Neural-Network Solutions to Real-Space Charge Density and Generalization

• URL: http://arxiv.org/abs/2609.14906v1
• Date: Mon, 14 Sep 2026 01:51:52 GMT
• Title: Neural-Network Solutions to Real-Space Charge Density and Generalization
• Abstract summary: We propose AIDEN to solve real-space charge density.<n>A continuous low-rank Gaussian decoder reconstructs the density at arbitrary spatial coordinates.<n> AIDEN provides substantially faster inference than both baseline models and full SCF calculations.
• Score: 0.28074364079901015
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Hohenberg-Kohn theorem establishes that, in principle, the ground state (GS) charge density contains all GS information of a many-electron system, such that all GS observables can be expressed as functionals of the GS charge density. Conventional Kohn-Sham density functional theory requires iterative solution of the self-consistent-field equations at substantial computational cost, motivating the development of deep learning surrogates for electronic structure calculations and, in turn, accelerating computer-aided materials design. Here, we propose \textbf{AIDEN}, an \underline{A}tomic-\underline{I}nteraction \underline{D}ensity \underline{E}quivariant \underline{N}etwork for solving real-space charge density. AIDEN separates the element-dependent one-center density from environment-induced density redistribution and represents the latter through complementary atom- and edge-centered tensor correlations. A continuous low-rank Gaussian decoder then reconstructs the density at arbitrary spatial coordinates while reusing atomic encodings independently of the evaluation grid. AIDEN achieves state-of-the-art accuracy on periodic crystal benchmarks while remaining competitive for molecular systems, and further demonstrates zero-shot transferability across several structurally distinct out-of-distribution case studies. Furthermore, AIDEN provides substantially faster inference than both baseline models and full SCF calculations, enabling efficient charge density reconstruction for large-scale electronic structure calculations.

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