A proposal on multi-response CADIS method to optimize reduction of regional variances in hybrid Monte Carlo simulation

For fixed source problems, it is known that the analog Monte Carlo simulation method can show low efficiencies. To increase the calculation efficiency, variance reduction techniques (VRT) have been introduced and utilized. To apply these techniques, parameters to control particle transport behaviors should be properly determined. The hybrid Monte Carlo methods were developed to automatically determine the VRT parameters using information estimated from a deterministic simulation. In the case of a single response, the Consistent Adjoint Driven Importance Sampling (CADIS) method is well derived to decide VRT parameters. Recently, for plural response problems, a variety of methods have been proposed. It is noted that Forward-Weighted CADIS (FW-CADIS) method gives the best performance to optimize the parameters for plural response problems. However, it can create inefficiencies due to an assumption that uniform particle density is used to uniformly obtain low variance in each response. In the Multi-Response CADIS (MR-CADIS) method proposed in this study, a new weight function is derived to effectively reduce plural relative errors. With the proposed method, VRT parameters are decided by that the sum of squared relative errors for plural responses has a minimum value. To verify the MR-CADIS method, simple shielding and duct problems are estimated and compared to those estimated with the FW-CADIS method. These results show that the MR-CADIS method can produce better efficiency and uniformity than the FW-CADIS method for plural response problems.