Taming nucleon density distributions with deep neural network

With the datasets of the density distributions calculated by Skyrme density functional theories, we elaborated deep neural networks to generate the density profile and provide a table of related hyperparameters set for similar applications of other structural models. In the process of machine learning with the objective/target functions that normalized mean square error and Kullback–Leibler divergence (cross entropy), there is a turning point showing the transition from the Fermi-like distribution to the realistic Skyrme distribution, while this property is transcended when Pearson ${\chi }^2$ divergence is employed. A training program of about 35 minutes with only about $5\text{\%}-10\text{\%}$ nuclei ($200-300$) is sufficient to describe the nucleon density distributions of all the nuclear chart within 2% relative error. We obtain similar results employing different datasets calculated by different Skyrme density functional theories. We further investigate the extrapolation properties, which show that an addition of 15 nucleons is acceptable. Based on the results, we propose a mixed dataset approach and a retraining approach in order to go beyond a single physical structure model.