EU Regional School - Scheichl Seminar
Prof. Scheichl - Efficient Use of Model Hierarchies in Uncertainty Quantification
University of Bath
The term “Uncertainty Quantification” is as old as the disciplines of probability and statistics, but as a field of study it is newly emerging. It combines probability and statistics, with mathematical and numerical analysis, large-scale scientific computing, experimental data, model development and application sciences to provide a computational framework for quantifying input and response uncertainties which ultimately can be used for more meaningful predictions with quantified and reduced uncertainty. We will motivate the central questions in computational uncertainty quantification through some illustrative examples from subsurface flow, weather and climate prediction, material science, nuclear reactor physics and biology. The key challenge that we face in all those applications is the need for fast (tractable) computational tools for high-dimensional quadrature. After a short overview of the available techniques, we study sampling-based approaches in more detail. In particular, we focus on multilevel (or multiscale) methods that exploit the natural model hierarchies in numerical methods for partial differential equations. In the final part of the course, we will consider the inverse problems of Bayesian inference, data assimilation and filtering and show how the multilevel techniques presented in the earlier parts of the course can be extended to these more challenging tasks and provide actual practical tools for large-scale Bayesian inference.