2023/11/22 by Byoungchan Jang, Alan A. Kaptanoglu, Jang, Byoungchan +9 · 1 citation
Engineering · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Magnetic confinement fusion research #Model Reduction and Neural Networks #Nuclear reactor physics and engineering #Plasma Physics (physics.plasm-ph)
paper · pdf · doi:10.48550/arxiv.2311.13491
openalex publication_date 2023/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.