利用神经算子学习Kohn-Sham映射实现准线性标度的密度泛函理论

中文摘要 AI 辅助

Kohn-Sham密度泛函理论（DFT）是电子结构模拟的基础，但重复的轨道对角化会导致立方标度，将量子计算限制在中等规模。消除这些辅助轨道同时保留Kohn-Sham精度是无轨道DFFT的核心目标，但此前的分析和机器学习方法均未达到要求。现有学习方法要么尝试学习变分动能泛函（该泛函病态），要么直接预测基态（对更大系统外推性差）。相反，本文确定Kohn-Sham映射是无轨道DFT的合适学习目标，它将Kohn-Sham势直接映射到对应的密度和非相互作用动能，而这些量原本需通过轨道对角化获得。本文聚焦密度分量，采用域不变的SE(3)等变傅里叶神经算子，以实空间网格上的势为输入学习预测密度，实现稳定的准线性标度自洽场（SCF）。该模型在8504个分子和固体上联合训练，可泛化到分布外的有机分子、绝缘体和金属。首次实现同一方法无需显式构建Kohn-Sham轨道即可在这些系统中收敛SCF，同时以Kohn-Sham DFT精度重现密度、电子光谱和结构可观测量。线性标度SCF还可在单个GPU上收敛含多达82500个价电子的镁位错密度。

英文摘要

Kohn--Sham density functional theory (DFT) underpins electronic-structure simulations, but repeated orbital diagonalizations lead to cubic scaling, restricting quantum calculations to modest scales only. Eliminating these auxiliary orbitals while retaining Kohn--Sham accuracy is the central goal of orbital-free DFT, but both analytical and machine-learning methods have so far fallen short. Prior learning approaches either try to learn the variational kinetic-energy functionals, which are ill-conditioned, or directly predict the ground state, which extrapolate poorly to larger systems. Instead, we identify the Kohn--Sham map as the right learning target for orbital-free DFT. It maps a Kohn--Sham potential directly to the corresponding density and noninteracting kinetic energy, quantities otherwise obtained through an orbital diagonalization. Focusing on the density component in this work, a domain-invariant $\mathrm{SE}(3)$-equivariant Fourier neural operator learns to predict it from the potential as input on real-space grids, enabling stable quasi-linear scaling SCFs. Trained jointly on 8,504 molecules and solids, a single model generalizes to out-of-distribution organic molecules, insulators, and metals. For the first time, the same method converges SCFs across these systems without explicitly constructing Kohn--Sham orbitals, while reproducing densities, electronic spectra, and structural observables at Kohn--Sham DFT accuracy. Linear-scaling SCFs additionally allow converging magnesium dislocation densities containing up to 82,500 valence electrons on a single GPU.

发表机构

• California Institute of Technology（加州理工学院）
• ETH Zürich（苏黎世联邦理工学院）

机构由 AI 辅助整理，请以论文原文为准。