How uncertainty is propagated within complicated non-linear systems is the crux of many fundamental challenges of this century such as climate change and artificial intelligence. While massive data sets for such large-scale problems are routinely becoming available, they often originate from indirect observations of the phenomenon of interest or poorly controllable experimental conditions. Therefore, the instability of the underlying mathematical problem needs to be taken carefully into account in any successful computational framework giving rise to so-called inverse problems. The proposed project answers to these challenges by building the underpinnings of robust non-parametric statistical procedures for non-linear inverse problems. In particular, the project develops computationally affordable methods of uncertainty quantification. Our theoretical findings are also applied to correlation based imaging, which is an emerging imaging modality among inverse problems.

2018

2023