Deterministic and probabilistic Deep Learning in predicting reactor physics of subcritical system driven by a pulsed source

Widely reported are the non-ideal response of standard techniques in reactivity measurement when the Subcritical Assembly (SCA) is far from critical. This emanates from the loose applicability of fundamental mode assumption in Point Reactor Kinetics from which the analytical formulae relating detector response to reactivity were derived. This work evaluated the potential of Deep Learning (DL) in overcoming these biasing effects particularly in an SCA driven by a Pulsed Neutron Source (PNS). Deterministic DL models processing core map and detector temporal response were trained using data from neutronics calculations, and subsequently compared with Area-ratio, and Slope-fit methods in a simulated PNS experiment. Results show the robustness of DL against spatial effect that severely affected Area-ratio method leading to severe underestimation, a non-conservative scenario in criticality safety. As illustration, $k_{eff}^{DL}=0.94158$ is approximately equal to $k_{eff}^{MCNP}=0.94093\pm 0.00034$; meanwhile $k_{eff}^{Area-ratio}=0.435\pm 0.00900\ll k_{eff}^{MCNP}$. Furthermore, DL did not indicate increasing bias as system becomes deeply subcritical unlike Slope-fit method. These advantages also extended to probabilistic variants based on Bayesian Neural Networks, which were found to be well-calibrated due to matching predicted and observed confidence levels. These findings suggest the strong potential of deploying DL in an operational context, helping assure safety margins in SCAs and safe approach to criticality in research reactors.