Nth-order multi-response CADIS method to optimize regional variances in a hybrid Monte Carlo simulation

Abstract

To increase the calculation efficiency of the Monte Carlo (MC) calculation, variance reduction (VR) techniques have been introduced. For an optimal MC calculation, it is necessary to properly determine the optimized parameters for VR techniques. To automatically determine those parameters, hybrid MC methods have been developed. For a single response, the Consistent Adjoint Driven Importance Sampling (CADIS) method, which uses a zero variance solution, was developed. For the inclusion of multiple responses, several methods have been proposed. Among them, the Forward-Weighted CADIS (FW-CADIS) method shows the best performance. In the previous study, the Multi-Response CADIS (MR-CADIS) method was proposed and it showed a better efficiency. However, it is noted that many adjoint calculations are needed to adopt the MR-CADIS method and the overall efficiency can be decreased. In this study, a new hybrid MC method, referred to as an Nth-order multi-response CADIS method (N-CADIS) is proposed for a more uniformly low variance. For verification of the proposed method, it is applied to simple problems and compared with the FW-CADIS method and the MR-CADIS method. These results show that the N-CADIS method can produce a better efficiency only for the MC calculation. Also, to avoid many deterministic calculations, the adjoint transport process was modified and applied in ADVANTG code. This process produces a VR parameter similar to that used in the N-CADIS method. This approach is also verified and compared with the FW-CADIS method. The results from the N-CADIS method have a more uniform and lower relative error than those from the FW-CADIS method. Therefore, it is expected that the N-CADIS method will contribute to efficient calculations for multiple responses in hybrid MC simulations.