The Chair for Numerical Methods in Plasma Physics at the TUM Department of Mathematics has an immediate vacancy for a PhD position “Reduced complexity models for Maxwell's equations”, (m/f/d, 3yrs, 75%).
The Chair for Numerical Methods in Plasma Physics at the Department of Mathematics, TUM is strongly linked with the division of the same name at the Max Planck Institute for Plasma Physics in Garching and is developing and analyzing numerical methods for plasma physics applications. In the framework of a DFG/ANR project in collaboration with Inria and the University of Strasbourg in France, we are looking for a PhD candidate to join our group, starting as soon as possible.
The PhD Project:
Many models used in scientific computing require significant amounts of computational resources and thus have only restricted applicability. Reduced complexity models can remedy this problem as they often represent a good compromise between numerical cost and physical completeness. Recently, data-driven approaches for the construction of such models have gained large popularity. Here, optimized approximation spaces are constructed by identifying dominant modes from a set of training simulations using e.g. modal decomposition methods.
In this project we want to develop surrogate models for Maxwell's equations and their extension to a cold plasma model using recent advances in machine learning techniques.
In the mathematical description of Maxwell's equations, a crucial algebraic structure appears: the deRham complex. This is a sequence of function spaces which represent differential forms and are connected by the exterior derivative. Preserving this structure in the numerical treatment of Maxwell's equations is of utmost importance as it facilitates the handling of the non-trivial null-spaces required in electrodynamics and thus guarantees essential relations like the divergence constraints of the electrostatic and magnetic field which will otherwise not be maintained at the discrete level. Thus the main objective of this project is to construct and adapt neural network architectures that encode this structure, in order to build robust and reliable surrogate models for Maxwell’s equations and the cold plasma model.
- Master degree in mathematics, physics, computer science or equivalent
- Knowledge of numerical methods for PDEs and machine learning tools
- Good programming skills in Python, Julia or similar
- Interdisciplinary cooperation and communication skills
- Very good writing and presentation skills in English (German language skills are not necessary)
We offer a challenging position as academic staff within an international, interdisciplinary team located at the Garching Campus of the TU München with the opportunity to pursue a doctoral degree whilst working in an innovative research project. The 75% position will be limited to three years. The position is paid according to the Civil Service rates of the German States “TV-L”.
As an equal opportunity and affirmative action employer, TUM explicitly encourages applications from women as well as from all others who would bring additional diversity dimensions to the university's research and teaching strategies. Preference will be given to candidates with disabilities who have essentially the same qualifications.
Please send your letter of application, your curriculum vitae, copies of key documents, such as transcripts and degree certificates, further documents and references with the subject line “PhD Plasma Physics” as a single PDF document to: Angelika Haß (firstname.lastname@example.org).
Do not hesitate to contact Dr. Michael Kraus (email@example.com) at the Max Planck Institute for Plasma Physics for any questions on the scientific work and environment.
The review of applications will begin on December 1st, 2021 and continue until the position is filled.