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Abstract:
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From both mathematical and statistical perspectives, the fundamental goal of Uncertainty Quantification (UQ) is to ascertain uncertainties inherent to parameters, initial and boundary conditions, experimental data, and models themselves to make predictions with improved and quantified accuracy. Some factors that motivate recent developments in mathematical UQ analysis include the following. The first is quantifying uncertainties for models and applications whose complexity precludes sole reliance on sampling-based methods. This includes simulation codes for discretized partial differential equation (PDE) models. Secondly, models are typically nonlinearly parameterized thus requiring nonlinear statistical analysis. Finally, there is often emphasis on extrapolatory or out-of-data predictions; e.g., using time-dependent models to predict future events. This presentation will detail recent mathematical techniques to address these issues and to construct prediction intervals for statistical quantities of interest. The presentation will conclude with discussion pertaining to the quantification of model discrepancies in a manner that preserves physical structures.
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