Towards active learning: A stopping criterion for the sequential sampling of grain boundary degrees of freedom

TL;DR

This paper introduces an active learning stopping criterion for sequential sampling of grain boundary energy landscapes, enabling efficient discovery of energy cusps with fewer simulations.

Contribution

It extends existing sampling methods by adding a criterion based on cusp count and energy change to determine when to stop sampling.

Findings

Few sequential iterations significantly improve sampling accuracy.

Unknown energy cusps can be identified within a few additional steps.

The method effectively evaluates sampling of 2D grain boundary subspaces.

Abstract

Many materials processes and properties depend on the anisotropy of the energy of grain boundaries, i.e.~on the fact that this energy is a function of the five geometric degrees of freedom (DOF) of the interface. To access this parameter space in an efficient way and to discover energy cusps in unexplored regions, a method was recently established, which combines atomistic simulations with statistical methods 10.1002/adts.202100615. This sequential sampling technique is now extended in the spirit of an active learning algorithm by adding a criterion to decide when the sampling has advanced enough to stop. In this instance, two parameters to analyse the sampling results on the fly are introduced: the number of cusps, which correspond to the most interesting and important regions of the energy landscape, and the maximum change of energy between two sequential iterations. Monitoring these two quantities provides valuable insight into how the subspaces are energetically structured. The combination of both parameters provides the necessary information to evaluate the sampling of the 2D subspaces of grain boundary plane inclinations of even non-periodic, low angle grain boundaries. With a reasonable number of data points in the initial design, only a few appropriately chosen sequential iterations already improve the accuracy of the sampling substantially and unknown cusps can be found within a few additional sequential steps.