A deep equivariant neural network approach for efficient hybrid density functional calculations

Hybrid density functional theory (DFT) fixes the notorious “band gap problem” of standard DFT by incorporating exact exchange, but at a daunting computational cost. We developed DeepH-hybrid, an equivariant neural network that learns the hybrid-functional Hamiltonian directly from material structure, bypassing costly self-consistent iterations. Trained on small structures, the model generalizes to large supercells — including magic-angle twisted bilayer graphene with over 11,000 atoms — making hybrid-DFT accuracy affordable for large-scale materials simulations for the first time.