Symmetry-Aware Prediction of Electron Localization Functions from Superposed Atomic Densities

The electron localization function (ELF) is a powerful diagnostic of bonding and electronic structure across materials conditions, including the extreme regimes relevant to high‑pressure chemistry. However, its direct generation from the chemical formula and crystal structure is very challenging due to its highly non-linear nature. We propose developing a supervised deep learning method that can transform the 3D superposition of atomic densities (SAD) and yield the ELF. The method can naturally incorporate pressure-implicit structural representations and can be used to rapidly score candidate metal sublattices (templates) for compounds under compression. Our approach combines a periodic 3D U‑Net with circular padding, an explicit symmetry‑pooling layer built from space‑group Seitz operators in the local patch frame, and memory‑aware training on periodic patches with epoch‑wise origin jitter. The model has been trained on 50,000 metal‑only structures drawn from a curated subset of Alexandria‑MP20, using a 90/10 train/test split. Reproducible and comparable results have been achieved after detailing the representation, symmetry handling, patching strategy, and learning objectives. Our implementation is symmetry‑aware at the data and network levels and is designed to scale to large unit cells without significant memory use.