Accurate band gap prediction based on an interpretable Δ-machine learning

Most materials science datasets are not so large that the accuracy of machine learning (ML) models is relatively limited if only simple features are used. Here, we constructed an interpretable ∆-machine learning (∆-ML) model to connect the hybrid functional HSE bandgap (E_g^HSE) with the PBE functional bandgap (E_g^PBE). The former can reproduce the band gap comparable with experiments, but the computational cost is much more challenging. The training is based on our high-throughput calculations on a set of two-dimensional semiconductors. Four complex descriptors, all based on the E_g^PBE are constructed using the sure independence screening and sparsifying operator (SISSO) algorithm. Using these descriptors, the ∆-ML can accurately predict the E_g^HSE of test set with a determination coefficient (R²) of 0.96. The error satisfies a normal distribution with a mean of zero. We provide a direct functional relationship between input descriptors and target properties. We find that E_g^HSE and the 5/6th power of E_g^PBE show a significant linear correlation, which may guide rapid prediction of E_g^HSE from E_g^PBE for materials with a E_g^HSE greater than 0.22 eV. We also discussed the correlation between the atomic radius and the E_g^HSE. Our work will provide an effective and interpretable model to construct the optimal physical descriptors for ML prediction on bandgaps in screening massive new 2D materials research.