GRK 2224:  Pi³ : Parameter Identification - Analysis, Algorithms, Implementations

• Subject Area: Mathematics
• Term: since 2016
• Website: Homepage
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281474342

The task of retrieving biological, physical, or technical parameters from measured data is as universal as the quest to determine system parameters for optimisation/controlling complex processes. Accordingly, parameter identification is at the core of multiple applications in all fields of natural sciences, engineering, life sciences, and industrial applications, which lead to numerous challenges in mathematical modelling, analysis, statistics and algorithmic research. We focus on non-linear and high-dimensional parameter identification tasks on the interface between applied mathematics, statistics and scientific computing. The different approaches share modelling characteristics as well as mathematical challenges and they meet when it comes to designing efficient algorithms. This was well mirrored by the PhD topics of the first cohort, which e.g. included scattering theory and contributions towards a mathematical-statistical foundation of deep learning. Our endeavour to strengthen statistical research and the advance of data-driven concepts has led us to broaden the scope of this RTG to four research areas: - R1 Dynamic inverse problems: parameter identification ans characterisation of singularities, (CT, magnetic particle imaging (MPI), dynamic properties of magnetic domain walls). - R2 Direct optimisation: Efficient parameter identification of high-dimensional, highly nonlinear systems (real-time capability, automotive applications, autonomous systems). - R3 Mathematical data analysis: Mathematical foundations of deep learning concepts for inverse problems, regularisation by architecture, topological data analysis. - R4 Statistics: Statistical inference for high-dimensional data and learned model interpretation, causality (application to functional magnetic resonance imaging (fMRI)). PI3 aims at educating internationally recruited PhD students in mathematics and statistics. The guiding principles for our training and supervision concepts are mathematical competence and scientific independence. In addition, our soft skills programme strongly promotes gender related topics and takes into account that – based on our experience with the first cohort of PhD student, which got interesting job offers as postdoc in Cambridge, as consultant in industry, or in research units of Fraunhofer MeVis – our PhD students are prepared for and will reach leading positions in science or business in their future careers.

• DFG Programme: Research Training Groups
• Applicant Institution: Universität Bremen
• Spokesperson: Professor Dr. Peter Maaß
• Participating Researchers: Professor Dr. Werner Brannath; Professor Dr. Christof Büskens; Professor Dr. Thorsten Dickhaus; Professorin Dr. Vanessa Didelez; Professor Dr. Dmitry Feichtner-Kozlov; Dr.-Ing. Tobias Kluth; Professorin Dr. Anke Pohl; Professor Dr. Jens Rademacher; Professor Andreas Rademacher, Ph.D.; Professor Dr. Alfred Schmidt