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Applied Mathematics Graduate Theses & Dissertations

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Low-Rank, Multi-Fidelity Methods For Uncertainty Quantification Of High-Dimensional Systems, Hillary Ruth Fairbanks Jan 2018

Low-Rank, Multi-Fidelity Methods For Uncertainty Quantification Of High-Dimensional Systems, Hillary Ruth Fairbanks

Applied Mathematics Graduate Theses & Dissertations

Characterizing and incorporating uncertainties when simulating physical phenomena is essential for improving model-based predictions. These uncertainties may stem from a lack of knowledge regarding the underlying physical processes or from imprecise measurements of quantities that describe properties of the physical system. Uncertainty quantification (UQ) is a tool that seeks to characterize the impact of these uncertainties on solutions of computational models, resulting in improved predictive models. In practice, these uncertainties are either treated as random parameters to inform the statistics of the solution of interest (forward UQ), or their statistics are inferred from noisy observations of the solutions (inverse UQ ...