstructure images. While CNNs can automatically extract features, they also lack the ability to explicitly model the interactions between neighboring grains, which are crucial for determining macroscopic material properties. This study aims to overcome these limitations by employing a graph-based representation and GNNs.

The researchers developed a GNN model to predict the microstructure-property link in polycrystalline materials. A polycrystalline microstructure is represented as a graph G = (F, A), where F is a feature matrix containing physical features of each grain (Euler angles for orientation, grain size, and number of neighboring grains), and A is an adjacency matrix representing the adjacency relationships between grains. The GNN model uses a graph convolutional network (GCN) architecture with message-passing layers (MPLs). Each MPL updates each node's feature vector based on its own features and the features of its neighbors. This process allows for the propagation of information between grains, considering their interactions. The updated feature matrix after the final MPL is then used as an embedding of the microstructure graph, which is combined with the applied magnetic field (Hx) as input to a fully connected layer (FL) for regressing the effective magnetostriction (λeff). The model's training involved generating 492 diverse 3D polycrystalline microstructures using Dream.3D and phase-field modeling to obtain their effective magnetostriction under various magnetic fields. The dataset was split into training, validation, and testing sets. The model's hyperparameters were optimized using the validation set to minimize the macro average relative error (MARE). The Integrated Gradient (IG) method was used to analyze the importance of individual features of each grain in the prediction of magnetostriction. For comparison, the computational efficiency of the GNN model was benchmarked against three different 3D CNN models.

The GNN model achieved a low prediction error of 8.24% MARE on an independent testing dataset of 492 microstructures with varying grain numbers (12 to 297). The model's performance remained robust even with smaller datasets, indicating its ability to generalize well. The analysis showed that the model achieves a low prediction error (~10%) even with relatively small datasets (down to 72 microstructures). The GNN model significantly outperformed the tested CNN models in terms of computational efficiency, especially for large-scale microstructures with billions of voxels. The IG analysis revealed that, for the examined dataset, grain orientation generally played a more significant role than grain size in determining the effective magnetostriction. This finding is consistent with the physical principle that magnetostriction depends on grain orientation. The GNN model showed a significant computational advantage over the CNN models; the training time of CNN models increased substantially with the number of voxels while the training time of GNN model remained manageable even with a large number of grains.

The results demonstrate the effectiveness of the proposed GNN model for accurate and interpretable prediction of polycrystalline material properties. By directly incorporating the interactions between neighboring grains through the graph representation, the model outperforms previous methods that rely solely on statistical correlations or image-based features. The computational efficiency of the GNN model is a significant advantage, particularly for handling large-scale 3D microstructure datasets. The ability to quantify the importance of individual grain features through IG analysis provides valuable insights into the microstructure-property relationship. The finding that grain orientation is generally more influential than grain size in determining effective magnetostriction aligns with established physical principles.

This study successfully developed a GNN model for accurate and interpretable prediction of polycrystalline material properties. The model achieves high accuracy with relatively small datasets and is computationally efficient compared to existing methods. Future research could extend this model to incorporate grain boundary features and other mesoscale defects, further enhancing its predictive power and understanding of complex microstructures. The use of pre-trained GNN models through transfer learning could also be explored to address challenges with limited training data for specific material systems.

The study focuses on a specific material system (Tb0.3Dy0.7Fe2 alloys) and property (magnetostriction). The generalizability of the model to other materials and properties needs further investigation. The phase-field simulations used to generate the training data involve certain approximations and assumptions that might influence the results. The IG analysis, while insightful, depends on the choice of baseline graph and requires careful interpretation, particularly when considering correlated features.