Analysis of a Skyrme energy density functional with deep learning
N. Hizawa, K. Hagino, Kenichi Yoshida
Abstract
Adapting a technique recently developed in atomic electron systems to nuclear physics, the authors employ a deep-learning method to analyze a Skyrme energy density functional (Skyrme-EDF) with the goal to construct an orbital-free functional that depends only on the particle density distribution. In a first step they compute the energy and particle densities of a nucleus using the Skyrme Kohn-Sham + Bardeen-Cooper-Schrieffer method. With those sets of data and a deep-learning approach they then train an orbital-free functional. When applied to the ${}^{24}$Mg nucleus, the newly constructed functional successfully reproduces the binding energy of the original Skyrme-EDF, with an accuracy of about 40 keV. The significant computational advantage compared to traditional EDF approaches promises useful alternatives for future applications such as for calculating more complex nuclear shapes in heavy and superheavy nuclei.