Hybrid neural PIC methods for Vlasov equations

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Type de contrat : Convention de stage

Niveau de diplôme exigé : Bac + 5 ou équivalent

Fonction : Stagiaire de la recherche

Mission confiée

he Vlasov 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. One of the standard methods for solving it is the PIC method, which uses a large number of particles deposited on a grid to calculate their interaction with the field. Neural methods have shown good ability to deal with high-dimensional problems at low cost, but are not very accurate and have difficulty in dealing with the fine structures generated by the Vlasov equation. We therefore propose to couple a new neural method with a PIC method in order to maintain accuracy at low impact.
The method will be tested on more or less simple transport problems before being tested on linear and nonlinear Vlasov.

Principales activités

Read the papers Neural methods (PINNs, Neural Galerkin)
- Read papers on PIC methods
- Valide the neural methods on some test cases
- Add the correction part based on PIC
- Validate the scheme on classical tests cases

Compétences

  • Python
  • ML
  • Numerical methods
  • if possible basics on kinetic equations

Avantages

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Rémunération

4.35 €/hour