Grad-Shafranov equilibria via data-free physics informed neural networks
This provides a method for faster equilibrium calculations in plasma physics, useful for uncertainty quantification and optimization, but it is incremental as it applies an existing PINN framework to a specific domain.
The paper tackles solving the Grad-Shafranov equation for magnetohydrodynamic equilibria using Physics-Informed Neural Networks (PINNs), showing that PINNs can accurately solve it with various boundary conditions and exploring trade-offs like reconstruction error versus computational speed.
A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics. In this paper, we explore a method for solving the Grad-Shafranov equation by using Physics-Informed Neural Networks (PINNs). For PINNs, we optimize neural networks by directly minimizing the residual of the PDE as a loss function. We show that PINNs can accurately and effectively solve the Grad-Shafranov equation with several different boundary conditions. We also explore the parameter space by varying the size of the model, the learning rate, and boundary conditions to map various trade-offs such as between reconstruction error and computational speed. Additionally, we introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity in order to handle a broader range of plasma scenarios within a single network. Parametrized PINNs could be used in future work to solve inverse problems such as shape optimization.