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.
AA5 evolved from a merger of selected projects of the Emerging Fields Extracting Dynamical Laws from Complex Data (EF1) and Model-Based Imaging (EF3).
Scientists in Charge: Michael Hintermüller, Sebastian Pokutta
- AA5-2: Robust Multilevel Training of Artificial Neural Networks
Michael Hintermüller, Carsten Gräser - AA5-4: Bayesian Optimization and Inference for Deep Networks
Claudia Schillings, Vladimir Spokoiny - AA5-5: Wasserstein Gradient Flows for Generalised Transport in Bayesian Inversion
Martin Eigel, Claudia Schillings, Gabriele Steidl - AA5-6: Convolutional Proximal Neural Networks for Solving Inverse Problems
Gabriele Steidl, Andrea Walther - AA5-8: Convolutional Brenier Generative Networks
Hanno Gottschalk, Gabriele Steidl - AA5-9: LEAN on Me: Transforming Mathematics through Formal Verification, Improved Tactics, and Machine Learning
Sebastian Pokutta, Christoph Spiegel - AA5-10: Robust Data-Driven Reduced-Order Models for Cardiovascular Imaging of Turbulent Flows
Alfonso Caiazzo, Jia-Jie Zhu, Leonid Goubergrits - AA5-11: Data-Adaptive Discretization of Inverse Problems
Tim Jahn
Successfully completed projects:
- AA5-1: Sparsity and Sample-Size Efficiency in Structured Learning
Sebastian Pokutta - AA5-3: Manifold-Valued Graph Neural Networks
Christoph von Tycowicz, Gabriele Steidl - AA5-7: Integrated Learning and Variational Methods for Quantitative Dynamic Imaging
Michael Hintermüller, Christoph Kolbitsch, Tobias Schäffter