Madsen, Jonathan Robert (2017-12). Disjoint Tally Method: A Monte Carlo Scoring Method Using Compressed Sensing to Reduce Statistical Noise and Memory. Doctoral Dissertation. Thesis uri icon

abstract

  • We present a methodology for using compressed sensing concepts to compute a global solution for Monte Carlo simulations with less memory and an accelerated reduction in statistical noise. The methodology utilizes a process known as total variation minimization to reconstruct the solution from the projection of the scoring array onto randomly constructed basis sets. In the disjoint tally method, the memory allocation of the basis sets and the projection is a fraction of the size of a standard scoring array and is a replacement for the array at runtime. Memory reduction results are approximately 25% for 1 thread and 1 tally quantity, ~ 35% for 16 threads and 1 tally quantity, and can exceed 75% at 16 threads and 8 tally quantities. The reconstruction method is peak-preserving and applies statistical denoising upon reconstruction. If a satisfactory global solution to scoring array A can be reached at fvN, where N is the number of particles simulated and i EUR 1; . . . ;N, then if ?i is the difference between fvi and fN, our method at fi consistently produces a smaller ?i than a standard scoring array at fi. Since N is arbitrary, the disjoint tally method effectively decreases computation time by producing results at fvp where i < p < N. We begin by introducing the concept of disjoint tallies and provide the procedure for local reconstruction on subsets of the global mesh. We present evidence of the validity of the solution produced by the methodology and the reduction in memory footprint via direct comparison to a memory-efficient storage implementation within the Monte Carlo transport toolkit, Geant4. Additionally, we present a method for reconstructing statistical quantities in the form of the variance, relative error, coefficient of variation, and root-mean-squared. Results are given for three different global reconstruction scenarios: a reactor bundle, a neutron shielding problem, and set of CT scans rendered directly from DICOM files. We believe the demonstration of the significant reduction of data allocation size, the evidence of acceleration towards the bounded total variation of the solution, ability to reconstruct the quantities required for statistical checks, and the local nature of our reconstruction will provide capabilities necessary for high-fidelity exascale computing.
  • We present a methodology for using compressed sensing concepts to compute a global
    solution for Monte Carlo simulations with less memory and an accelerated reduction in
    statistical noise. The methodology utilizes a process known as total variation
    minimization to reconstruct the solution from the projection of the scoring array onto
    randomly constructed basis sets.

    In the disjoint tally method, the memory allocation of the basis sets and the projection
    is a fraction of the size of a standard scoring array and is a replacement for the array
    at runtime. Memory reduction results are approximately 25% for 1 thread and 1 tally
    quantity, ~ 35% for 16 threads and 1 tally quantity, and can exceed 75% at 16 threads and
    8 tally quantities.

    The reconstruction method is peak-preserving and applies statistical denoising upon
    reconstruction. If a satisfactory global solution to scoring array A can be reached at fvN,
    where N is the number of particles simulated and i EUR 1; . . . ;N, then if ?i is the
    difference between fvi and fN, our method at fi consistently produces a smaller ?i than a
    standard scoring array at fi. Since N is arbitrary, the disjoint tally method effectively
    decreases computation time by producing results at fvp where i < p < N.

    We begin by introducing the concept of disjoint tallies and provide the procedure for
    local reconstruction on subsets of the global mesh. We present evidence of the validity of
    the solution produced by the methodology and the reduction in memory footprint via
    direct comparison to a memory-efficient storage implementation within the Monte Carlo
    transport toolkit, Geant4. Additionally, we present a method for reconstructing statistical quantities in the form of the variance, relative error, coefficient of variation, and
    root-mean-squared. Results are given for three different global reconstruction scenarios:
    a reactor bundle, a neutron shielding problem, and set of CT scans rendered directly from
    DICOM files.

    We believe the demonstration of the significant reduction of data allocation size, the
    evidence of acceleration towards the bounded total variation of the solution, ability to
    reconstruct the quantities required for statistical checks, and the local nature of our
    reconstruction will provide capabilities necessary for high-fidelity exascale
    computing.

publication date

  • December 2017