A Novel Bayesian Neural Network Approach for Nuclear Root-Mean-Square Charge Radii

Prodigious progress has recently been made in describing nuclear root-mean-square charge radii (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\mathrm { ch}}$ </tex-math></inline-formula>) using machine learning techniques. Nevertheless, significant error underestimation in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\mathrm { ch}}$ </tex-math></inline-formula> prediction, due to the lack of explicit consideration for the aleatoric uncertainty inherited from experimental measurements in the training stage, is found. To address this issue, we develop a novel Bayesian neural network (BNN) approach that explicitly considers the aleatoric uncertainty along with the epistemic uncertainty. Its capability of not only predicting the central values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\mathrm { ch}}$ </tex-math></inline-formula> with high accuracy but also providing comprehensive error quantification for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\mathrm { ch}}$ </tex-math></inline-formula> is demonstrated by comparing with the experimental data and theoretical simulations. State-of-the-art results related to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R_{\mathrm { ch}}$ </tex-math></inline-formula> may become accessible making use of the novel BNN approach in future.