QUANTIFYING UNCERTAIN SYSTEM OUTPUTS VIA THE MULTI-LEVEL MONTE CARLO METHOD-DISTRIBUTION AND ROBUSTNESS MEASURES

International Journal for Uncertainty Quantification, vol. 13, pp. 61–98

Abstract

In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk (CVaR), of output quantities of complex random differential models by the Multilevel Monte Carlo (MLMC) method. We follow an approach that recasts the estimation of the above quantities to the computation of suitable parametric expectations. In this work, we present novel computable error estimators for the estimation of such quantities, which are then used to optimally tune the MLMC hierarchy in a continuation type adaptive algorithm. We demonstrate the efficiency and robustness of our adaptive continuation-MLMC in an array of numerical test cases.

Authors 3

1. Q. Ayoul-Guilmard

   École Polytechnique Fédérale de Lausanne

   Affiliation as printed

   Institute of Mathematics, EPF Lausanne, 1015 Lausanne

2. Sebastian Krumscheid Aachen Department of Mathematics

   RWTH Aachen University

   Affiliation as printed

   Department of Mathematics, RWTH Aachen University, Aachen, Germany

3. Fabio Nobile

   École Polytechnique Fédérale de Lausanne

   Affiliation as printed

   Institute of Mathematics, EPF Lausanne, 1015 Lausanne, Switzerland