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.