Magdeburg Lectures on Optimization and Control: Uncertainty quantification in inverse problems

Uncertainty quantification in inverse problems

Uncertainty quantification is an interesting, fast growing research area aiming at developing methods to address, characterize and minimize the impact of parameter, 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 applications or nano-optics, biochemical networks and finance. The efficient treatment of uncertainties in mathematical models requires ideas and tools from various disciplines including numerical analysis, statistics, probability and computational science. In this talk, we will focus on 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. We will discuss efficient methods to approximate the so lution of the resulting high/ infinite dimensional systems.