STAGE (Internship) in learning non local structure preserving closure for Vlasov equation

The offer description be low is in French

Contract type : Internship agreement

Level of qualifications required : Graduate degree or equivalent

Fonction : Internship Research

Assignment

The Vlasov-BGK equation used to simulate the dynamics of weakly or strongly collisional plasma is a very expensive PDE to solve, as it is posed in 6 dimensions. In strongly collisional regimes, the Euler and Navier-Stokes approximations are very effective in reducing computation time. In intermediate regimes, work has shown that non-local closures in space are relevant. The first step was to build a closure based on CNN. The results were positive, but long-time instability appeared. To solve this problem, we propose to change the architecture, moving towards Greenet-type neural operators and imposing entropy growth in the learned closure. Once this has been achieved, we propose to build a scheme that preserves entropy growth.

Main activities

-read the papers on learning to close
-read papers on neural operators
-generate data with kinetic code
-test different architectures
-validate the chosen architecture on classisque test cases

Skills

-python

-numerical methods

-basics of ML

Benefits package

  • Restauration subventionnée
  • Transports publics remboursés partiellement
  • Congés: 7 semaines de congés annuels + 10 jours de RTT (base temps plein) + possibilité d'autorisations d'absence exceptionnelle (ex : enfants malades, déménagement)
  • Possibilité de télétravail (après 6 mois d'ancienneté) et aménagement du temps de travail
  • Équipements professionnels à disposition (visioconférence, prêts de matériels informatiques, etc.)
  • Prestations sociales, culturelles et sportives (Association de gestion des œuvres sociales d'Inria)
  • Accès à la formation professionnelle
  • Sécurité sociale

Remuneration

4.35 €/hour