We present a parallel implementation of the Multilevel Monte Carlo (MLMC) method to estimate moments characterizing the output of a mathematical model under uncertainty. MLMC is typically used to estimate the mean; we describe how to estimate higher moments, such as variance, to more fully characterize the output. Analysis indicates under what conditions MLMC is less expensive than Monte Carlo for estimating higher moments as opposed to just the mean. Results are shown for an implementation in Legion, a task-based parallel computing language under development at Stanford.
University
Stanford University