  A Kohn-Sham scheme based multi-task neural network is elaborated for the
supervised learning of nuclear shell evolution. The training set is composed of
the single-particle wave functions and occupation probabilities of 320 nuclei,
calculated by the Skyrme density functional theory. It is found that the
deduced density distributions, momentum distributions, and charge radii are in
good agreements with the benchmarking results for the untrained nuclei. In
particular, accomplishing shell evolution leads to a remarkable improvement in
the extrapolation of nuclear density. After a further charge-radius-based
calibration, the network evolves a stronger predictive capability. This opens
the possibility to infer correlations among observables by combining
experimental data for nuclear complex systems.
