Multilevel and multi-index sampling for the forward propagation of many uncertainties in industrial applications

Computational models in science and engineering are subject to uncertainty, that is present under the form of uncertain parameters or model uncertainty. Any quantity of interest derived from simulations with these models will also be uncertain. The efficient propagation of the uncertainties is often the computational bottleneck in other UQ problems, such as robust optimisation and risk analysis. The Monte Carlo method is the method of choice to deal with these many uncertainties. However, the plain Monte Carlo method is impractical due to its expense. We investigate how extensions of the Monte Carlo method, such as Multilevel Monte Carlo and Multi-Index Monte Carlo, and their respective Quasi-Monte Carlo variants, can be used efficiently to solve uncertainty quantification problems in real engineering applications.status: publishe