Study program
© Matthias Knauer
Providing a common mathematical ground for the diverse and international group of PhD students is a challenge. To this end, a structured study program is implemented, which equips the PhD students with the necessary mathematical knowledge and sufficient insight into the application areas. Moreover, the soft skills program aims at enhancing scientific independence and the capability of working in interdisciplinary teams; special measures exist for developing leadership qualities.
The study program consists of:
- A first part of basic courses focusing on the necessary mathematical background knowledge (T1-T3) and an introduction to benchmark applications (A1-A3) during the first nine months. After the feedback from the 1st cohort of PhD students, the extent of the courses was somewhat reduced to one week for T-courses and 3 days for A-courses. For the third cohort, the compact courses might be adjusted due to the introduction of the fourth research area R4 (Statistics) and the corresponding benchmark application functional magnetic resonance imaging (fMRI).
- The biweekly RTG research seminar where PhD student present and discuss their latest work is also of great importance for our qualification strategy.
- Study groups of several PhD students working on related subjects inside one or between different research areas. Initially guided by a PostDoc or PI, a group should become rather independent and self-organized after some time.
- A subsequent second part of advanced courses for providing special mathematical components and details on benchmark applications; this is organized in small group lectures or reading courses.
Every course combines four components:
- Teaching by experts, i.e., a principal investigator, an associate researcher or a visiting researcher. Typically, the material is presented in daily morning lectures of two hours each. The lecturers will provide handouts or literature references as well as exercise problems (theoretical, programming) for the covered material.
- Self study time for the students for reviewing the mathematical content, solving exercise problems and working on basic programming tasks.
- Exercises and tutorials, supported by postdocs, for revisiting intensively the topic of the day. We plan two groups per course with a maximum of 15 students each. Exercises and tutorials will take about four hours per day. Typically, this time will be split equally for going through the exercise problems of the previous day, reviewing the new material covered in the morning lecture, and hands-on computer exercises.
- An individual assessment for each student at the end of the block course, in order to identify possible lack of knowledge. If required, the PhD supervisors of the students concerned will be informed. PhD student and primary supervisor will discuss and decide on an individual training programme.
For the 1st cohort of PhD students the compulsory courses were:
- T1: Functional analysis, differential equations and inverse problems
- T2: Minimisation of functions and functionals
- T3: Data analysis and image processing
- A1: Electromagnetic wave scattering from optical surface structures
- A2: Applications in automotive motor and exhaust management
- A3: Hyperspectral data analysis: MALDI imaging
With an addition of optional courses on:
- Neural networks
- Simulation Environment for Deep Neural Networks
- Statistics
Moreover, the following advanced reading courses took place:
- Understanding Machine Learning (winter term 2017/18)
- Randomisation approaches in data analysis (winter term 2017/18)
- No problems with inverse Problems (winter term 2017/18)
- Methods for MALDI (winter term 2017/2018)
- Sparse and redundant representation systems (winter term 2017/18)
- Clustering and classification of hyperspectral data (winter term 2017/18)
- Statistical analysis and evaluation of data mining algorithms (winter term 2017/18)
- Selected Papers from nonlinear optimisation and dynamical systems (winter term 2017/18)
- Parameter Identification in Magnetic Particle Imaging (summer term 2018)
- Efficient algorithms for large scale optimisation problems / Solution of large-scale PDE problems (summer term 2018)
- Optimierungs- und Steuerungsprobleme für nichtlineare dynamische Systeme (summer term 2018)
- Inversion of light scattering: non-linear functional analysis, algorithms (summer term 2018)
- Algorithms in Inverse Problems (winter term 2018/19)
- Stability analysis of dynamical systems, robust optimisation and dual control (winter term 2018/19)
- Data analysis and inverse problems in engineering (summer term 2019)
Organization
© Alfred Schmidt
Prof. Dr. Alfred Schmidt
Zentrum für Technomathematik (ZeTeM)
Office: MZH 2430
Phone: +49 421 218-63851
E-Mail: schmidtprotect me ?!math.uni-bremenprotect me ?!.de
© Jens Rademacher
For the 2nd cohort of PhD students, the updated set of compulsory courses is:
- T1: Inverse problems (cancelled)
- T2: Minimisation of functions and functionals
- T3: Statistical data analysis
- A1: Topological data analysis and mathematical data analysis
- A2: Selected applications from the automotive and energy sectors
- A3: Deep learning for inverse problems and digital pathology
Moreover, the following advanced reading courses took place:
- Bayesian Deep Learning (winter term 2019/20) [Johannes Leuschner, Maximilian Schmidt]
- Novel Neural Network Architectures (winter term 2019/20) [Johannes Leuschner, Maximilian Schmidt]
- Numerical Optimization (winter term 2020/21) [Eva Dierkes, Ivan Mykhailiuk, Grace Anulika Eze, Vladimir Vutov]
- Statistical Inference (winter term 2020/21) [Jonathan von Schroeder, Pascal Rink, Vladimir Vutov, Serhat Günay, Vladimir Vutov, Pascal Rink]
- Deep learning and inverse problems (winter term 2020/21) [Johannes Leuschner, Maximilian Schmidt, Alexander Denker]
- Basics of Topological Data Analysis (winter term 2020/21) [Vladimir Vutov, Lena Ranke, Gideon Klaila]
- Machine Learning Methods (summer term 2021) [Johannes Leuschner, Maximilian Schmidt, Alexander Denker, Eva Dierkes, Vladimir Vutov, Serhat Günay, Pascal Rink]
- Deep Learning Optimizers (summer term 2021) [Eva Dierkes, Lennart Evers, Ivan Mykhailiuk, Grace Anulika Eze, S?ren Dittmer]
- Deep Learning (summer term 2021) [Pascal Rink, Serhat Günay]
- Applied topological data analysis (winter term 2021/22) [Lena Ranke, Vladimir Vutov, Gideon Klaila]
Organization
© Alfred Schmidt
Prof. Dr. Alfred Schmidt
Zentrum für Technomathematik (ZeTeM)
Office: MZH 2430
Phone: +49 421 218-63851
E-Mail: schmidtprotect me ?!math.uni-bremenprotect me ?!.de
© Jens Rademacher
For the 3rd cohort of PhD students, the updated set of compulsory courses is:
- T1: Data-driven Dynamical Systems
- T2: Aspects of Direct Optimization
- T3: Foundations of Tpological Data Analysis
- T4: Causal Inference
- A3: Introduction to Deep Learning & PyTorch
Moreover, the following advanced reading courses took place:
- Constrained Optimization and Deep Learning (winter term 2022/23) [Ivan Mykhailiuk, Graze Eze]
- Semiparametrische Statistik (winter term 2022/23) [Pascal Rink, Lasse Fischer]
- Nonlinear Inverse Problems (winter term 2022/23) [Meira Iske, Clemens Arndt, Nick Heilenk?tter, Alexander Denker]
- Stability of persistence models (winter term 2022/23) [Lena Ranke, Gideon Klaila]
- Parameter Identification and Optimal Control of PDEs (summer term 2023) [Annika Osmers, Magdalena Thode, Dennis Zvegincev, Tom Freudenberg]
- Flows in networks (PoA, PoS) / Network Creation Games (PoA, PoS) / How to hunt an ivisible rabbit on a infinite graph in finite time (summer term 2023) [Torben Schürenberg, Nicole Schr?der]
- Statistical testing using e-values (winter term 2023/24) [Friederike Preu?e, Daniel Ochieng, Lasse Fischer, Remi Luschei]
- Koopman Spectral Analysis via DMD (winter term 2023/24) [Renu Yadav, Daniel Ochieng]
- Discrete Mathematics (Optimization and Finite Element Grids) (winter term 2023/24) [Tom Freudenberg, Torben Schürenberg]
- Algorithmic Learning in a Random World (winter term 2023/24) [Friederike Preusse]
- FEM Implementation in C++ (summer term 2024)[Annika Osmers]
- Game-Theoretic statistics (winter term 2024/25) [Lasse Fischer, with joint reading group of researchers from CMU, Pittsburgh, and CWI, Amsterdam]
Ongoing:
- Torch Physics - Implementation of Operator Learning Methods (start winter term 2024/25) [Tom Freudenberg, Janek G?deke, Nick Heilenk?tter)
- Bayesian Inverse Problems (summer term 2025) [Meira Iske, Nick Heilenk?tter]
Organization
© Alfred Schmidt
Prof. Dr. Alfred Schmidt
Zentrum für Technomathematik (ZeTeM)
Office: MZH 2430
Phone: +49 421 218-63851
E-Mail: schmidtprotect me ?!math.uni-bremenprotect me ?!.de