Bayesian optimization of chemical composition: a comprehensive framework and its application to $R$Fe$_{12}$-type magnet compounds

Abstract

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 (PAW) method. We apply our framework to optimization of $R$Fe$_{12}$-type magnet compounds (R$_{1-α}$Z$_α$)(Fe$_{1-β}$Co$_β$)$_{12-γ}$Ti$_γ$, and benchmark the efficiency in determination of the optimal choice of elements (R and Z) and ratio ($α$, $β$ and $γ$) with respect to magnetization, Curie temperature and formation energy. We find that the optimization efficiency depends on descriptors significantly. The variable $β$, $γ$ 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.

16 pages, 13 figures