Exploration of stable atomic configurations in graphene-like BCN systems by Bayesian optimization

h-BCN is an intriguing material system where the bandgap varies considerably depending on the atomic configuration, even at a fixed composition. Exploring stable atomic configurations in this system is crucial for discussing the energetic formability and controllability of desirable configurations. In this study, this challenge is tackled by combining first-principles calculations with Bayesian optimization. An encoding method that represents the configurations as vectors, while incorporating information about the local atomic environments and domain knowledge, is proposed for the search. The proposed encoding method proved effective in the search, resulting in the discovery of two interesting and stable semiconductor configurations. Furthermore, the optimization behavior is discussed through principal component analysis, confirming that the ordered BN network and the C configuration features are well embedded in the search space. While our approach provided a tailored encoding for the h-BCN system in this study, it holds promise for broader application to other materials by adapting the domain knowledge matrix to each target system.