Don Estep, Mathematics, Colorado State

Model Sensitivity Analysis, Uncertainty Quantification, and Error Control in a Complex World

Friday November 17th, 4pm, Phillips 383
(refreshments served in Phillips 330 starting at 3:30)

Abstract: The investigation of multiscale, multiphysics systems occupies a central position in science and engineering. The cost and complexity of physical experimentation on such systems leads to a strong reliance on mathematical modeling and numerical simulation as analysis and design tools. Complexity (happily for mathematicians) also increases the need for quantitative estimates of computational, data, and model errors in simulations and the ability to control such errors when possible. In this talk, I will describe a mathematical foundation for investigating model sensitivity and quantifying uncertainty and error based on adjoint problems, variational analysis, and generalized Green's functions. These tools have a long history of application in science and engineering and are connected to relatively recent advances in a posteriori error analysis of finite element methods. In this talk, I will show these tools apply to numerical error estimation, model sensitivity analysis, data and parameter error, operator decomposition for multiphysics problems, and adaptive error control. I will expose the basic ideas in the context of finite dimensional problems, where the mathematics is simple. Then, I will explain how they apply to various differential equations and demonstrate their effectiveness using a variety of examples.