  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.
