Nuclear mass predictions based on Bayesian neural network approach with pairing and shell effects

TL;DR

This paper uses Bayesian neural networks with physical features like pairing and shell effects to significantly improve nuclear mass predictions, especially in unknown regions.

Contribution

It introduces a BNN model incorporating pairing and shell effects, optimizing noise error estimation for better nuclear mass and energy predictions.

Findings

Improved accuracy in nuclear mass predictions.

Better modeling of shell effects in unknown regions.

Enhanced predictive performance with physical feature inclusion.

Abstract

Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN approach. By including a distribution for the noise error, an appropriate value can be found automatically in the sampling process, which optimizes the nuclear mass predictions. Furthermore, two quantities related to nuclear pairing and shell effects are added to the input layer in addition to the proton and mass numbers. As a result, the theoretical accuracies are significantly improved not only for nuclear masses but also for single-nucleon separation energies. Due to the inclusion of the shell effect, in the unknown region, the BNN approach predicts a similar shell-correction structure to that in the known region, e.g., the predictions of underestimation of nuclear mass around the magic numbers in the relativistic mean-field model. This manifests that better predictive performance can be achieved if more physical features are included in the BNN approach.