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Uncertainty quantification (UQ) is an interesting, fast growing research area aiming
at developing methods to address, characterize and minimize the impact of param-
eter, data and model uncertainty in complex systems. Applications of uncertainty
quantification include all areas of engineering, environmental, physical and biological
systems, e.g., groundwater flow problems, shape uncertainties in aerodynamic ap-
plications or nano-optics, biochemical networks and finance. The efficient treatment
of uncertainties in mathematical models requires ideas and tools from various disci-
plines including numerical analysis, statistics, probability and computational science.
This course will provide an introduction to the basic theory for random elliptic partial dif-
ferential equations and computational methods to efficiently approximate the solution
and its moments such as mean or variance.
Whereas the focus of the first part is on the forward problem, i.e. the efficient propagation
of input uncertainties to quantities of interest in the output of the model, we will discuss in
the second part of the course the identification of parameters through observations of
the response of the system - the inverse problem. The uncertainty in the solution of
the inverse problem will be described via the Bayesian approach.
The aim of the course is to introduce the concepts of UQ for forward and inverse problems
and state-of-the-art computational methods to approximate the resulting problems. |
