Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning

We use voxel deep neural networks to predict energy densities and functional derivatives of electron kinetic energies for the Thomas-Fermi model and Kohn-Sham density functional theory calculations. We show that the ground-state electron density can be found via direct minimization for a graphene lattice without any projection scheme using a voxel deep neural network trained with the Thomas-Fermi model. Additionally, we predict the kinetic energy of a graphene lattice within chemical accuracy after training from only two Kohn-Sham density functional theory (DFT) calculations. We identify an important sampling issue inherent in Kohn-Sham DFT calculations and propose future work to rectify this problem. Furthermore, we demonstrate an alternative, functional derivative-free, Monte Carlo based orbital-free density functional theory algorithm to calculate an accurate two-electron density in a double inverted Gaussian potential with a machine-learned kinetic energy functional.

Automated summary

In this study, voxel deep neural networks were used to predict energy densities and functional derivatives in electron kinetic energies for the Thomas-Fermi model and Kohn-Sham density functional theory calculations. The researchers demonstrated that the ground-state electron density of a graphene lattice can be directly found via minimization without the need for a projection scheme, using a voxel deep neural network trained with the Thomas-Fermi model. Additionally, they were able to predict the kinetic energy of a graphene lattice with chemical accuracy after training from only two Kohn-Sham density functional theory calculations. The researchers also identified a sampling issue in Kohn-Sham density functional theory calculations and proposed future work to address this problem.