基于机器学习的晶体间隙种局部能量极小值的采样方法

K. Toyoura, Kansei Kanayama
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引用次数: 1

摘要

提出了一种有效的基于机器学习的方法,结合传统的局部优化技术来探索晶体中间隙种的局部能量极小值。在该方法中,每次迭代从搜索空间中给定的可行集中采样一个有效的局部优化起始点。本文将有效初始点定义为最可能通过局部优化收敛到新的局部能量最小值和/或位于能量盆地边界附近的网格点。具体来说,每个可行集中的网格点都用表示该网格点收敛到的局部能量最小值的预测标签进行分类。在每次迭代中使用关于早期迭代的局部优化的已知信息创建和更新分类器,这些信息基于支持向量机(SVM)。支持向量机分类器使用我们设计的原始核函数来反映宿主晶体和间隙物种的对称性。将分类边界上距离观测点最远的未观测点作为下一个初始点进行局部优化。将该方法应用于六个驼峰驼背函数、锆酸锶中具有正交钙钛矿结构的质子和硫酸镧中具有单斜结构的水分子三个模型案例,验证了该方法的高性能。
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Machine-learning-based sampling method for exploring local energy minima of interstitial species in a crystal
An efficient machine-learning-based method combined with a conventional local optimization technique has been proposed for exploring local energy minima of interstitial species in a crystal. In the proposed method, an effective initial point for local optimization is sampled at each iteration from a given feasible set in the search space. The effective initial point is here defined as the grid point that most likely converges to a new local energy minimum by local optimization and/or is located in the vicinity of the boundaries between energy basins. Specifically, every grid point in the feasible set is classified by the predicted label indicating the local energy minimum that the grid point converges to. The classifier is created and updated at every iteration using the already-known information on the local optimizations at the earlier iterations, which is based on the support vector machine (SVM). The SVM classifier uses our original kernel function designed as reflecting the symmetries of both host crystal and interstitial species. The most distant unobserved point on the classification boundaries from the observed points is sampled as the next initial point for local optimization. The proposed method is applied to three model cases, i.e., the six-hump camelback function, a proton in strontium zirconate with the orthorhombic perovskite structure, and a water molecule in lanthanum sulfate with the monoclinic structure, to demonstrate the high performance of the proposed method.
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