Forward-Weighted CADIS Method for Global Variance Reduction

Recent applications’ needs/desires have motivated efforts to develop approaches for optimizing Monte Carlo calculations for global distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as response at multiple localized detectors and spectra. Recent efforts at Oak Ridge National Laboratory (ORNL) have led to the development of a variation on the Consistent Adjoint Driven Importance Sampling (CADIS) method for effective global variance reduction. This method, referred to as Forward-Weighted CADIS (FW-CADIS), and an example of its application are presented in this paper. To the authors’ knowledge, this is a new method and novel use of the adjoint methodology for biasing Monte Carlo simulations. It has long been recognized that the adjoint function (i.e., the solution to the adjoint form of the Boltzmann transport equation) has physical significance [1] as a measure of the importance of a particle to some objective function (e.g., the response of a detector) and that this physical interpretation makes the adjoint function well suited for biasing Monte Carlo simulations. Accordingly, recent trends in Monte Carlo code development have reflected a recognition of the benefits of using deterministic adjoint (importance) functions for Monte Carlo variance reduction.[2] The CADIS methodology [2,3], which has been incorporated into codes such as ADVANTG [4] (based on MCNP) and the MAVRIC [5] sequence of SCALE, is being routinely used at ORNL for three-dimensional (3-D) Monte Carlo simulations of real applications. Although the CADIS methodology has proven to be very effective for automated optimization of localized quantities, until very recently, efforts to optimize global distributions have not been nearly as successful. A number of heuristic approaches, such as specification of the adjoint source (response function) throughout the problem phase space, have been tested and found to be ineffective. Specification of the adjoint source at the outer boundaries of a problem in an attempt to encourage particles to move outward through the entire system was found to be reasonably effective. Previous work by Cooper and Larsen, which used the inverted forward flux as the importance function (no adjoint calculation) in an attempt to distribute particles uniformly throughout the system has demonstrated some benefit [6]. While this approach does encourage particles toward regions of lower flux and discourage particles from moving toward regions of higher flux, the forward flux does not represent the expected contribution to the desired response, which is uniform particle density (or response) throughout the system. When applied to a large realistic application, this method was not found to be effective. Hence, a need has remained for an effective method for global variance reduction of Monte Carlo simulations.