Geometry-Based Neural-Network Prediction of Electron Localization Function Topology in Dense Hydrogen

We develop a machine-learning framework to predict the electron localization function (ELF) of pure, dense hydrogen directly from atomic geometry, bypassing explicit electronic-structure calculations. Trained on first-principles data spanning multiple pressure regimes in dense fluid hydrogen, the model achieves high accuracy ((Formula presented.)) and faithfully reproduces the global distribution of the ELF. A combined real- and reciprocal-space analysis reveals that the residual error is dominated by smooth, long-wavelength components with correlation lengths exceeding typical H─H bonding scales, and that the magnitude of these components increases systematically with pressure. Despite being trained exclusively on dense fluid hydrogen networks, the model transfers robustly to crystalline hydrogen configurations, preserving key features of ELF topology, including critical points and hydrogen-network connectivity. Taken together, these results suggest a viable route toward geometry-based, high-throughput evaluation of hydrogen-networking characteristics in both fluid and crystalline hydrogen.