I am working on inverse problems for mathematical models governed by partial differential equations. This means that, given observations of a technical or physical system, I want to infer underlying properties of that system. For instance, this could be the estimation of the different materials in the earth mantle from seismographic recordings, or of the origination of a hurricane from weather station data. To incorporate uncertainties of the model and measured data into the inference, and thereby assess the reliability of the predictions, I follow a Bayesian approach.
My research leads me through a wide range of topics at the interface between applied mathematics and computer science, such as spatial statistics, functional optimization, reduced order modeling, machine learning and Markov Chain Monte Carlo techniques. Furthermore, I aim to transfer theoretical procedures into reliable and reusable software tools.
The main application of my work is the inverse problem of cardiac electrophysiology. More specifically, I want to infer properties of human heart tissue from minimally invasive electrical measurements. Such knowledge on a personalized level could be utilized for the diagnosis of heart disease and guide clinical interventions.