Abstract
Various machine learning models have been used to predict the properties of polycrystalline materials, but none of them directly consider the physical interactions among neighboring grains despite such microscopic interactions critically determining macroscopic material properties. Here, we develop a graph neural network (GNN) model for obtaining an embedding of polycrystalline microstructure which incorporates not only the physical features of individual grains but also their interactions. The embedding is then linked to the target property using a feed-forward neural network. Using the magnetostriction of polycrystalline Tb0.3Dy0.7Fe2 alloys as an example, we show that a single GNN model with fixed network architecture and hyperparameters allows for a low prediction error of ~10% over a group of remarkably different microstructures as well as quantifying the importance of each feature in each grain of a microstructure to its magnetostriction. Such a microstructure-graph-based GNN model, therefore, enables an accurate and interpretable prediction of the properties of polycrystalline materials.
Highlights
Polycrystalline materials are ubiquitously used in everyday life and industry
We present the third type of machine learning model for predicting the properties of polycrystalline materials, where a polycrystalline microstructure is represented using a graph, which refers to a data structure comprising a set of interacting nodes
There are five components in each feature vector, including three Euler angles (α, β, γ) for describing the grain orientation, grain size which is defined as the number of voxels occupied by a specific grain, and the number of neighboring grains, as shown in the left panel of Fig. 1
Summary
Polycrystalline materials are ubiquitously used in everyday life and industry. The properties of such materials are governed by the atomic lattice structure within each grain, and their microstructures which typically refer to the size (nm–μm), shape, orientation, and adjacency relation of the grains. Convolutional neural network (CNN) can be used to obtain low-dimensional microstructure embeddings (known as “feature maps”) in an automated manner with little bias from human researchers[7,8,9,10,11,12,13,14]. In both types of models, the physical features at different positions/voxels of a microstructure are somewhat correlated, there are no reported means to let the physical features from neighboring grains interact with each other because of the adjacency relations of the grains are not stored. The inability to directly consider such interactions could negatively affect the performance of the subsequent property prediction because the macroscopic properties of polycrystalline materials are critically determined by such microscopic interactions[16,17]
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