Improved predictions of phenomenological nuclear charge radius formulae with Bayesian optimization approach

Abstract

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.