Bayesian Evaluation of Incomplete Fission Yields

Fission product yields are key infrastructure data for nuclear applications in many aspects. It is a challenge both experimentally and theoretically to obtain accurate and complete energy-dependent fission yields. We apply the Bayesian neural network (BNN) approach to learn existing fission yields and predict unknowns with uncertainty quantification. We demonstrated that the BNN is particularly useful for evaluations of fission yields when incomplete experimental data are available. The BNN evaluation results are quite satisfactory on distribution positions and energy dependencies of fission yields.

Figure 1

The BNN learning of fission yields of $n+{}^{235}\mathrm{U}$ at an energy of 0.5 MeV from JENDL [10] (a) use six neurons and (b) use six neurons and resampling. The shadow region corresponds to the CI of the BNN estimated at 95%.

Figure 2

The $\mathrm{BNN}+\mathrm{T}\mathrm{ALYS}$ learning of induced fission yields from the JENDL library. The Talys results with default parameters are also given for comparison. The shadow region corresponds to the CI estimated at 95%.

Figure 3

The $\mathrm{BNN}+\mathrm{T}\mathrm{ALYS}$ predictions of fission yields of $n+{}^{235}\mathrm{U}$ compared with JENDL, with neutron incident energies at (a) 0.5 and (b) 14 MeV. The shadow region corresponds to the CI estimated at 95%.

Figure 4

The BNN evaluation of fission yields of $n+{}^{235}\mathrm{U}$ at energies of 1.37 (a) and 14.8 MeV (b), after learning the available experimental data [36]. The dashed line denotes the BNN prediction without learning the experimental data. The shadow region corresponds to the CI estimated at 95%.

Figure 5

Similar to Fig. 4 but for fission yields at energies of 4.49 (a) and 8.9 MeV (b).

Figure 6

The compiled evaluations of fission yields of $n+{}^{235}\mathrm{U}$ at different incident energies. The evaluations at 0.5 and 14 MeV are taken from JENDL [10], and BNN evaluations at other energies are taken from Figs. 4 and 5.