发表机构
University of Science and Technology of China; Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学; 中国科学技术大学苏州高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出AIDEN等变神经网络，通过分离单中心密度与环境重分布并用低秩高斯解码器重建实空间电荷密度，在晶体和分子基准上达到最先进精度，并实现零样本迁移和快速推理。
AI 中文摘要
Hohenberg-Kohn定理确立了原则上基态电荷密度包含多电子系统的所有基态信息，因此所有基态可观测量都可以表示为基态电荷密度的泛函。传统的Kohn-Sham密度泛函理论需要迭代求解自洽场方程，计算成本高昂，这推动了用于电子结构计算的深度学习替代模型的发展，进而加速了计算机辅助材料设计。在此，我们提出了AIDEN，一个用于求解实空间电荷密度的原子-相互作用-密度-等变网络（Atomic-Interaction Density Equivariant Network）。AIDEN将依赖于元素的单中心密度与环境诱导的密度重分布分离，并通过互补的原子中心和边中心张量相关性来表示后者。然后，一个连续的低秩高斯解码器在任意空间坐标处重建密度，同时独立于评估网格重用原子编码。AIDEN在周期性晶体基准上达到了最先进的精度，同时在分子系统上也保持了竞争力，并进一步在几个结构不同的分布外案例研究中展示了零样本迁移能力。此外，AIDEN的推理速度比基线模型和完整的自洽场（SCF）计算都快得多，从而能够为大规模电子结构计算实现高效的电荷密度重建。
英文摘要
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 AIDEN, an Atomic-Interaction Density Equivariant Network 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.
