  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.
