  The binding energy (BE) or mass is one of the most fundamental properties of
an atomic nucleus. Precise binding energies are vital inputs for many nuclear
physics and nuclear astrophysics studies. However, due to the complexity of
atomic nuclei and of the non-perturbative strong interaction, up to now, no
conventional physical model can describe nuclear binding energies with a
precision below 0.1 MeV, the accuracy needed by nuclear astrophysical studies.
In this work, artificial neural networks (ANNs), the so called ``universal
approximators", are used to calculate nuclear binding energies. We show that
the ANN can describe all the nuclei in AME2020 with a root-mean-square
deviation (RMSD) around 0.2 MeV, which is better than the best
macroscopic-microscopic models, such as FRDM and WS4. The success of the ANN is
mainly due to the proper and essential input features we identify, which
contain the most relevant physical information, i.e., shell, paring, and
isospin-asymmetry effects. We show that the well-trained ANN has excellent
extrapolation ability and can predict binding energies for those nuclei so far
inaccessible experimentally. In particular, we highlight the important role
played by ``feature engineering'' for physical systems where data are
relatively scarce, such as nuclear binding energies.
