In this project, we introduce the characteristic mapping method to address the complexity of high- dimensional kinetic equations, such as those involving ion-electron interactions in plasma fusion, by integrating mathematical modeling with high-performance computing. This semi-Lagrangian method achieves exponential resolution in linear time, revealing fine-scale details of the solutions and providing insights into the filamentation structure of plasmas. By employing reduced-order models, we significantly lower the numerical complexity of the computations. Our approach, which combines dimensionality reduction of sub-maps with refinement through map compositions via the solution operator, is innovative and paves the way for efficient evaluation of high-dimensional distribution functions across extended time intervals and multi-scale spatial domains. This project is designed to test the potential to enhance existing semi-Lagrangian techniques and advance our understanding of intricate local thermodynamic non-equilibrium phenomena in plasmas, with applications in magnetically confined fusion.

Team:

LAGA, UMR 7030, Université Paris 13
Olivier Lafitte (PI and coordinator)

CEA - IRFM, Cadarache
Kevin Obrejan and Philipp Krah

I2M, UMR 7373, Aix-Marseille Université
Kai Schneider

McGill University, Montreal
Jean-Christophe Nave

Positions Available:

Master projects:

We are looking for talented and motivated master students in computational physics, applied mathematics or data-science. The proposed Master’s projects can be carried out either as a 6-month internship or as part of a Master’s thesis. These projects are funded, and we only accept Master’s students who are interested in pursuing a PhD afterwards. The projects can take place within one of three teams: CEA, LAGA–Paris, or I2M (Aix-Marseille University).

• Evolving flow maps using neural-semi Lagrangian method: Proposal
• Data-assimilation for plasma simulations: Proposal
• Learning neural flow maps for drift kinetic equations: [Proposal]

PhD positions:

Two PhD positions are available that can take place in one of our teams.

For interested candidates please contact: philipp.krah@cea.fr

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