Nuclear mass predictions with machine learning reaching the accuracy required by $r$-process studies

TL;DR

This paper presents a Bayesian neural network model for predicting nuclear masses with an accuracy of 84 keV, suitable for r-process nucleosynthesis studies, while properly estimating uncertainties and revealing nuclear shell features.

Contribution

The study introduces a Bayesian machine learning approach that combines physics-informed models with neural networks to accurately predict nuclear masses and their uncertainties.

Findings

Achieved 84 keV accuracy in nuclear mass predictions.

Properly evaluated uncertainties increase along isotopic chains.

Predicted new magic numbers and shell quenching phenomena.

Abstract

Nuclear masses are predicted with the Bayesian neural networks by learning the mass surface of even-even nuclei and the correlation energies to their neighbouring nuclei. By keeping the known physics in various sophisticated mass models and performing the delicate design of neural networks, the proposed Bayesian machine learning (BML) mass model achieves an accuracy of $84$~keV, which crosses the accuracy threshold of the $100$~keV in the experimentally known region. It is also demonstrated the corresponding uncertainties of mass predictions are properly evaluated, while the uncertainties increase by about $50$~keV each step along the isotopic chains towards the unknown region. The shell structures in the known region are well described and several important features in the unknown region are predicted, such as the new magic numbers around $N = 40$, the robustness of $N = 82$ shell, the quenching of $N = 126$ shell, and the smooth separation energies around $N = 104$.