Improvement of the Bayesian neural network to study the photoneutron yield cross sections

This work is an attempt to improve the Bayesian neural network (BNN) for studying photoneutron yield cross sections as a function of the charge number Z, mass number A, and incident energy ε. The BNN was improved in terms of three aspects:numerical parameters, input layer, and network structure. First, by minimizing the deviations between the predictions and data, the numerical parameters, including the hidden layer number, hidden node number, and activation function, were selected. It was found that the BNN with three hidden layers, 10 hidden nodes, and sigmoid activation function provided the smallest deviations. Second, based on known knowledge,such as the isospin dependence and shape effect, the optimal ground-state properties were selected as input neurons. Third, the Lorentzian function was applied to map the hidden nodes to the output cross sections, and the empirical formula of the Lorentzian parameters was applied to link some of the input nodes to the output cross sections. It was found that the last two aspects improved the predictions and avoided overfitting, especially for the axially deformed nucleus.