In order to be able to predict severe weather events or the melting of ice in the Arctic, information in the form of heterogeneous data must be linked with numerical models of dynamic systems. This is done through data assimilation, which makes it possible to better investigate processes and predict their further development. In the field of data assimilation, the professorship is concerned with the further development of data science algorithms by incorporating physical conservation laws, and solving correspondingly large optimisation problems in the environmental sciences. Quantifying the uncertainties of predictions, numerical models and observations also plays a central role here.
Prof. Oliver works on modeling and simulation of complex multi-scale systems, in particular in climate science, but also in the bio and material sciences. In such systems, the range of relevant scales is so vast that we cannot expect that the exponentially growing capacity of modern supercomputers alone will suffice to make scientific progress. We also need to improve our algorithms, develop parametrizations - simplified models for small scale processes - and learn from data and observations. The research of the group includes structure preserving and energy consistent algorithms, mathematical approaches for model reduction, and dynamic, stochastic, and/or data driven models to represent processes at scales below the computational grid.
Research interests include compressive sensing, sampling theory for signals and operators, applied harmonic analysis, and information theory. A recurring theme in the work of the chair is the measurement, analysis and representation of continuous signals by finite sequences.
Prof. Stöger's research interests lie in the development and analysis of mathematical methods in machine learning and signal processing. A particular area of focus for his research is the analysis of overparameterized models in machine learning and algorithms for Compressed Sensing and Low-Rank Matrix Recovery. It combines tools from a broad range of mathematical disciplines ranging from high-dimensional probability theory to optimization. He has been collaborating with scientists from different application areas such as wireless communications and image recognition.
Chair of Reliable Machine Learning: Prof. Dr. Felix Voigtlaender
Funded by the Hightech Agenda Bavaria as part of the consortium "Resource Aware Artificial Intelligence for Future Technologies" of the KU Eichstätt-Ingolstadt, the FAU Erlangen-Nürnberg, the TU Munich and the University of Bayreuth.
The research group "Reliable Machine Learning" mathematically studies the properties of machine learning algorithms. Particular attention is paid to the question of stability or robustness of neural networks. Although trained neural networks often perform extremely well on real data, empirical studies have shown time and again that they are vulnerable to so-called "adversarial examples": A minimal perturbation of the input, invisible to a human, can cause the network to produce an incorrect output. The research group "Reliable Machine Learning" mathematically studies the underlying mechanisms leading to the existence of such adversarial examples, with the aim of developing novel training methods that produce provably robust neural networks. More information on research and teaching of the group can be found here and here.
Chair of Geomatics and Geomathematics: ongoing appointment procedure
Endowed professorship of the city of Ingolstadt.
The focus of the professorship is geomatics, geomathematics or a related mathematical field related to the geosciences. This includes expertise in inverse problems, modeling in the geosciences, geomonitoring based on mathematical-statistical methods, and the analysis and visualization of spatial data and their integration into geographic information systems. The latter is the basis for long-term planning in transport, infrastructure and natural hazard prevention.
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