The Institute of Mathematical Sciences (ICMAT), Madrid, Spain seeks highly motivated candidates to fill a 2-year Postdoctoral position for the AEI-DFG project Discretization and optimal control of Lagrangian and Hamiltonian field theories
Description
Classical Lagrangian and Hamiltonian field theories are at the core of continuum mechanics, electromagnetism and general relativity. These theories have a rich geometric structure of which multisymplecticity may prove highly valuable when performing numerical simulations.
The structure of optimal control problems is analogous to that of Lagrangian and Hamiltonian mechanics and field theories. Therefore, the numerical treatment of these, particularly when applied to mechanical and field theoretical systems, may benefit from the use of structure-preserving numerical methods.
In this project we will study and develop high-order multisymplectic numerical integrators for continuum systems with and without constraints. These discretisations will be then applied in optimal control problems. We will also attempt to imbue structure-preserving properties to non-preserving methods using neural networks.
The project will be carried out in collaboration with our partner team at Institute of Applied Dynamics (LTD) in the Department of Mechanical Engineering of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU).
Qualifications
- Highly motivated candidates with PhD. in mathematics, physics, engineering, computer science, or
related fields. - Knowledge of analytical mechanics, differential geometry, numerical methods and programming.
- Good written and oral communication skills in English.
Deadline: 15th January 2025
The position has no teaching duties and includes a yearly stipend of approx. 40k euro (before taxes) + social security.
The start date is to be negotiated.
We offer an interdisciplinary research environment and travel opportunities to collaborate with our partner team in Germany.
Please send your application (including CV, degree certificates, short summary of research interests, references and publications list when applicable), via e-mail in a single pdf file to:
Dr. David Martín de Diego (david.martin@icmat.es)
