Predicting correlation coefficients for Monte Carlo eigenvalue simulations with multitype branching process

Highlights: • Novel correlation prediction was developed for Monte Carlo simulations. • Evolution of various moments of Multitype Branching Processes (MBP) was derived. • MBP results were applied to simulation by expanding tallies around their expectations. • Details on constructing the MBP model for Monte Carlo simulation were discussed. • Predictive accuracy was verified by various quantities from the 2D BEAVRS benchmark. - Abstract: This paper provides a prediction method of the generation-to-generation correlations as observed when solving large scale eigenvalue problems such as full core nuclear reactor simulations. Knowing the correlations enables correction of the variance underestimation that occurs when assuming that the active generations are independent. The Monte Carlo power iteration is cast in the Multitype Branching Process (MBP) framework by discretizing the neutron phase space which allows calculation of spatial and temporal moments. These moments can then provide auto-correlation coefficients between the generations of MBP and are shown to accurately predict the auto-correlation coefficients of the original Monte Carlo simulation. This prediction capability was demonstrated on the full core 2D PWR BEAVRS benchmark and compared successfully with variance estimates from independent simulations.