Prediction model of band gap for inorganic compounds by combination of density functional theory calculations and machine learning techniques

Machine learning techniques are applied to make prediction models of the ${G}_{0}{W}_{0}$ band gaps for 270 inorganic compounds using Kohn-Sham (KS) band gaps, cohesive energy, crystalline volume per atom, and other fundamental information of constituent elements as predictors. Ordinary least squares regression (OLSR), least absolute shrinkage and selection operator, and nonlinear support vector regression (SVR) methods are applied with two levels of predictor sets. When the KS band gap by generalized gradient approximation of Perdew-Burke-Ernzerhof (PBE) or modified Becke-Johnson (mBJ) is used as a single predictor, the OLSR model predicts the ${G}_{0}{W}_{0}$ band gap of randomly selected test data with the root-mean-square error (RMSE) of 0.59 eV. When KS band gap by PBE and mBJ methods are used together with a set of predictors representing constituent elements and compounds, the RMSE decreases significantly. The best model by SVR yields the RMSE of 0.24 eV. Band gaps estimated in this way should be useful as predictors for virtual screening of a large set of materials.