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.

翻译：许多材料过程与性质取决于晶界能量的各向异性，即该能量是界面五个几何自由度（DOF）的函数。为高效探索该参数空间并发现未探索区域中的能量尖点，近期建立了一种结合原子模拟与统计方法的技术（10.1002/adts.202100615）。本工作将这种序贯采样技术以主动学习算法的思路进行拓展，通过增加一个判据来决定采样何时达到充分程度并停止。具体而言，引入了两个参数用于实时分析采样结果：代表能量地貌中最具研究价值且最重要区域的尖点数量，以及相邻迭代间能量的最大变化量。监测这两个量可深入了解子空间能量结构特性。两者组合可提供评估二维子空间（含非周期小角晶界的晶界平面取向）采样所需的必要信息。在初始设计中包含合理数量的数据点后，仅需少量精心选择的序贯迭代即可显著提升采样精度，并能在额外几步序贯步骤内发现未知尖点。