Simultaneous improvements of nuclear mass and charge radius predictions using multi-task Gaussian process approaches

Abstract

A multi-task Gaussian process (GP) machine learning model is introduced to simultaneously predict two important nuclear observables across the nuclear chart, namely nuclear masses and charge radii. Utilizing 12 physical input features, our multi-task GP consistently outperforms single-task learning, achieving overall root-mean-square deviations of 0.136 MeV for masses and 0.007 fm for charge radii. The good performance of the present model is confirmed by three complementary validations, namely various fractions for training and testing data, further extrapolations for newly reported nuclei far from stability, and popular Garvey-Kelson mass relations. The correlations between the two observables are explicitly analyzed within the multi-task learning framework. Furthermore, by employing the SHapley Additive exPlanations (SHAP) method, we interpret the importance of different features for mass and radius predictions across distinct nuclear regions. These results demonstrate the effectiveness of the multi-task GP approach for high-accuracy nuclear property predictions.