Many applications across sciences and technology require a careful quantification of nondeterministic effects to system outputs, for example when evaluating a system’s reliability or when gearing it towards robust operating conditions. To quantify the effects of input uncertainties propagated through a computational model, the multilevel Monte Carlo (MLMC) method constitutes an efficient sampling method for the approximation of expected system outputs, which is applicable to a wide range of applications. However, its use for quantities of interest that cannot be expressed as expected values is not straightforward. In this talk, we will review recent advances on MLMC techniques that go beyond expected values, which allow for a more informative characterization of a system output’s distribution. Specifically, we will first introduce a methodology for accurately estimating higher-order central moments, such as a random system output's variance or characteristics related to its skewness and kurtosis. We will discuss both theoretical and practical aspects of these MLMC estimators and showcase their effective use. We will then introduce MLMC techniques for approximating generic parametric expectations, that is, expected values that depend on a parameter. The resulting MLMC estimator for functions allows deriving efficient approximations to further characterize a system output’s distribution. In particular, we will outline a procedure for constructing MLMC estimators for robustness indicators, focusing on those quantifying “tail” risk-based quantiles (value-at-risk) or conditional values-at-risk. In addition to the estimator’s theoretical properties, we will discuss novel error estimators that allow an efficient practical implementation.


08. Dezember 2022, 14:00-15:00


S4|10 142
Dolivostr. 15
64293 Darmstadt


AG Numerik und wissenschaftliches Rechnen




Mathematik, Numerik