601 Pao Yue-Kong Library
Bayesian estimation is a method to learn unknown features from data. In particular, we use computational Bayesian inversion based on PDE (partial differential equation) models as a machine-learning method in order to identify unknown parameters which correspond to physical or geometrical properties in various applications in nanotechnological sensors and in tomography. Applications such as electrical-impedance tomography, nanoelectrode sensors, and nanowire field-effect sensors lead to deterministic and stochastic partial differential equations that model electrostatics and charge transport in these devices. The main model equations are the nonlinear Poisson-Boltzmann equation and the stochastic drift-diffusion-Poisson-Boltzmann system. The main question how as much information as possible can be extracted from measurements naturally arises next. We use computational Bayesian inversion to reconstruct physical and geometric parameters of the body interior in electrical-impedance tomography, of nanoelectrodes and the liquid in nanoelectrode sensors, and of nanowires and target molecules in nanowire field-effect sensors. The main advantage of computational Bayesian inversion is that it not only yields the unknown parameters whenever possible, but also their probability distributions and hence the uncertainties in the reconstructions, which is essential in the case of ill-posed inverse problems. In addition to showing the well-posedness of the Bayesian inversion problem for the nonlinear Poisson-Boltzmann equation, the numerical methods are presented and numerical results for the three applications such as multifrequency reconstruction for nanoelectrode sensors are shown.
Clemens Heitzinger received his master’s and PhD degrees from TU Wien. He was a visiting researcher in the Department of Mathematics and Statistics at Arizona State University, a research associate in the School of Electrical and Computer Engineering at Purdue University, and a senior research associate in the Department of Applied Mathematics and Theoretical Physics (DAMTP) at the University of Cambridge. In 2015, he returned to TU Wien as an Associate Professor in the Department of Mathematics and Geoinformation. He was awarded the START Prize by the Austrian Science Fund (FWF), Austria’s most prestigious award for young scientists. His research interests are uncertainty quantification (stochastic partial differential equations and Bayesian inversion) as well as machine learning (reinforcement learning).