Mathematics

This presentation will focus on the use of sensitivity analysis and uncertainty quantification for applications arising in science and engineering.First, pertinent issues will be illustrated in the context of weather and climate modeling, applications utilizing smart materials for energy harvesting, biology models, radiation source localization in an urban environment, and simulation codes employed for nuclear power plant design. This will demonstrate that the basic UQ goal is to ascertain uncertainties inherent to parameters, initial and boundary conditions, experimental data, and models themselves to make predictions with quantified and improved accuracy.The use of data, to improve the predictive accuracy of models, is central to uncertainty quantification and we will discuss the use of Bayesian techniques to construct distributions for model inputs. Specifically, the focus will be on algorithms that are both highly robust and efficient to implement. The discussion will subsequently focus on the use of sensitivity analysis to isolate critical model inputs and reduce model complexity. This will include both local sensitivity analysis, based on derivatives of the response with respect to model parameters, and variance-based techniques which determine how uncertainties in responses are apportioned to uncertainties in parameters. The presentation will conclude with a discussion detailing the manner in which model discrepancy must be addressed to construct time-dependent models that can adequately predict future events. An important aspect of this presentation is that all concepts will be illustrated with a suite of both fundamental and large-scale examples from biology and engineering.