Multilevel Monte Carlo via a Low Rank Control Variate
Hillary Fairbanks
Applied Mathematics, University of Colorado Boulder
Date and time:
Tuesday, November 17, 2015 - 11:00am
Location:
GRVW 105
Abstract:
Multilevel Monte Carlo (MLMC) has been shown to be a cost effective way to compute moments of desired quantities of interest in stochastic partial differential equations, when the uncertainty in the data is high-dimensional. As compared to standard Monte Carlo, the use of a series of nested grids in MLMC allows one to improve the convergence of the mean square error by allocating more computational work onto the coarse grids and less onto the costly, fine grid solves. In this talk, we present a variation of MLMC, called Multilevel Control Variates (MLCV), which relies on a low rank approximation of fine grid solutions from the samples of the coarse grid solutions to construct control variates for the estimation of expectations involved in MLMC. In addition, we present cost estimates as well as numerical examples demonstrating the advantage of this new MLCV approach.