A Physics-Informed Neural Network for Solving the Quasi-static Magnetohydrodynamic Equations

TL;DR

This paper introduces a physics-informed neural network (PINN) that learns to solve quasi-static magnetohydrodynamic equations in tokamak geometry without data, demonstrating its ability to predict plasma behavior with good accuracy.

Contribution

The paper presents the first application of PINNs to quasi-static MHD equations in tokamak geometry, showing their potential for plasma physics modeling.

Findings

PINN successfully learned the MHD solution in tokamak geometry.

The model predicted plasma displacement consistent with ground truth simulations.

Demonstrated potential of physics-constrained deep learning for complex plasma behavior.

Abstract

A physics-informed neural network (PINN) is developed, for the first time, to learn the time-dependent quasi-static magnetohydrodynamic (MHD) equations in axisymmetric tokamak geometry, without any experimental or synthetic data. The initial study considered an ITER-like tokamak and found that a PINN, after careful treatment, was capable of learning the solution to the MHD system and predict a vertically displacing plasma, where general agreement with ground truth simulation was observed. The proof-of-principle demonstration highlights the potential of physics-constrained deep learning to learn complex plasma behavior.