Neural Methods with Natural Gradient Acceleration for Plasma Simulations
Please login to view abstract download link
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. Numerical experiments demonstrate the benefits of Natural Gradient acceleration and compare the performance of the different neural methods on relevant plasma benchmark configurations. The results highlight the potential of neural solvers for high-dimensional or stiff PDEs, especially in scenarios where classical methods face mesh constraints or strong anisotropies.
