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

• URL: http://arxiv.org/abs/2608.23895v1
• Date: Mon, 24 Aug 2026 23:05:42 GMT
• Title: Learning the Kohn-Sham map with neural operators for quasi-linear scaling density functional theory
• Abstract summary: Kohn--Sham density functional theory (DFT) underpins electronic-structure simulations.<n>Repeated orbital diagonalizations lead to cubic scaling, restricting quantum calculations to modest scales only.<n>We develop a learning target for orbital-free DFT that maps a Kohn--Sham potential directly to the corresponding density and noninteracting kinetic energy.
• Score: 57.90994363143731
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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