Effect of a Parameter in a Descriptor on the Efficiency of a Crystal Structure Search Using Bayesian Optimization

A crystal structure search method using Bayesian optimization (BO) has been developed recently. BO is a machine learning technique for the global optimization. It has been reported that the method can search a stable structure efficiently. In this method, a crystal structure is represented by a numerical vector referred to as a descriptor. Descriptors often have a parameter which should be predetermined. We reveal by case studies for crystalline silicon, silicon oxide, and yttrium–cobalt alloy that the efficiency of a crystal structure search depends heavily on a parameter value. Our analysis indicates that the efficiency is related to the distribution of the descriptor. Therefore, we introduce an information measure based on the descriptor distribution, which is evaluated only from a set of crystal structures. The measure succeeds in estimating a parameter value where the crystal structure search works efficiently, and thus, can be used to predetermine the value of a parameter.