Neural Operators Learn the Local Physics of Magnetohydrodynamics

TL;DR

This paper introduces a modified Fourier neural operator model that efficiently approximates ideal MHD equations, enabling continuous, fast, and generalizable inference for complex plasma and fluid dynamics.

Contribution

It presents a novel neural operator architecture tailored for MHD, improving accuracy, speed, and generalization over existing models for simulating plasma and conductive fluids.

Findings

Outperforms existing neural operators in accuracy and speed.

Enables continuous inference and better generalization.

Reduces computational costs compared to classical numerical methods.

Abstract

Magnetohydrodynamics (MHD) plays a pivotal role in describing the dynamics of plasma and conductive fluids, essential for understanding phenomena such as the structure and evolution of stars and galaxies, and in nuclear fusion for plasma motion through ideal MHD equations. Solving these hyperbolic PDEs requires sophisticated numerical methods, presenting computational challenges due to complex structures and high costs. Recent advances introduce neural operators like the Fourier Neural Operator (FNO) as surrogate models for traditional numerical analyses. This study explores a modified Flux Fourier neural operator model to approximate the numerical flux of ideal MHD, offering a novel approach that outperforms existing neural operator models by enabling continuous inference, generalization outside sampled distributions, and faster computation compared to classical numerical schemes.