Learning density functional theory mappings with extensive deep neural networks and deep convolutional inverse graphics networks

In this work, we show that deep neural networks (DNNs) can be used in conjunction with Kohn-Sham density functional theory (KS-DFT) for two-dimensional electron gases in simple harmonic oscillator and random potentials. Using calculations from the Octopus real-space DFT code we show that extensive DNNs (EDNNs) can learn the mappings between the electron density and exchange, correlation, external, kinetic and total energies simultaneously. Our results hold for local, semi-local, and hybrid exchange-correlation functionals. We then show that the external potential can also be used as input for an EDNN when predicting the aforementioned energy functionals, bypassing the KS scheme. Additionally, we show that EDNNs can be used to map the electron density calculated with a local exchange-correlation functional to energies calculated with a semi-local exchange correlation functional. Lastly, we show that deep convolutional inverse graphics networks can be used to map external potentials to their respective self-consistent electron densities. This work shows that EDNNs are generalizable and transferable given the variability of the potentials and the ability to scale to an arbitrary system size with an O(N) computational cost.