A Compressed Sensing Framework for Monte Carlo Transport Simulations Using Random Disjoint Tallies

ABSTRACT

In this work, we present a methodology for using compressed sensing ideas to reduce the memory footprint of a Monte Carlo simulation where the scalar flux over the entire problem is desired. We first introduce the idea of disjoint tallies, i.e., Monte Carlo particle tallies that are not contiguous in space. Then we give a prescription for choosing these tallies randomly and performing a local reconstruction using a small number of these tallies based on minimizing the total variation (TV) norm of the reconstruction. Results for a TRIGA reactor simulation indicate that our method can give accurate flux maps for thermal and fast fluxes using about 10% the total number of tallies. Additionally, we present evidence that our procedure improves the solution when statistical noise is present. We believe that our work could provide capability necessary for data reduction and solution analysis for exascale computing due to the local nature of our reconstruction.

KEYWORDS:

• compressed sensing; Monte Carlo methods; neutronics

Notes

1 Two bases are said to be coherent when they have a large value when integrated against each other (Donoho and Huo, 2001).