  Kohn-Sham density functional theory is the base of modern computational
approaches to electronic structures. Their accuracy vitally relies on the
exchange-correlation energy functional, which encapsulates electron-electron
interaction beyond the classical one. The functional provides a way to obtain
the density and energy without solving the many-body equation and can, in
principle, be determined to reproduce the exact ones universally. However, the
past approaches are dependent on the theoretical development, which limits the
possibility of the functional to human's intuition. Here, we demonstrate a
systematic way to machine-learn a functional from a database, without
complicated assumptions. The density and energy are related with a flexible
feed-forward neural network, which is trained to reproduce accurate dataset,
and the KS-DFT is solved by taking the functional derivatives with the
back-propagation technique. Surprisingly, a trial functional, trained for just
a few molecules, has been shown to be applicable to hundreds of molecular
systems with comparable accuracy to the standard functionals. Also, by adding
the nodes connected to the hidden layers, a non-local term is straightforwardly
included to improve accuracy, which has been hitherto impractically difficult.
Utilizing the strategy of rapidly advancing machine learning techniques, this
novel approach is expected to enrich the DFT framework by constructing a
functional just from a database for materials conventionally difficult to
calculate accurately.
