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

TL;DR

This paper demonstrates the use of deep neural networks to predict electron kinetic energies and densities in density functional theory, enabling orbital-free calculations with small data sets and improved accuracy.

Contribution

It introduces voxel deep neural networks for predicting energy densities and derivatives, and proposes a Monte Carlo-based orbital-free DFT algorithm, advancing small data set applications.

Findings

Achieved chemical accuracy in kinetic energy prediction for graphene with minimal training data

Successfully found ground-state electron densities via direct minimization without projection schemes

Identified sampling issues in Kohn-Sham DFT and suggested future solutions

Abstract

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 2 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 2-electron density in a double inverted Gaussian potential with a machine-learned kinetic energy functional.