Final Report: Quantification of Uncertainty in Extreme Scale Computations (QUEST)
QUEST (\url{www.quest-scidac.org}) is a SciDAC Institute that is focused on uncertainty quantification (UQ) in large-scale scientific computations. Our goals are to (1) advance the state of the art in UQ mathematics, algorithms, and software; and (2) provide modeling, algorithmic, and general UQ expertise, together with software tools, to other SciDAC projects, thereby enabling and guiding a broad range of UQ activities in their respective contexts. QUEST is a collaboration among six institutions (Sandia National Laboratories, Los Alamos National Laboratory, the University of Southern California, Massachusetts Institute of Technology, the University of Texas at Austin, and Duke University) with a history of joint UQ research. Our vision encompasses all aspects of UQ in leadership-class computing. This includes the well-founded setup of UQ problems; characterization of the input space given available data/information; local and global sensitivity analysis; adaptive dimensionality and order reduction; forward and inverse propagation of uncertainty; handling of application code failures, missing data, and hardware/software fault tolerance; and model inadequacy, comparison, validation, selection, and averaging. The nature of the UQ problem requires the seamless combination of data, models, and information across this landscape in a manner that provides a self-consistent quantification of requisite uncertainties in predictions from computational models. Accordingly, our UQ methods and tools span an interdisciplinary space across applied math, information theory, and statistics. The MIT QUEST effort centers on statistical inference and methods for surrogate or reduced-order modeling. MIT personnel have been responsible for the development of adaptive sampling methods, methods for approximating computationally intensive models, and software for both forward uncertainty propagation and statistical inverse problems. A key software product of the MIT QUEST effort is the MIT Uncertainty Quantification library, called MUQ (\url{muq.mit.edu}).