Nuclear mass based on the multi-task learning neural network method

The global nuclear mass based on the macroscopic–microscopic model was studied by applying a newly designed multi-task learning artificial neural network (MTL-ANN). First, the reported nuclear binding energies of 2095 nuclei (Z≥8,N≥8)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(Z \ge 8,N \ge 8)$$\end{document} released in the latest Atomic Mass Evaluation AME2020 and the deviations between the fitting result of the liquid drop model (LDM) and data from AME2020 for each nucleus were obtained. To compensate for the deviations and investigate the possible ignored physics in the LDM, the MTL-ANN method was introduced in the model. Compared to the single-task learning (STL) method, this new network has a powerful ability to simultaneously learn multi-nuclear properties, such as the binding energies and single neutron and proton separation energies. Moreover, it is highly effective in reducing the risk of overfitting and achieving better predictions. Consequently, good predictions can be obtained using this nuclear mass model for both the training and validation datasets and for the testing dataset. In detail, the global root mean square (RMS) of the binding energy is effectively reduced from approximately 2.4 MeV of LDM to the current 0.2 MeV, and the RMS of Sn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{n}}$$\end{document}, Sp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{p}}$$\end{document} can also reach approximately 0.2 MeV. Moreover, compared to STL, for the training and validation sets, 3–9% improvement can be achieved with the binding energy, and 20–30% improvement for Sn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{n}}$$\end{document}, Sp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{\mathrm{p}}$$\end{document}; for the testing sets, the reduction in deviations can even reach 30–40%, which significantly illustrates the advantage of the current MTL.