  We investigate the density distributions of finite nuclei employing a
well-designed deep neural network method. We calculate the target nucleon
density distributions with Skyrme density functional theories, which are used
to train the networks. We find that the training with only about $10\%$ nuclei
($300-400$) is sufficient to describe the nucleon density distributions of all
the nuclear chart within 2\% relative error. The relative error comes to 5\%
when about 200 proton(neutron) density distributions are used for training. We
obtained very similar results for different Skyrme density functional theories.
Therefore the ability to train networks is weakly dependent on the theoretical
model. Moreover, in the process of machine learning, there is a turning point
showing the transition from the Fermi-like distribution to the realistic Skyrme
distribution, which provides significant properties of convergence process.
