Research Associate in "Optimal Transport in Control and Machine Learning" (m/w/d)
Research Framework
Optimal transport (OT) is a mathematical framework for finding the most efficient way to move a mass distribution from one location to another. It is based on the idea of minimizing the cost of transporting the mass, where the cost can be measured in terms of distance, time, or some other metric. OT has a long history, dating back to the 18th century when it was first introduced by the mathematician Gaspard Monge. However, it has only become widely studied in recent years due to the advances in computational optimization and the growing interest in OT from other fields such as machine learning, biology, and economics. Unbalanced OT (UOT) is a generalization of OT that allows for the possibility that the total mass of the two distributions may not be the same. This can be useful in situations where we want to transport mass from one distribution to another, but we may not be able to transport all of the mass from one distribution to the other. UOT is typically formulated as a constrained optimization problem. The goal is to minimize the cost of transporting mass from one distribution to the other, subject to the constraint that the total mass of the two distributions is preserved.
Task Description
The research compiles from the following list of tasks.
- Developing novel optimization schemes for solving OT and UOT problems keeping in mind the aspects of computational efficiency and scalability.
- Compare the above developed schemes with the state of the art methods
- Developing machine learning methods for solving OT and UOT problems.
- Develop connections to PDEs and to consider relevant classes of PDEs for which OT formulation can be obtained. It is specifically important to consider the case of (fully) nonlinear PDE.
- Collaborating closely with academic researchers who are specialized in one or more areas such as control, machine learning and PDEs.
- Applying OT formulation to design feedback controllers, robust controllers, optimal control laws.
- Apply the above developed schemes to specific problems in the domains of Biology, Processes engineering and Autonomous driving.
Qualification
- Above average university degree in mathematics and optimization
- Knowledge of at least one programming language: Matlab, Python, C++ is expected
- Knowledge in dynamical systems and PDEs
- Proficiency in English or / and German is essential
- Highly motivated, eager to work within a team or independently.
Application procedure and deadline:
- Applications must include the following elements (as a single PDF file):
- Cover letter with a brief description of why you want to pursue research studies, about what your academic interests are, and how they relate to your previous studies and future goals
- CV including your relevant professional experience and knowledge
- Copies of diplomas and grades from previous university studies
- Two references
- List of publications
Send an email with the required documents to the address: @mec-apps@mv.uni-kl.de. The application deadline is 28. February 2025.
Interested candidates are encouraged to apply promptly, as applications will be processed as received, and the position may be filled before the deadline.
For more information, visit our webpage: https://mv.rptu.de/fgs/mec/research
