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This paper addresses the computational limitations of Kohn-Sham density functional theory (DFT) by introducing a novel approach that eliminates the need for auxiliary orbitals, which typically lead to cubic scaling. The authors leverage a domain-invariant SE(3)-equivariant Fourier neural operator to learn the Kohn-Sham map, enabling the prediction of electron density from the potential directly, thereby achieving stable quasi-linear scaling self-consistent fields (SCFs). Remarkably, their method demonstrates the ability to generalize across diverse materials while maintaining Kohn-Sham DFT accuracy, allowing for the simulation of large systems with up to 82,500 valence electrons on a single GPU.
Achieving Kohn-Sham DFT accuracy without the computational burden of orbital diagonalization opens the door to simulating massive electronic systems efficiently.
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.
NVIDIA