Predicting ²⁸Si projectile fragmentation cross sections with Bayesian neural network method*

Abstract

This study utilizes the Bayesian neural network (BNN) method in machine learning to learn and predict the cross-section data of 28Si projectile fragmentation for different targets at different energies, and to quantify the uncertainty. The detailed modeling process of BNN is presented, and its prediction results are compared with Cummings, Nilsen, EPAX2, EPAX3, and FRACS models, as well as experimental measurement values. The results reveal that the BNN method achieves the smallest root-mean-square error (RMSE) and the highest agreement with the experimental values compared to other models. Only the BNN method and FRACS model show a significant odd-even staggering effect, but BNN method is more closer to the experimental value. Furthermore, the BNN method is the only model capable of reproducing data features with low cross-section values at Z = 9, and the average ratio of the BNN's predicted to experimental values is close to 1.0. These results demonstrate that the BNN method can accurately reproduce and predict the fragment production cross sections of the 28Si projectile fragmentation, as well as its ability to capture key data characteristics.