Probing the refined performance of the Categorical-Boosting algorithm to the Hartree-Fock-Bogoliubov mass model with different Skyrme forces

Nuclear mass can offer profound insights into many physical branches, e.g., nuclear physics and astrophysics, while the predicted accuracy by nuclear mass models is usually far from satisfactory until now, especially within the fully microscopic self-consistent mean-field theory. In this project, we present the predictive power for the binding energy within the the Hartree-Fock-Bogoliubov (HFB) methods with six widely used Skyrme forces (SkM*, SkP, SLy4, SV-min, UNEDF0 and UNEDF1) and evaluate the refined performance of the machine learning based on a novel Categorical Boosting (CatBoost) algorithm to the Skyrme HFB mass models. The root-mean-square (rms) deviations between the bare HFB calculations with different Skyrme forces and the available experimental data range from the minimum, about 1.43 MeV, for the UNEDF0 parameter set to the maximum, about 7.03 MeV, for the SkM* paraterer set. For the CatBoost-refined HFB predictions, the predictive power can be significantly improved. All the prediction accurancies on the testing set can reach the level around 0.2 MeV and, meanwhile, the large model bias can be reduced. The model-repair coefficients for the adopted Skyrme parameter sets are uniformly more than 80\%. Moreover, for 21 newly measured nuclei outside AME2020, the predicted masses by the CatBoost-refined HFB models are also in good agreement with the experimental data, illustrating their good generalization abilities. Intrestingly, it is found that the optimal Skyrme parameter set that possesses the highest predictive power for the bare HFB mass calculations may be not the best candidate for the CatBoost-refined HFB model, indicating the different abilities of picking up the missing ``physics'' for different Skyrme forces by the CatBoost algorithm.