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Séminaire Doctorants

organisé par l'équipe DOCT

  • Nicolas Pailliez

    Neural Methods with Natural Gradient Acceleration for Plasma Simulations

    13 mai 2026 - 16:30Salle de conférences IRMA

    In nuclear fusion, simulations are essential for understanding and controlling tokamak instabilities, phenomena that can severely damage reactors. Neural approaches for solving partial differential equations (PDEs) are gaining interest due to their mesh-free nature, flexibility, and scalability. These methods rely on neural networks as approximation spaces instead of classical polynomial bases, and this work investigates the efficiency of several neural techniques applied to plasma simulations. We first study stationary elliptic equations, with particular attention to the Grad–Shafranov equation, solved using Physics-Informed Neural Networks (PINNs). We then address time-dependent problems such as anisotropic diffusion, relying on adapted neural schemes, including Discrete PINNs and Neural Galerkin methods. In both cases, the Natural Gradient method is employed to significantly accelerate and stabilize the optimization process during training.