A microscopic description of nuclear fission represents one of the most
challenging problems in nuclear theory. While phenomenological coordinates,
such as multipole moments, have often been employed to describe fission, it is
not obvious whether these parameters fully reflect the shape dynamics of
interest. We here propose a novel method to extract collective coordinates,
which are free from phenomenology, based on multi-task deep learning in
conjunction with a density functional theory (DFT). To this end, we first
introduce randomly generated external fields to a Skyrme-EDF and construct a
set of nuclear number densities and binding energies for deformed states of
236U around the ground state. By training a neural network on such
dataset with a combination of an autoencoder and supervised learning, we
successfully identify a two-dimensional latent variables that accurately
reproduce both the energies and the densities of the original Skyrme-EDF
calculations, within a mean absolute error of 113 keV for the energies. In
contrast, when multipole moments are used as latent variables for training in
constructing the decoders, we find that the training data for the binding
energies are reproduced only within 2 MeV. This implies that conventional
multipole moments do not provide fully adequate variables for a shape dynamics
of heavy nuclei.Comment: 15 pages, 11 figure