Compressed Sensing Methods for Memory Reduction in Monte Carlo Simulations

TL;DR

This paper explores applying compressed sensing with overlapping cells to reduce memory in Monte Carlo neutronic simulations, achieving up to 81.25% memory savings while maintaining high reconstruction accuracy.

Contribution

It introduces a novel implementation of compressed sensing using overlapping cells for memory-efficient Monte Carlo simulation reconstructions.

Findings

Memory reductions up to 81.25% in 2D and 96.25% in 3D reconstructions.

Reconstruction errors within 1 standard deviation of high-fidelity results.

Increased samples improve accuracy with diminishing returns.

Abstract

Monte Carlo simulations of neutronic systems are computationally intensive and demand significant memory resources for high-fidelity modeling. Compressed sensing enables accurate reconstruction of signals from significantly fewer samples than traditional methods. The specific implementation of compressed sensing investigated here involves the use of overlapping cells to collect tallies. Increasing the number of samples improves the reconstruction accuracy, although the marginal gains diminish with more samples. Reconstruction quality is strongly influenced by the sparsity parameter used in basis pursuit denoising. Across the three test cases considered, memory reductions of up to 81.25% (96.25%) are demonstrated for 2D (3D) reconstructions, with select scenarios achieving reconstruction errors within 1 standard deviation of the corresponding high-fidelity reference results.