Multiscale Methods for High Performance Uncertainty Quantification

Mathematical models of complex real-world phenomena result in computational challenges, often necessitating the use of modern High Performance Computing (HPC) systems and therefore parallelization. When solving Uncertainty Quantification (UQ) problems on such models, these challenges only increase: Uncertainties in input data or (in case of inverse problems) in measurements essentially contribute to the overall dimensionality of the problem at hand. This dissertation aims to close the gap between advanced models and advanced UQ methods by three approaches: A parallelization scheme for an efficient hierarchical inverse UQ method is devised, allowing to leverage the full potential of HPC systems; efficient model hierarchies based on Localized Model Order Reduction (LMOR) are investigated, allowing automatic generation of coarse models; and the resulting tools are made available to the wider community as part of the modular and open source MIT Uncertainty Quantification Library (MUQ)