Our research group is looking to supervise master student projects! Below are two ideas for possible research directions that are suitable as master thesis projects. If you are interested, do not hesitate to contact us. Do not be put off if you do not understand the details of the project descriptions below. Your willingness to learn new concepts and your passion are the most important factors.

Project 1: Optimisation algorithms

Many computational tasks, such as training neural networks (machine learning), require finding optimal solutions to high dimensional problems. The need for highly efficient and robust optimisation algorithms is ubiquitous in modern applied mathematics. It is, therefore, of interest to take a closer look at optimisation algorithms, acceleration techniques and tricks to make algorithms more robust. For this, it is necessary to understand why some of the existing optimisation algorithms work better than others. The use of classical mathematical notions for the analysis of state-of-the-art optimisation algorithms is just heading off!

We are looking for an interested student who is keen to implement and compare different optimisation algorithms in their master thesis and to discover whether and how underlying mathematical structure helps to improve existing algorithms. The student should have some programming skills (any language such as MATLAB, Python, C++, ...) and be interested in learning about optimisation algorithms and mathematical structures such as Hamiltonian systems and symplecticity.

Project 2: Backward error analysis

Ordinary differential equations are ubiquitous in mathematical models that describe, for instance, the motions of planets, molecules, or stock prices. As the equations are typically complicated, exact solutions are not immediately available but need to be approximated using numerical methods. Efficient and reliable numerical methods are, thus, of high importance. They provide approximate solutions at certain time-steps. There are two conflicting ideas to obtain good numerical methods:

1. The method adapts the time-steps during the computation. The step-size is chosen based on local error estimates or on the position of the motion in phase space. This can lead to highly accurate and efficient methods.
2. The method is designed to preserve mathematical structure of the original equation. This means that if exact solutions preserve certain integrals of motion, exhibit certain symmetries, lie on periodic orbits, so do the numerically computed solutions. This gives rise to robust numerical methods which show excellent long-term behaviour and produce solutions which share important properties of exact solutions and look qualitatively correct.

These two approaches are hard to combine: unfortunately, structure preserving numerical integrators lose their favourable properties when combined with adaptive time-stepping strategies.

Mathematical tools, such as backward error analysis, can not only be used to understand why some numerical methods work better than others, they can also be used to improve existing methods. We are looking for a student who is interested in trying out recently developed mathematical tools to improve step-size adaptive numerical methods while preserving underlying mathemtical structure. The student should have some programming skills (any language such as MATLAB, Python, C++, ...) and be interested in learning about backward error analysis and state-of-the-art numerical methods.

Seminare

L.105.65166 Oberseminar AG Ober-Blöbaum (Prof. Dr. Sina Ober-Blöbaum)

Vorlesungen

L.105.57522 Geometrische numerische Integration (Prof. Dr. Sina Ober-Blöbaum)

L.105.94300 Mathematik 3 für Maschinenbauer (Prof. Dr. Sina Ober-Blöbaum)
 

Seminare

L.105.65166 Oberseminar AG Ober-Blöbaum (Prof. Dr. Sina Ober-Blöbaum)

L.105.57811 Seminar (Prof. Dr. Sina Ober-Blöbaum) (Boris Wembe Moafo)

Übungen

L.105.94301 Mathematik 3 für Maschinenbauer (Dr. Sofya Maslovskaya)

L.105.57523 Geometrische numerische Integration (Dr. Khaled Hariz Belgacem)

Vorlesungen

L.105.50000 Mathematisches Praktikum (Prof. Dr. Sina Ober-Blöbaum)

L.105.57526 Numerische Methoden in der Optimalen Steuerung (Prof. Dr. Sina Ober-Blöbaum)

L.105.94200 Mathematik 2 für Maschinenbauer (Prof. Dr. Sina Ober-Blöbaum)

Seminare

L.105.65166  Oberseminar (Prof. Dr. Sina Ober-Blöbaum)

L.105.57809  “Port-Hamiltonian systems” (Sofya Maslovskaya)

L.105.33903   "How to compute with Julia" (Khaled Hariz Belgacem)

Übungen

L.105.94201 Mathematik 2 für Maschinenbauer  (Christian Offen)

Tutorien

L.105.57527 Numerical Methods in Optimal Control (Boris Wembe Moafo)

Betreute Abschlussarbeiten

 Master-Arbeit: Maschinelles Lernen numerischer Verfahren für modellprädiktive Steuerungen 

Vorlesungen 

L.105.94100 Mathematik 1 für Maschinenbauer (Prof. Dr. Sina Ober-Blöbaum)

L.105.57524 Optimale Steuerung  (Prof. Dr. Sina Ober-Blöbaum)

Seminare

L.105.65166 Oberseminar AG (Prof. Dr. Sina Ober-Blöbaum)

L.105.33901 Seminar (Prof. Dr. Sina Ober-Blöbaum)

L.105.57807 Seminar Turnpike properties in optimal control (Boris Wembe Moafo)

Übungen

L.105.57525 Optimale Steuerung (Sofya Maslovskaya)

L.105.94101 Mathematik 1 für Maschinenbauer (Christian Offen)

Betreute Abschlussarbeiten

Bachelor-Arbeit: Beschreibung und Anwendung von Lie-Gruppen-Integratoren auf das Mehrfachpendel

Vorlesungen

Lineare Optimierung (Prof. Dr. Sina Ober-Blöbaum)

Geometrische numerische Integration (Prof. Dr. Sina Ober-Blöbaum)

Mathematik 4 für Maschinenbau: Numerische Methoden (Christian Offen)

Übungen

Lineare Optimierung (Sofya Maslovskaya)

Andere

Mathematisches Praktikum (Prof. Dr. Sina Ober-Blöbaum)

Tutorien

Mathematik 1 für Maschinenbau  (Emina Hadzialic)

Mathematik 1 für Maschinenbau (Christian Offen)

Übungen

Numerik 2 (Sofya Maslovskaya)

Seminare

Seminar aus dem Bereich Numerik (Prof. Dr. Sina Ober-Blöbaum)

Vorlesungen

Mathematical Control Theory (Sofya Maslovskaya)

Mathematik 4 für Maschinenbau: Numerische Methoden (Christian Offen)

Andere

Mathematisches Praktikum (Emina Hadzialic und Sofya Maslovskaya)

Vorlesungen

Mathematik Vorkurs P2 (Prof. Dr. Sina Ober-Blöbaum)

Online-Veranstaltung über MOODLE

Geometrische Numerische Integration (Christian Offen)

Online-Veranstaltung, Mittwoch 16:00-19:00 Uhr

Seminare

Seminar in der Angewandten Mathematik: Geometrische Mechanik und Integration

Online-Blockkurs 26.10-13.11.2020

Vorbesprechung: 7.10.2020, 12:00 Uhr