The origin of elements is a significant research topic in nuclear physics and astrophysics. Some heavy nuclei are produced through photonuclear reactions, known as p-nuclei. The study of photonuclear reactions plays a crucial role in understanding the origins of elements. The existing data on photoneutron reactions have significant discrepancies. It is well-known that the(γ,n) reaction cross-sections from Saclay are higher than those from Livermore, while conversely, the (γ,2n) cross-sections from Livermore are higher than those from Saclay. To resolve these divergences, we need to either remeasure these data or evaluate them based on theoretical models.

This study aims to predict the photoneutron reaction cross-sections, specifically (γ,n) and γ,2n reactions, using a Bayesian neural network (BNN). The goal is to develop a physics-informed BNN model that improves the accuracy of photoneutron reaction predictions and resolves divergence in experimental data from different laboratories.

A physics-informed Bayesian Neural Network (PIBNN) model was constructed using PyTorch, designed to predict the photoneutron reaction cross-sections. The network was trained with a consistent dataset from Livermore's photoneutron experimental data, incorporating physics-informed such as cross-sections are zero, below reaction thresholds. The B2, B3 and B4 network architectures include various hidden layers (2, 3, and 4 layers), with an Adam optimizer and a learning rate of 0.000 1.

As the number of hidden layers increases, the model's description of the training set improves with the same number of training iterations. Among them, the B4 model not only effectively reproduces the single and double giant dipole resonance (GDR) peak structures of the (γ,n) reaction channel in the training set, but also accurately captures the magnitude of the γ,2n cross-section. The physics-informed incorporated into the training set, particularly the inclusion of zero cross-sections below reaction thresholds, improved the model's accuracy in predicting the cross-section near the threshold and ensuring that cross-sections approach zero at high energies. The predictions of the (γ,n) and γ,2n reaction cross sections for 175Lu by the three models are compared with the Saclay experimental data. The B4 model accurately provides the position and relative heights of the double-peak structure, reflecting the inherent systematics of the training set. By predicting the (γ,n) and γ,2n reaction cross-sections for 197Au and 175Lu, it has been validated that the trained physics-informed Bayesian neural network model possesses generalization ability.

Based on the physics-informed Bayesian neural network, the model can effectively learn the (γ,n) and γ,2n reaction cross-sections, reproducing the data in the training set and predicting cross-section data outside the training set. Furthermore, as the number of hidden layers increases, the model's learning ability gradually improves. In the future, the trained B4 model can be used to predict reliable photoneutron reaction cross-sections, resolve data discrepancies between different laboratories.