  We show that deep neural networks can be integrated into, or fully replace,
the Kohn-Sham density functional theory scheme for multi-electron systems in
simple harmonic oscillator and random external potentials with no feature
engineering. We first show that self-consistent charge densities calculated
with different exchange-correlation functionals can be used as input to an
extensive deep neural network to make predictions for correlation, exchange,
external, kinetic and total energies simultaneously. Additionally, we show that
one can also make all of the same predictions with the external potential
rather than the self-consistent charge density, which allows one to circumvent
the Kohn-Sham scheme altogether. We then show that a self-consistent charge
density found from a non-local exchange-correlation functional can be used to
make energy predictions for a semi-local exchange-correlation functional.
Lastly, we use a deep convolutional inverse graphics network to predict the
charge density given an external potential for different exchange-correlation
functionals and assess the viability of the predicted charge densities. This
work shows that extensive deep neural networks are generalizable and
transferable given the variability of the potentials (maximum total energy
range $\approx100$ Ha), because they require no feature engineering, and
because they can scale to an arbitrary system size with an $\mathcal{O}(N)$
computational cost.
