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.

Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders.

We examine unsupervised machine learning techniques to learn features that best describe configurations of the two-dimensional Ising model and the three-dimensional XY model. The methods range from principal component analysis over manifold and clustering methods to artificial neural-network-based variational autoencoders. They are applied to Monte Carlo-sampled configurations and have, a priori, no knowledge about the Hamiltonian or the order parameter. We find that the most promising algorithms are principal component analysis and variational autoencoders. Their predicted latent parameters correspond to the known order parameters. The latent representations of the models in question are clustered, which makes it possible to identify phases without prior knowledge of their existence. Furthermore, we find that the reconstruction loss function can be used as a universal identifier for phase transitions.