The ratio of volume and surface symmetry energy coefficients, $\kappa =E_{\mathrm{sym}}^V/E_{\mathrm{sym}}^S$, is investigated using the difference of the mirror pair root-mean-square charge radii ($R_{\mathrm{ch}}$), $\mathrm{\Delta }{R}_{\mathrm{ch}}^{\mathrm{mir}}$, with the aid of an improved Bayesian neural network (BNN) method with the explicit considerations of the BNN parametrization uncertainties and the experimental uncertainties in the training phase. The BNN method proves to have a robust predictive capability both in reproducing the existing $R_{\mathrm{ch}}$ data and in extrapolating the unmeasured data. Among all $A\ge 30$ isotopes with available experimental masses, 60 mirror pairs, of which 52 pairs contain at least one unmeasured nucleus, are found, and their $\mathrm{\Delta }{R}_{\mathrm{ch}}^{\mathrm{mir}}$ values are calculated using the BNN-predicted $R_{\mathrm{ch}}$ values. Within the droplet model by Myers and Swiatecki, $\kappa$ is deduced to be $\kappa =3.2_{-0.7}^{+1.0}$ from the obtained $\mathrm{\Delta }{R}_{\mathrm{ch}}^{\mathrm{mir}}$ values. This $\kappa$ value agrees well with $\kappa =3.0_{-0.5}^{+0.5}$ deduced from the neutron skin ($\mathrm{\Delta }{R}_{np}$) data in this work within the error, demonstrating the feasibility of our aim to investigate $\kappa$ using $\mathrm{\Delta }{R}_{\mathrm{ch}}^{\mathrm{mir}}$ with the aid of the BNN method. Our results, both from the predicted $\mathrm{\Delta }{R}_{\mathrm{ch}}^{\mathrm{mir}}$ and from the neutron skin data, are further compared with those from previous analyses of experimental observables, such as nuclear mass, $\mathrm{\Delta }{R}_{np}$, and isobaric analog states (IAS). It is found that our results show close agreement with those from the previous analyses of $\mathrm{\Delta }{R}_{np}$, IAS, and their combination, converging tightly around $\kappa \approx 3.1$, and are systematically larger than those obtained with the incorporation of nuclear mass data, $\kappa \approx 2.2$. Such a significant difference between the results unrelated to mass and those related to mass is briefly discussed.

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• Neutron skin thickness
• Nuclear charge radii
• Nuclear radii
• Bayesian methods
• Neural network simulations
• Nuclear data analysis & compilation