Density functionals from deep learning

Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional (DF) are necessary. Machine learning has recently been proposed as a novel approach to discover such a DF (or components of it)\footnote{J.\ C.\ Snyder, M.\ Rupp, K.\ Hansen, K.-R.\ M\"uller, and K.\ Burke, \textit{Phys. Rev. Lett.} \textbf{108}, 253002 (2012).}. Conventional machine learning algorithms, however, are limited in their ability to process data in their raw form, leading to invariance and/or sensitivity issues. In this presentation, an alternative approach based on deep learning will be demonstrated\footnote{J.\ M.\ McMahon, \textit{Submitted} (2015).}. Deep learning allows computational models that are capable of discovering intricate structure in large and/or high-dimensional data sets with multiple levels of abstraction, and do not suffer from the aforementioned issues. Results from the application of this approach to the prediction of the kinetic-energy DF of noninteracting electrons will be presented. Using theoretical results from computer science, a connection between the underlying model and the theorems of Hohenberg and Kohn will also be suggested.