Grad-Shafranov equilibria via data-free physics informed neural networks

• URL: http://arxiv.org/abs/2311.13491v1
• Date: Wed, 22 Nov 2023 16:08:38 GMT
• Title: Grad-Shafranov equilibria via data-free physics informed neural networks
• Authors: Byoungchan Jang, Alan A. Kaptanoglu, Rahul Gaur, Shaw Pan, Matt Landreman, William Dorland
• Abstract summary: We show that PINNs can accurately and effectively solve the Grad-Shafranov equation with several different boundary conditions. We introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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