Estimation of Continuous Distribution of Iterated Fission Probability Using an Artificial Neural Network with Monte Carlo-Based Training Data

Abstract

The Monte Carlo neutron transport method is used to accurately estimate various quantities, such as k-eigenvalue and integral neutron flux. However, in the case of estimating a distribution of a desired quantity, the Monte Carlo method does not typically provide continuous distribution. Recently, the functional expansion tally (FET) and kernel density estimation (KDE) methods have been developed to provide a continuous distribution of a Monte Carlo tally. In this paper, we propose a method to estimate a continuous distribution of a quantity in all phase-space variables using a fully connected feedforward artificial neural network (ANN) model with Monte Carlo-based training data. As a proof of concept, a continuous distribution of iterated fission probability (IFP) was estimated by ANN models in two distinct fissile systems. The ANN models were trained on the training data created using the Monte Carlo IFP method. The estimated IFP distributions by the ANN models were compared with the Monte Carlo-based data that include the training data. Additionally, the IFP distributions by the ANN models were also compared with the adjoint angular neutron flux distributions obtained with the deterministic neutron transport code PARTISN. The comparisons showed varying degrees of agreement or discrepancy; however, it was observed that the ANN models learned the general trend of the IFP distributions from the Monte Carlo-based training data.

Keywords

• iterated fission probability
• continuous distribution
• Monte Carlo neutron transport
• artificial neural network
• machine learning