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

TL;DR

This work addresses the challenge of simultaneously predicting nuclear masses and charge radii with high accuracy. It introduces a multi-task Gaussian process based on the intrinsic coregionalization model to exploit correlations between the two observables, using 12 physics-informed input features. The approach achieves rms deviations of $0.136$ MeV for masses and $0.007$ fm for radii with the 12-feature set, outperforming single-task models and demonstrating strong generalization via train/test splits, extrapolation to newly measured data, and consistency with Garvey–Kelson relations. SHAP analysis provides interpretable, region-dependent insights into feature importance, revealing that bulk terms drive mass predictions while $A^{1/3}$ governs radii, thereby validating the physical relevance of the learned correlations. Overall, the method offers a unified, accurate, and interpretable framework for nuclear-property predictions with potential impact on nuclear theory and astrophysical modeling.

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.

Figures (4)

• Figure 1: Absolute errors between model predictions and experiment for nuclear masses and charge radii. Upper panels (a, b, c, d) show mass prediction results for the STL and MTL models, while lower panels (e, f, g, h) show charge radius prediction results for the STL and MTL models. Rms deviations calculated by Eq. (\ref{['EQ:1']}) for the training, testing, and total sets are listed in each panel. Color bars indicate the magnitude of the absolute error (in MeV or fm). See text for details.
• Figure 2: Rms deviations of masses (top) and charge radii (bottom) with respect to the AME2020 and CR2013 datasets as functions of the training proportion, for the MTL-M9 and MTL-M12 models.
• Figure 3: Histogram of $\Delta GK =|GK^{\mathrm{ML}} - GK^{\mathrm{exp}}|$ for 3106 GK relations.
• Figure 4: Feature importances for MTL-M12 in predicting nuclear mass shown in panel (a) and charge radius shown in panel (b) for $\beta$-stable, proton-rich, and neutron-rich regions, respectively. Each bar represents the mean absolute SHAP value, reflecting the importance of each physical feature in the specified nuclear region.