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IRTG Modern Inverse Problems (MIP)
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SSD Seminar Series with Prof. Sebastian Krumscheid, Ph.D.

15. Juni 2020 @ 16:00 - 17:00

Prof. Sebastian Krumscheid, Ph.D. – Beyond Multilevel Monte Carlo Methods for Expected Values

Department of Mathematics for Uncertainty Quantification, RWTH Aachen

 

Abstract

Many applications across sciences and technologies require a careful quantification of nondeterministic effects to a system output, for example when evaluating the system’s reliability or when gearing it towards more robust conditions. These considerations rely on an accurate yet efficient characterisation of uncertain system outputs. For the approximation of (raw) moments of said outputs, the multilevel Monte Carlo (MLMC) method has been established as a computationally efficient sampling method that is applicable to a wide range of applications. In this talk we will review recent advances in MLMC techniques for a characterisation of an uncertain system output’s distribution. Specifically, we will first introduce efficient methods for accurately estimating higher order central moments and showcase their use in aeronautics problems. We will then discuss MLMC techniques for approximating general parametric expectations, i.e. expectations that depend on a parameter, uniformly on some interval. The resulting MLMC estimators of such functions enable to derive efficient approximations of various means to characterise a system output’s distribution, e.g. to the characteristic function or to the cumulative distribution function. A further important consequence of these results is that they allow to construct MLMC for various robustness indicators, such as for quantiles (value-at-risk) or for the conditional value-at-risk, which we will also exemplify. This is joint work with F. Nobile (EPFL).

Details

Datum:
15. Juni 2020
Zeit:
16:00 - 17:00

Veranstaltungsort

a link for the Zoom meeting room will be send in the newsletter one week before the seminar starts. If you need any organizational help please contact office@aices.rwth-aachen.de

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IRTG-2379 MIP