Physics-Embedded Bayesian Neural Network (PE-BNN) to predict Energy Dependence of Fission Product Yields with Fine Structures

Abstract: We present a physics-embedded Bayesian neural network (PE-BNN) framework that integrates fission product yields (FPYs) with prior nuclear physics knowledge to predict energy-dependent FPY data with fine structure. By incorporating an energy-independent phenomenological shell factor as a single input feature, the PE-BNN captures both fine structures and global energy trends. The combination of this physics-informed input with hyperparameter optimization via the Watanabe-Akaike Information Criterion (WAIC) significantly enhances predictive performance. Our results demonstrate that the PE-BNN framework is well-suited for target observables with systematic features that can be embedded as model inputs, achieving close agreement with known shell effects and prompt neutron multiplicities.