Dynamic mode decomposition application to dominance ratio assessment in Monte Carlo k-eigenvalue calculation

Abstract

Dynamic mode decomposition (DMD) is applied to assess the dominance ratio (the ratio of the second-largest to the largest k-eigenvalue) from the fission source convergence during Monte Carlo power iterations. The fission source transition in each discretized tally region toward convergence is viewed as snapshots for DMD analysis. DMD is found to yield satisfactory results for the dominance ratio when various arbitrary parameters are selected, even for systems that have a dominance ratio that is very close to unity (∼0.999). The accuracy of the method depends on the parameters, especially in a system that has a low dominance ratio due to a reduced number of cycles before convergence. The spatial discretization of tally regions where fission sources accumulate can be coarse, in contrast to that in the fission matrix method, which is an advantage of the proposed method.