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The data-driven Bayesian model averaging is a rigorous statistical approachto combining multiple models for a unified prediction. Compared with theindividual model, it provides more reliable information, especially forproblems involving apparent model dependence. In this work, within both thenon-relativistic Skyrme energy density functional and the nonlinearrelativistic mean field model, the effective proton-neutron chemical potentialdifference $\Delta \mu^*_{\rm{pn}}$ of neutron-rich nuclei is found to bestrongly sensitive to the symmetry energy $E_{\rm{sym}}(\rho)$ around$2\rho_0/3$, with $\rho_0$ being the nuclear saturation density. Givendiscrepancies on the $\Delta \mu^*_{\rm{pn}}$-$E_{\rm{sym}}(2\rho_0/3)$correlations between the two models, we carry out a Bayesian model averaginganalysis based on Gaussian process emulators to extract the symmetry energyaround $2\rho_0/3$ from the measured $\Delta \mu^*_{\rm{pn}}$ of 5 doubly magicnuclei $^{48}$Ca, $^{68}$Ni, $^{88}$Sr, $^{132}$Sn and $^{208}$Pb.Specifically, the $E_{\mathrm{sym}}(2\rho_0/3)$ is inferred to be$E_{\mathrm{sym}}(2\rho_0/3) = 25.6_{-1.3}^{+1.4}\,\mathrm{MeV}$ at $1\sigma$confidence level. The obtained constraints on the $E_{\mathrm{sym}}(\rho)$around $2\rho_0/3$ agree well with microscopic predictions and results fromother isovector indicators.

Bayesian model averaging for nuclear symmetry energy from effective proton-neutron chemical potential difference of neutron-rich nuclei