Computational Uncertainty Quantification in Nanotechnology

The project focuses on the analysis, mathematical and computational aspects of the inverse Uncertainty Quantification (UQ) in nanoelectronics. The goal is to develop statistical Bayesian inversion and optimal experimental design (OED) methods for inverse problems, which are governed by PDE models of nanoelectronic devices including bio-, gas, and nanopore sensors. Appli- cations range from medicine and healthcare to engineering. These methods lead to the robust model calibration of nanoelectronic devices by reducing the uncertainty of the models unknown parameter(s), given some measurement data. The acquisition of the most informative (measurement) data is a huge chal- lenge, as some experiments are very expensive, time-consuming, or delicate to perform. The main questions are under which experimental circumstances, the most information from the measurement data can be extracted, and what designs and experimental setup are optimal for (sequential) experi- ments. There are various optimality criteria for Bayesian OED including A-optimality and the expected information gain (EIG). The EIG criterion measures how much the information entropy of the uncertain parameter is reduced. However, the evaluation of EIG for PDE-based OED problems is usually computationally expensive. The aim of this project is to explore ef- ficient computational strategies including multilevel methods and (machine learning) surrogate modeling to accelerate the inverse UQ and optimal ex- perimental design process.