Reactor Physics Monitoring of a Source-Driven Subcritical System in Stationary State by Deterministic and Probabilistic Deep Neural Networks

Abstract

Reactivity measurement methods, like the Amplified Source Method (ASM), link observable quantities to integral physics parameters characterizing subcritical assemblies (SCAs). These methods were mostly derived from point reactor kinetics, which assumes fundamental mode distribution. However, in SCAs, external sources cannot be neglected, leading to a nonideal response, such as the detector position dependence of measured $k_{\mathit{eff}}$.

This work investigates deterministic and probabilistic deep learning (DL) in determining $k_{\mathit{eff}}$ and kinetics/subcritical parameters using core map and foil/active detector responses as inputs, which distinguishes DL from neutronics codes. Convolutional neural networks surpassed dense neural networks with higher accuracy, while assigning a strong signature to appropriate core map features. Expansion into multi-input networks, which also process reaction rates, highlighted DL’s flexibility by accurate prediction regardless of reaction type.

Uncertainty quantification of DL was done using Monte Carlo (MC) Dropout and Bayesian neural network (BNN). The results favored BNN over MC Dropout, showing greater improvement with increasing data. An assessment of ASM, applicable in a SCA at source equilibrium, showed a reactivity bias of up to −3.59%Δk/k (−4.86 $). In contrast, DL had a maximum bias of only 0.38%Δk/k (0.5 $). Underestimation by ASM represents a nonconservative scenario in criticality safety, while DL proved robust against spatial effects. This demonstrates DL’s potential in ensuring reactivity margins and a safe approach to criticality in reactor operation regimes where standard techniques can fail.

Keywords:

• Subcritical assembly
• deep learning
• uncertainty quantification
• Monte Carlo Dropout
• probabilistic Bayesian neural network

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This material was based on work supported by the Department of Science and Technology—Science Education Institute of the Republic of the Philippines under its Foreign Graduate Scholarship Program. The Philippine Nuclear Research Institute is the sending institution.