Compressed Sensing Methods for Memory Reduction in Monte Carlo Simulations

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.