Thursday, February 28, 2008
Mathematical Sciences Colloquium
Speaker: Donald Estep (Colorado State University) "Stability, Adjoints, and Uncertainty"

From the spread of disease in a national livestock distribution system to the storage of nuclear waste underground, from building fusion reactors to designing MEMs devices, from climate modeling to the performance of automobile tires, science and engineering is increasingly concerned with understanding and predicting the behavior of multiscale, multiphysics systems. The range of scales and complexity in such systems makes physical experimentation, modeling, and simulation difficult, sometimes impossible, and always expensive. This reality is leading to a fusion of experiment and model simulation as the basis of predictive science and engineering. As a consequence, there is an increasing – even strident - demand for quantification of error and uncertainty in model predictions, which has become a literal bonanza for mathematicians and statisticians.

In this talk, I will describe a powerful approach for quantifying sensitivity, error, and uncertainty based on duality and adjoint operators. These are old ideas – at least dating back to Lagrange - however, they are being applied in new ways to tackle difficult multiscale, multiphysics problems. These notions are central because they provide a way to measure the stability of particular information accurately, and stability is the key to uncertainty quantification. I will explain my view of stability, describe the connection to duality and adjoints, and apply these ideas to a variety of error estimation and adaptive error control problems.