Learning the grain boundary manifold: tools for visualizing and fitting grain boundary properties

With the proliferation of grain boundary data in materials science from both experiments and simulations, tools are needed to explore the five dimensional space of grain boundaries and visualize and fit structure property relationships along arbitrary paths through this space. In this work, we leverage a recently developed geodesic metric for grain boundaries to visualize the global geometry of grain boundary datasets and fit grain boundary energy to macroscopic grain boundary geometry. It is found that the 5D connectivity of the 388 grain boundary Olmsted dataset can be visualized via dimensionality reduction in 3D with a high degree of interpretability. Furthermore, after selectively adding new grain boundaries to the dataset, these visualizations suggest new global features of grain boundary space, including the existence of a grain boundary fundamental zone with well defined subsets of high symmetry boundaries along faces. Geodesic sampling is shown to be an effective tool to extend grain boundary datasets to new regions of the 5D space. Finally, a simple grain boundary energy kernel regression model with only one fitting parameter is demonstrated to predict grain boundary energy in the Olmsted dataset to within 10% RMSE.