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Uncertainty quantification cuts across all branches of science and engineering. It has been recognized in all recent reports and initiatives from various scientific organizations and funding agencies as being on the critical path for advancement in prediction science, life-cycle design and societal sustainability. For example, the recent Blue Ribbon Panel and the International Assessment of Research and Development in Simulation-based Engineering and Science conducted by the World Technology Evaluation Center (WTEC) featured uncertainty quantification very prominently as one of the pillars of simulation-based capabilities. The topic of uncertainty remains, in general, elusive and susceptible to philosophical arguments. However, a well-defined subset of science and engineering problems, namely those whose behavior can be suitably modeled with conservation or variational laws with stochastic coefficients, lends itself to analysis that inherits its rigor from the vast knowledge accumulated over centuries in approximation theory. Within this subset of problems, namely ordinary and partial differential equations with stochastic coefficients, an analysis and approximation path based on a marriage of probability theory and functional analysis has taken shape over the last two decades with a demonstrated ability to handle equations that are relevant across the spectrum of science and engineering. These approaches based on Polynomial Chaos expansions (PCE) and related expansions have in recent years attracted the attention of scientists, engineers and mathematicians, from many disciplines. This Workshop will provide a forum where the state of the art in these methods is delineated and challenges and opportunities identified. The Workshop will accelerate the maturity of these methods and bring them, much faster, to a point where they can fulfill their promise as an enabling technology in scientific discovery and engineering design.
The objective of the workshop is to identify challenges and opportunities in the use of the PCE formalism for addressing uncertainty in predictive systems. The Workshop will feature surveys of the current state-of-the art in PCE research delivered by leading researchers in the field. Following that, participants will break into three groups, for in-depth discussions related to Modeling, Algorithms and Software issues associated with PCE. In the Modeling arena, we will focus on methods that capitalize on the PCE formalism in order to develop reduced order models and integrated models for interacting systems. These will include multiphysics, multiscale, and hybrid systems involving both continuous and discrete models. We will also explore issues of decision-making under uncertainty and ways in which this problem can benefit from and be adapted to the structure of the PCE framework. On the algorithmic side, we will focus on methods for convergence acceleration; adaptive refinement in space, time, and random dimensions; reduced models using geometric and probabilistic tranformation techniques; and model validation. On the software side, we will focus both on procedures for relying on existing software tools to implement the various versions of PCE, as well as specifications for emerging software tools.
The Workshop will be co-chaired by