Seitz-Invariant Prediction of Electron Localization Functions from Superposed Atomic Densities via a 3D-Convolutional Network

The Electron Localization Function (ELF) is a powerful descriptor of chemical bonding and electronic structure. Our recent study showed that the ELF associated with the metal sublattices measures chemical template strength, a key factor in stability of many compounds such as metal superhydrides [1]. However, the highly non-linear nature of the ELF makes its ML prediction from crystal structure a significant challenge. To address this, we present a symmetry-aware deep learning method. Our method transforms a 3D superposition of atomic densities (SAD), a pressure-implicit representation, directly into the corresponding ELF using a periodic 3D U-Net [2]. This network is augmented with a symmetry-pooling layer that averages network features over the crystal's space-group Seitz operators, ensuring the predicted ELF is physically invariant. The model was trained and validated on a large, curated subset of the Alexandria-MP20 database. This work provides a fast, accurate route for ELF prediction, and enables rapid screening of candidate compounds under extreme conditions.