Nth-order multi-response CADIS method for optimizing variance reduction parameter in Monte Carlo simulation

The Monte Carlo method has been used to solve particle transport problems including nuclear reactor analysis, radiation shielding, and the others related to the nuclear research field. Generally, the Monte Carlo method produces lower efficiency than deterministic methods. To increase the efficiency in the Monte Carlo simulation, a lot of variance reduction techniques (VRT) have been developed. In these days, the hybrid Monte Carlo methods were introduced to automatically apply VRT parameters. For a single response, consistent adjoint driven importance sampling (CADIS) method is well derived. For the multiple responses, Forward Weight CADIS (FW-CADIS) presents the best efficiencies among global variance reduction method. In this study, N^th-order Multi-Response CADIS (N-CADIS) method was proposed to optimize the relative errors for multiple responses using a concept that minimizing the sum of n^th order weighted relative error for the individual response can achieve uniformly low uncertainty. To evaluate and compare the efficiency of the N-CADIS method, a shielding problem was estimated. The mean based and tail-based penalty FOMs using N-CADIS method was improved by factor 2.03 and 1.46 compared to FW-CADIS. However, the computational time for FOM values does not include deterministic calculation time to estimate weight map. Therefore, it was concluded that if a deterministic transport code to estimate n^th order adjoint values is developed, the proposed N-CADIS method can show improved efficiency. (authors)