Data Assimilation Method for Experimental and First-Principles Data: Finite-Temperature Magnetization of (Nd,Pr,La,Ce)$_{2}$(Fe,Co,Ni)$_{14}$B

We propose a data-assimilation method for evaluating the finite-temperature magnetization of a permanent magnet over a high-dimensional composition space. Based on a general framework for constructing a predictor from two data sets including missing values, a practical scheme for magnetic materials is formulated in which a small number of experimental data in limited composition space are integrated with a larger number of first-principles calculation data. We apply the scheme to (Nd$_{1-alpha-beta-gamma}$Pr$_{alpha}$La$_{beta}$Ce$_{gamma}$)$_{2}$(Fe$_{1-delta-zeta}$Co$_{delta}$Ni$_{zeta}$)$_{14}$B. The magnetization in the whole $(alpha, beta, gamma, delta, zeta)$ space at arbitrary temperature is obtained. It is shown that the Co doping does not enhance the magnetization at low temperatures, whereas the magnetization increases with increasing $delta$ above 320 K.