Covariance linkage assimilation method for unobserved data exploration

This study proposes a materials search method combining a data assimilation technique based on a multivariate Gaussian distribution with Bayesian optimization. The efficiency of the search using this method was demonstrated using a pair of example functions. By combining Bayesian optimization with the data assimilation technique, the maximum value of the example function was found more efficiently compared to ordinary Bayesian optimization without the data assimilation. A practical demonstration was also conducted by constructing a data assimilation model for the band gap of $({\mathrm{Sr}}_{1\ensuremath{-}{x}_{1}\ensuremath{-}{x}_{2}}{\mathrm{La}}_{{x}_{1}}{\mathrm{Na}}_{{x}_{2}})({\mathrm{Ti}}_{1\ensuremath{-}{x}_{1}\ensuremath{-}{x}_{2}}{\mathrm{Ga}}_{{x}_{1}}{\mathrm{Ta}}_{{x}_{2}}){\mathrm{O}}_{3}$. The concentration dependence of the band gap was analyzed, and synthesis was performed with chemical compositions in the sparse region of the training data points to validate the predictions.