A Non-parametric Bootstrap Method for Kinetic Monte Carlo Variance Reduction

Abstract

A new variance reduction technique for Monte Carlo transport methods is investigated. This approach is based on non-parametric bootstrapping, a statistical inference and resampling method which is used to generate simulated samples of Monte Carlo scores to estimate the statistical properties of underlying integral response distributions. It is also used to quantify the uncertainty of the corresponding estimates as well as any bias introduced by bootstrapping, which then can be corrected. In this context, non-parametric bootstrapping is used to estimate the first and second-order moments of estimations of Monte Carlo responses for time-dependent neutron transport problems, which are particularly time-consuming. This variance reduction technique was implemented in SCONE - Stochastic Calculator Of Neutron transport Equation, developed at the University of Cambridge. Results show that the non-parametric bootstrap method can improve the trade-off between simulation time and variance of integral response estimates, especially when the number of responses is kept to a moderate level. As the number of responses increases, however, challenges with bias, memory and computational efficiency become more prominent, which is addressed.