Learning the Kohn-Sham map with neural operators for quasi-linear scaling density functional theory

2026-08-24

AI Summary

本文通过神经算子学习Kohn-Sham映射，解决了密度泛函理论中因轨道对角化导致的计算效率问题，实现了无需显式构建Kohn-Sham轨道的大规模系统稳定准线性缩放自洽场计算。

Abstract

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.

Problem

• Kohn-Sham DFT
• orbital-free DFT
• cubic scaling
• quantum calculations
• auxiliary orbitals

Innovation

• Kohn-Sham map
• neural operators
• orbital-free DFT
• quasi-linear scaling
• SE(3)-equivariant