Learning k-Resolved Electronic Structure via Soft Energy Occupancy Prediction

Predicting electronic structure from crystal geometry is essential for computational materials discovery, as it determines key physical quantities such as band gaps, DOS, and energy isosurfaces. While per-band prediction has been explored, it requires fixing the number of bands or indexing each band across k-points, limiting generality across materials. Predicting k-resolved electronic structure avoids these constraints; we propose kRESForge, which predicts energy bin occupancy at each k-point. Given a crystal structure and a query k-point, the model predicts a probability distribution over 256 energy bins spanning $\pm10$ eV from the Fermi level, providing native uncertainty estimates. Band structure visualization follows directly from k-path queries, and downstream physical quantities such as band gaps, DOS, and energy isosurfaces can be derived through k-space aggregation without additional training. On 28,517 non-magnetic materials from the Materials Project, kRESForge achieves a band gap MAE of 0.39 eV, 90\% metal/non-metal classification accuracy, and DOS MAE of 2.64 states/eV.