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An efficient machine-learning-based method combined with a conventional localoptimization technique has been proposed for exploring local energy minima ofinterstitial species in a crystal. In the proposed method, an effective initialpoint for local optimization is sampled at each iteration from a given feasibleset in the search space. The effective initial point is here defined as thegrid point that most likely converges to a new local energy minimum by localoptimization and/or is located in the vicinity of the boundaries between energybasins. Specifically, every grid point in the feasible set is classified by thepredicted label indicating the local energy minimum that the grid pointconverges to. The classifier is created and updated at every iteration usingthe already-known information on the local optimizations at the earlieriterations, which is based on the support vector machine (SVM). The SVMclassifier uses our original kernel function designed as reflecting thesymmetries of both host crystal and interstitial species. The most distantunobserved point on the classification boundaries from the observed points issampled as the next initial point for local optimization. The proposed methodis applied to three model cases, i.e., the six-hump camelback function, aproton in strontium zirconate with the orthorhombic perovskite structure, and awater molecule in lanthanum sulfate with the monoclinic structure, todemonstrate the high performance of the proposed method.

Machine-learning-based sampling method for exploring local energy minima of interstitial species in a crystal