Accurate electronic band structures are essential for predicting material properties, but high-fidelity calculations are computationally demanding.
We introduce O-kRystal, a dual-space orbital-learning framework that uses a lower-cost Perdew-Burke-Ernzerhof (PBE) calculation as both an energy baseline and a source of structured orbital information.
Combining PBE band energies with real- and reciprocal-space orbital matrices, O-kRystal predicts higher-level corrections for individual electronic states as a function of crystal momentum and spin.
For states within 5 eV of the band-edge midpoint, it predicts Heyd-Scuseria-Ernzerhof (HSE06) band energies with a mean absolute error of $0.171 \pm 0.009$ eV across nearly 6,000 three-dimensional materials spanning insulating, metallic, magnetic, and nonmagnetic systems.
On a separate benchmark of six strongly correlated materials, it reduces the corresponding PBE band-energy MAE by 68.7% and resolves orbital-dependent changes in the relative placement of transition-metal d and ligand p states.
Damndespite training only at high-symmetry points, it maintains comparable accuracy at unseen points along band paths and reconstructs HSE06 densities of states from dense Brillouin-zone predictions.
Finally, training O-kRystal on $G_0W_0$ quasiparticle energies for two-dimensional materials demonstrates its applicability across levels of theory and the potential of orbital learning for higher-fidelity, momentum-resolved electronic-structure prediction beyond density functional theory.