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.

Figures (8)

• Figure 1: Comparison of reproduced results (upper) and validated results of the FPYs (lower) with and without the shell factor. The neutrons n$_{th}$, n$_f$ , and n$_{14}$ refer to thermal, fast and 14 MeV incident neutron energies, respectively.
• Figure 2: Comparison between the FPY by the BNN model and the experimental results.
• Figure 3: The FPYs of $^{235}$U and $^{232}$Th from JENDL-5 (0.5 MeV with dotted line and 14 MeV with dashed line) and BNN predictions (colored solid lines) in the case of our previous model Chen01 only with data augmentation without SF. In the lower right $^{232}$Th data, the 14 MeV yield from JENDL-5 is omitted to plot due to its large uncertainty.In the right panels, independent mass yields for the heavy peak are shown.
• Figure 4: The FPYs of $^{235}$U and $^{232}$Th from JENDL-5 (0.5 MeV and 14 MeV) and BNN predictions (solid lines) in the case of present model with SF. In the lower right $^{232}$Th data, the 14 MeV yield from JENDL-5 is omitted to plot due to its large uncertainty. In the right panels, independent mass yields for the heavy peak are shown.
• Figure 5: The energy dependence of fission product yields and prompt neutron multiplicity for $^{235}$U in the case of selective learning of nuclides with high practical demand. Colors of solid lines are the same as in Fig.\ref{['fig:explaining_1B']}.