Comparison of different kernel functions in nuclear charge radius predictions by the kernel ridge regression method

摘要: Using two nuclear models, i) the relativistic continuum Hartree-Bogoliubov (RCHB) theory
and ii) the Weizs acker-Skyrme (WS) model WS$^ ast$,
the performances of nine kinds of kernel functions in the kernel ridge regression (KRR) method
are investigated by comparing the accuracies of describing the experimental nuclear charge
radii and the extrapolation abilities.
It is found that, except the inverse power kernel, other kernels can reach the same level
around 0.015-0.016~fm for these two models with KRR method.
The extrapolation ability for the neutron rich region of each kernel depends on the trainning data.
Our investigation shows that the performances of the power kernel and Multiquadric kernel are
better in the RCHB+KRR calculation, and the Gaussian kernel is better in the WS$^ ast$+KRR calculation.
In addition, the performance of different basis functions in
the radial basis function method is also investigated for comparison.
The results are similar to the KRR method.
The influence of different kernels on the KRR reconstruct function is discussed
by investigating the whole nuclear chart.
At last, the charge radii of some specific isotopic chains have been investigated
by the RCHB+KRR with power kernel and the WS$^ ast$+KRR with Gaussian kernel.
The charge radii and most of the specific features in these isotopic chains
can be reproduced after considering the KRR method.