  The extended kernel ridge regression (EKRR) method with odd-even effects was
adopted to improve the description of the nuclear charge radius using five
commonly used nuclear models. These are: (i) the isospin dependent $A^{1/3}$
formula, (ii) relativistic continuum Hartree-Bogoliubov (RCHB) theory, (iii)
Hartree-Fock-Bogoliubov (HFB) model HFB25, (iv) the Weizs\"acker-Skyrme (WS)
model WS$^\ast$, and (v) HFB25$^\ast$ model. In the last two models, the charge
radii were calculated using a five-parameter formula with the nuclear shell
corrections and deformations obtained from the WS and HFB25 models,
respectively. For each model, the resultant root-mean-square deviation for the
1014 nuclei with proton number $Z \geq 8$ can be significantly reduced to
0.009-0.013~fm after considering the modification with the EKRR method. The
best among them was the RCHB model, with a root-mean-square deviation of
0.0092~fm. The extrapolation abilities of the KRR and EKRR methods for the
neutron-rich region were examined and it was found that after considering the
odd-even effects, the extrapolation power was improved compared with that of
the original KRR method. The strong odd-even staggering of nuclear charge radii
of Ca and Cu isotopes and the abrupt kinks across the neutron $N=126$ and 82
shell closures were also calculated and could be reproduced quite well by
calculations using the EKRR method.
