PI-EDG: Physics-Informed Full-Space Electron Density Generation from Molecular Geometry

Full-space electron density generation is fundamental to modeling molecular quantum states, ground-state properties, and chemical interactions. DFT provides a principled route to electron density, but high-fidelity calculations require costly self-consistent iterations, limiting large-scale quantum-chemical modeling. Deep learning offers a promising surrogate, yet existing methods often rely on indirect density-related prior, including coordinate queries, predefined basis functions, orbital coefficients, or spherical atomic density grids. These prior introduce reconstruction overhead and can hinder continuous full-space modeling across sharp nuclear cores and sparse vacuum regions. Here, we introduce PI-EDG, a physics-informed voxel-space framework that maps molecular geometries directly to full-space electron-density fields by combining quantum-mechanical prior injection, hybrid FNO-CNN modeling of local and non-local interactions and magnitude-aware DS-LMoE routing for extreme density ranges. On EDBench, PI-EDG achieves an MAE of 3.405$\times$10$^{-3}$, a total electron-number MAE of 0.472, and an average inference time of 133.4 ms for one molecule. Compared with graph-based, basis-based, and voxel-based baselines, PI-EDG demonstrates better predictive accuracy, improved robustness across extreme density regimes, and better physical consistency while maintaining efficient full-space generation. These results suggest that PI-EDG offers a new, direct, and efficient route for accelerating DFT-based electron density calculations.