GGA-PBE band gap machine learning correction with a reduced set of features

It is widely known that the density functional theory's (DFT) generalized gradient approximation (GGA) underestimates the energy gap [1]. The most commonly used GGA functional in the physics community is the Perdew-Burke-Ernzerhof (PBE) functional [2]. In this paper, we introduce a machine-learning correction to the energy gap estimated by PBE, utilizing a much smaller set of only eight features. These features do not require any additional calculations. They are based on GGA-PBE calculations (such as GGA-PBE band gap, cohesive energy, and inverse of average atomic distance) and standard atomic and ionic tables (such as average oxidation states, atomic period, and atomic electronegativity). The models were trained using 268 inorganic semiconductors and insulators with a G₀W₀ gaps ranging from 0.36 eV to 14.55 eV as the target features. G₀W₀ is a many-body perturbation theory calculation that provides high accuracy for band gaps but requires a very costly computation [3]. The models were trained with various regression methods, all yielding comparable accuracies. However, the most accurate model was based on Gaussian process regression (GPR), resulting in a 0.232 eV root-mean-square error (RMSE) test accuracy and an R-squared of 0.9943. Using a simple set of features and the relatively efficient GGA-PBE method, these models shall provide more accurate DFT-GGA band gap calculations without deteriorating the computational efficiency.