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We propose a data-assimilation method for evaluating the finite-temperaturemagnetization of a permanent magnet over a high-dimensional composition space.Based on a general framework for constructing a predictor from two data setsincluding missing values, a practical scheme for magnetic materials isformulated in which a small number of experimental data in limited compositionspace 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 $(\alpha, \beta, \gamma, \delta, \zeta)$ spaceat arbitrary temperature is obtained. It is shown that the Co doping does notenhance the magnetization at low temperatures, whereas the magnetizationincreases with increasing $\delta$ above 320 K.

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