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

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.

-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

-python

-numerical methods

-basics of ML

• 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

4.35 €/hour