Application Area 5 “Variational Problems in Data-Driven Applications”

Application Area 5 is a research field that focuses on designing and implementing algorithms for variational and continuous optimization problems involving data-driven components. This area aims to develop solutions that consider the problem’s complexity, fairness, hierarchical structures, and energy efficiency of the problem. Researchers in this field tackle challenges related to the analytical and numerical treatment of non-smooth and stochastic structures, as well as addressing data and model uncertainty in optimization and inverse problems. Furthermore, they aim to efficiently handle hybrid model-based constraints in cases where ab initio modeling is intertwined with learning-related components or other data-driven techniques. Application Area 5 is particularly relevant in the field of quantitative imaging, where researchers develop advanced applications for transient phenomena and multimodality.