Uncertainty Quantification and Data Assimilation (UQDA)
This course will take place in the fall semester of 2018 at the University of Amsterdam.
Uncertainty Quantification and Data Assimilation are concerned with two closely related questions. In Uncertainty Quantification (UQ), the central question is how to deal with uncertainties in mathematical models for simulation and prediction of complex phenomena. Examples are uncertainties about the initial state of a dynamical system, uncertain model input parameters, and model discrepancy (or model error).
Quantifying these uncertainties and assessing their propagation into model prediction uncertainties are key topics. A prototypical problem is to characterize the probability distribution of a model output variable given the distribution of an input parameter, and to do so in an efficient manner. To this end, methods such as stochastic Galerkin, polynomial chaos expansion and stochastic collocation have been developed.
For Data Assimilation (DA), the main question is how to incorporate data (e.g. from physical measurements) in models in a suitable way, in order to improve model predictions and quantify prediction uncertainty. Here, the focus is on the prediction of nonlinear dynamical systems (the classical application example being weather forecasting). The main techniques developed to approach this question are variational data assimilation, Kalman filtering and particle filtering.
UQ and DA are both very active areas of research and have relevance for a wide range applications including biology, climate science and engineering. Both involve a modern combination of elements from dynamical systems, numerical analysis, probability and statistics.
The focus of this course will be on the mathematical techniques and methodologies developed for UQ and DA. We will cover a selection of the following topics: Stochastic Galerkin method, polynomial chaos expansion, stochastic collocation, sparse grids and quadrature, surrogate modeling techniques, sensitivity analysis, Sobol indices, model calibration, Kalman filter, variational data assimilation, particle filter, ensemble Kalman filter.
Literature: Dongbin Xiu, Numerical Methods for Stochastic Computations. A Spectral Method Approach. Princeton University Press, 2010.
The course starts on Wednesday 5 September 2018. Consult the time table in Datanose for time and location details.