Machine learning is a quickly evolving and exciting research area which becomes more and more important. The majority of research in this field is empirical and often lacks a profound understanding and theoretical foundation. In many applications, for example medical imaging, it is absolutely necessary to get a better understanding of neural network predictions and their reliability. Thus, we focus our research on the mathematical and theoretical analysis of deep learning methods.
Some of our Research Topics
Our research topics in machine learning are related to some of our other research interests, such as using deep learning methods for image processing , solving inverse problems , or solving PDEs . The research can be broadly divided into several categories:
- approximation (related to harmonic analysis  and sparse representations ),
- generalization (related to statistical learning and high-dimensional data analysis ),
- interpretability (related to inverse problems  and uncertainty quantification).