Research
π3 focuses on deterministic parameter identification tasks on the interface between applied mathematics and scientific computing that are formulated as functional minimisation problems. The different scientific approaches considered share modelling characteristics as well as mathematical challenges and they naturally meet when it comes to designing efficient algorithms for our benchmark applications. The PhD topics of the RTG address three research areas:
- R1 Dynamic Inverse Problems: Parameter identification and 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)).
- Benchmark applications: Magnetic particle imaging, nanomagnetic devices, autonomous driving, computed tomography, functional magnetic resonance imaging.
For each research area several PhD projects were proposed by the PIs. However, the PhD students of the 1st cohort were free to choose their specific topic, which led to a noticeable change of weight in favor of dynamic inverse problems, deep learning and statistical inference. Also, the applied projects with a focus on scientific computing and transfer were attractive for our PhD candidates. For scientific highlights see the description of the different research areas and of the individual PhD projects.
