  The model inputs play a key role in the performance of the Bayesian
optimization approach. In this paper, we investigate the influence of the
inputs on the improved predictions of phenomenological nuclear charge radius
formulas using an approach combining those original formulas and the Bayesian
neural network (BNN). We find that there is no improvement in predictions after
the abnormal odd-even staggering effect of 181,183,185Hg is injected into the
BNN, while the original phenomenological formulas themselves possess rich
physical information or rigid constraints. It indicates the abundance and
intensity of physical inputs affect the performance of the Bayesian
optimization approach as well as the robustness of the BNN. We further
demonstrate that, by ensuring that the number of neurons in the hidden layer is
larger than the number of NN inputs, adding hidden layers into the BNN can
significantly improve the predictions of nuclear charge radii formulas within
the Bayesian optimization approach.
