Neural operators learn the local physics of magnetohydrodynamics

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 analysis. This study proposes a modified Flux Neural Operator (Flux NO) model to approximate the numerical flux of ideal MHD, offering a novel approach with enhanced generalization capabilities and significant computational efficiency. Our methodology adapts the Flux NO to process each physical quantity individually and incorporates loss functions ensuring total variation diminishing (TVD) property and divergence freeness for numerical stability. The proposed method achieves superior generalization beyond sampled distributions compared to existing neural operators and demonstrates computation speeds 25 times faster than the reference numerical scheme.