Physically consistent learning of electronic structures via bidirectional atomic-DOS mapping

The electronic density of states (DOS) is key to understanding material behavior, but is computationally expensive to calculate via density functional theory (DFT), especially for complex systems. We propose a self-consistent encoder-decoder neural network that learns bidirectional mappings between local atomic environments and projected DOS (pDOS), trained via dual-loss optimization to enforce physical consistency. Applied to equiatomic HfNbTiZr high-entropy alloys, the model achieves root-mean-square errors of 2.55 meV for the d-band center and 0.02 states/(eV atom) for Fermi-level DOS, surpassing direct structure-level predictions. The approach generalizes well to SrTiO3 and vacancy-ordered perovskites, demonstrating broad applicability. By enabling accurate DOS prediction, multi-objective optimization, and potential inverse design, this framework offers a robust pathway for data-driven electronic structure modeling in complex materials.