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${}_{1-\alpha }$Z${}_{\alpha }$)(Fe${}_{1-\beta }$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 variable $\beta$, $\gamma$ 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.

16 pages, 13 figures

References in corpus (3)

• Big Data of Materials Science - Critical Role of the Descriptor
• Matrix- and tensor-based recommender systems for the discovery of currently unknown inorganic compounds
• Intrinsic magnetic properties of {$R$(Fe${}_{1-x}$Co${}_x$)${}_{11}$Ti$Z$} ($R$ = Y and Ce; $Z$ = H, C, and N)