Microstructure evolution depends on the anisotropy of grain boundary energies. Since the grain boundary energy itself is a function of 5 degrees of freedom (DOF) - rotation axis (2 DOFs), misorientation angle (1 DOF) and the grain boundary inclination (2 DOFs) - the sampling of this parameter space is very challenging. Several methods, including machine learning methods, have been developed to tackle this problem.  So far, however, all of these methods have in common that they are not able to find the cusps - the most important areas in the energy landscape - without explicit addition of their positions and energies to the sampling/the training data. This is changed with the active learning approach proposed in this work. It is based on the sequential sampling method introduced in [1] extended by a stopping criterion, which consists of topological as well as statistical aspects [2]. This method is able to find cusps automatically, while sampling the energy precisely. It is especially suitable for inclination subspaces of non-periodic grain boundaries, as e.g. low angle grain boundaries. A comparison of the energy landscape learned by this method with grain boundary distributions as they are gained by electron-backscatter diffraction experiments, shows that the former can explain the difference of a polycrystalline nickel microstructure before and after heat treatment.

[1] Kroll, M., Schmalofski, T., Dette, H. and Janisch, R. (2022), Efficient Prediction of Grain Boundary Energies from Atomistic Simulations via Sequential Design. Adv. Theory Simul. 2100615.

[2] Schmalofski, T., Kroll, M., Dette, H. and Janisch, R. (2023), Towards active learning: A stopping criterion for the sequential sampling of grain boundary degrees of freedom, https://arxiv.org/abs/2302.01603