Uncertainty estimation of the improved deterministic Truncation of Monte Carlo method using the Dirichlet distribution

The Monte Carlo method simulates neutron transport with minimal assumptions, providing high accuracy but at significant computational cost. The improved deterministic Truncation of Monte Carlo (iDTMC) method addresses this limitation by accelerating the convergence of the fission source distribution using partial-current based Coarse Mesh Finite Difference (p-CMFD) and obtaining a pin-wise reactor solution from a partial-current based Fine Mesh Finite Difference (p-FMFD) equation. The parameters used to construct the p-FMFD problem are tallied during transport, and thus the solution itself also contains uncertainty. To quantify this uncertainty, multiple parameter sets are sampled and the variance of the corresponding solutions are used as an estimate of the real variance. However, these parameters exhibit strong node-wise and parameter-wise correlations, that must be preserved for accurate estimation. To achieve this, we introduce the implicit Correlated Sampling (iCS) method using Dirichlet distribution that implicitly conserves these correlations when generating parameter sets. With this approach, the variance of iDTMC solutions can be reliably estimated without the need for independent batch calculations. This development enhances the reliability of the iDTMC method in reactor analysis.