Physics-Guided Learning of Kohn-Sham Hamiltonians for Periodic Solids

Deep learning prediction of Kohn-Sham Hamiltonians overcomes the computational bottleneck of density functional theory (DFT) in large-scale electronic structure calculations. Most existing methods, however, fit Hamiltonians numerically without fully using the rich quantum-mechanical priors in DFT. We propose two methods guided by physical priors: the HSE Hamiltonian model H2Net and the variational surrogate loss (VSLoss). Inspired by the separation of short- and long-range interactions in the HSE functional, H2Net uses a dual-branch architecture. Fewer layers in the long-range branch limit the receptive field and reduce training memory requirements. The model also incorporates the non-self-consistent part of the Hamiltonian and a PBE Hamiltonian from a pretrained model as input features, explicitly introducing physical priors to improve prediction accuracy. VSLoss guides the model toward minimizing the ground-state energy, bringing the Hohenberg–Kohn variational principle into training to improve the accuracy of downstream physical properties calculated from the Hamiltonian. By improving model representations and optimization objectives, respectively, the two methods make comprehensive use of DFT priors from basis sets, pseudopotentials, functionals, and the variational principle. Together, they offer a new approach to learning Kohn–Sham Hamiltonians for periodic solids.