In recent years, machine learning methods have been widely applied to the predictions of nuclear masses.

This study aims to employ the continuous Bayesian probability (CBP) estimator and the Bayesian model averaging (BMA) to optimize the descriptions of sophisticated nuclear mass models.

The CBP estimator treated the residual between the theoretical and experimental values of nuclear masses as a continuous variable, deriving its posterior probability density function (PDF) from Bayesian theory. The BMA method assigned weights to models based on their predictive performance for benchmark nuclei, thereby balancing each model's unique strengths.

In global optimization, the CBP method improves the Hartree-Fock-Bogoliubov (HFB) model by approximately 90%, and the relativistic mean-filed (RMF) and semi-empirical formulas by 70% and 50%, respectively. In extrapolation analysis, the CBP method improves the prediction accuracy for the HFB models, RMF models, and semi-empirical formulas by approximately 80%, 55%, and 50%, respectively, demonstrating the strong generalization ability of the CBP method. To assess the reliability of the BMA method, the two-neutron separation energy for Ca isotopes was extrapolated, and its two-neutron drip line was predicted.

The methods proposed in this paper provide an effective way to accurately predict the nuclear mass, with potential applications to research on other nuclear properties.