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Subject:

The context of this work is the modelling of plasma physics for nuclear fusion. Plasma are described either by kinetic models, valid in all physical regimes but very expensive to solve, or by fluid models, which are easier to solve but only valid around thermodynamic equilibria. Several works have been performed to extend the domain of validity of these fluid models by constructing so-called closures that appropriately modify the heat flux and the pressure tensor to capture non-equilibrium dynamics. For instance, based on analytical developments, the Harmett-Perkins closure has been proposed to incorporate Landau damping effect [1]. More recently, the possibility of constructing these closures using deep learning methods and data from kinetic numerical simulations has been studied. We have for instance proposed in [2] a convolutional network closure for the Euler-Poisson model. The objective of this postdoc is to extend this work to more complicated models. First we want to consider more complex collisional operators like Fokker-Planck-Laudau [4]. We propose to compare the closure approach with an approach where we construct a reduced model for Vlasov compressing the micro-part using deep-learning methods like auto-encoder. One key point will be to assure at the theoretical level the stability of the reduced model obtained. In a second time we will propose to extend this work for the equation with magnetic field.

[1] A neural network closure for the Euler-Poisson system based on kinetic simulations , L. Bois, E. Franck, L. Navoret, V. Vigon. Accepted in "Kinetic and related models".

[2] G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64, 3019 (1990).

[3] Uniform accurate machine learning-based hydrodynamics models for kinetic equations, J. Han, C. Ma, Z. Ma, E. Weinan. PNAS October 29, 2019 116 (44) 21983-21991

[4] Micro-macro decomposition based asymptotic-preserving numerical schemes and numerical moments conservation for collisional nonlinear kinetic equations, Irene M. Gamba, Shi Jin, and Liu Liu.

Details:

Supervisors: Emmanuel Franck (INRIA), Laurent Navoret (IRMA strasbourg), Vincent Vigon (IRMA strasbourg), Clémentine Courtès (IRMA strasbourg).
Practical condition: it is a two years position funding by ANR project MILK and hosted at the mathematics laboratory of Strasbourg University (IRMA), France. The project also includes exchanges and visits with the German partner: the Max Planck Institute of Plasma Physics in Munich, Germany.
Date for beginning: The start of the position would preferably be between 05/2022 and 10/2022.

Competence:

  • PhD in applied mathematics, scientific computing or PDE.
  • We look for a specialist of numerical methods and PDE, if possible applied to kinetic or hypebolic PDE's.
  • We also require a solid knowledge of Python and somes basic skills in scientific computing language like C/C++, Fortran or Julia.
  • A background in machine learning would be appreciated but is not considered necessary.