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IRTG Modern Inverse Problems (MIP)

A Hierarchical Framework for Bayesian Optimal Experimental Design

09. Juli 2020 | von

Prof. Dr. Raul F. Tempone

The project will advance the state of the art in hierarchical non-intrusive UQ techniques, such as multi-level and multi-index methods, for goal-oriented optimal experimental design within complex models with high dimensional inputs.

Experimental design is an essential topic in engineering and science. Acquiring relevant information about processes and environments is paramount nowadays. Such cases include, among others, recording weather patterns, measuring traffic density, and tracking industrial process parameters. These data once obtained, provide input for predictive modeling and process optimization. Experiments are meant to provide meaningful information about selected quantities of interest. An experiment may assume different set-ups in a broad sense and can be time consuming or expensive to perform. Therefore, the design of experiments plays a vital role in improving the information gain of the experiment.

Experimental design allows us to optimize the locations of sensors to achieve the best estimates and minimize uncertainties, especially for real, noisy measurements. For instance, determining exactly how many sensors (shown in the figures) to use and their optimal location has significant implications for the reliability and value of the information obtained and for the cost of the measurement system itself. Thus, finding the best set-up for the design of experiments is the main concern of Optimal Experimental Design (OED). In Bayesian OED, one attempts to optimize the experimental set-ups so that the sensitivities between the unknown model parameters and the measurements are maximized.

Our goals in this project are:

Development of advanced hierarchical uncertainty quantification (UQ) techniques for complex systems;
Construction of the corresponding hierarchical Bayesian Optimal Experimental Design techniques for both static and dynamic inverse problems;
Develop novel stochastic optimization approaches tailored to the Bayesian Optimal Experimental Design setting.

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