Capturing Random Error Terms in Monte Carlo Fission Source Distributions Using the Sw Distance Measure

Abstract

Previous studies have shown that random error term in the fission power iteration process is the key problem that influence the convergence and variance underestimation. This study uses the Sliced Wasserstein (SW) distance of the fission source distributions (FSDs) to estimate the error term in the Monte Carlo power iteration method. The SW distance method is used to capture the random error term for the OECD source convergence fissile slab model, the sphere array model, and the BEAVRS model to verify the universality of this error estimation method. The numerical results show that this method can more accurately capture the random error than the Shannon entropy diagnosis method. The numerical and theoretical deviations of the SW distances between the FSD of cycle i and cycle 1 as well as between cycle i and cycle i- 1 are less than 6%. In addition, inter-cycle correlations of the FSDs have been observed.

Keywords: Sliced Wasserstein distance, Monte Carlo, power iteration method, stochastic error analysis, random error term