Bayesian optimization of chemical composition: A comprehensive framework and its application to RFe12-type magnet compounds

We propose a framework for optimization of the chemical composition of multinary compounds with the aid of machine learning. The scheme is based on first-principles calculation using the Korringa-Kohn-Rostoker method and the coherent potential approximation (KKR-CPA). We introduce a method for integrating datasets to reduce systematic errors in a dataset, where the data are corrected using a smaller and more accurate dataset. We apply this method to values of the formation energy calculated by KKR-CPA for nonstoichiometric systems to improve them using a small dataset for stoichiometric systems obtained by the projector-augmented-wave method. We apply our framework to optimization of RFe12-type magnet compounds (R(1-alpha)Z(alpha))(Fe1-beta Co beta)(12-gamma)Ti-gamma, and benchmark the efficiency in determination of the optimal choice of elements (R and Z) and ratio (alpha, beta, and gamma) with respect to magnetization, Curie temperature, and formation energy. We find that the optimization efficiency depends on descriptors significantly. The variables beta, gamma, and the number of electrons from the R and Z elements per cell are important in improving the efficiency. When the descriptor is appropriately chosen, the Bayesian optimization becomes much more efficient than random sampling.