Over the past decade, machine learning has been successfully applied in
various fields of science. In this study, we employ a deep learning method to
analyze a Skyrme energy density functional (Skyrme-EDF), that is a Kohn-Sham
type functional commonly used in nuclear physics. Our goal is to construct an
orbital-free functional that reproduces the results of the Skyrme-EDF. To this
end, we first compute energies and densities of a nucleus with the Skyrme
Kohn-Sham + Bardeen-Cooper-Schrieffer method by introducing a set of external
fields. Those are then used as training data for deep learning to construct a
functional which depends only on the density distribution. Applying this scheme
to the 24Mg nucleus with two distinct random external fields, we
successfully obtain a new functional which reproduces the binding energy of the
original Skyrme-EDF with an accuracy of about 0.04 MeV. The rate at which the
neural network outputs the energy for a given density is about 105--106
times faster than the Kohn-Sham scheme, demonstrating a promising potential for
applications to heavy and superheavy nuclei, including the dynamics of fission.Comment: 16 pages, 9 figure