Nuclear binding energies in artificial neural networks

The binding energy 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 the nonperturbative 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, 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 inaccessible experimentally. In particular, we highlight the important role of "feature engineering"for physical systems where data are relatively scarce, such as nuclear binding energies.