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.
Abstract (translated)
磁流体动力学（MHD）在描述等离子体和导电液体的动力学中起着关键作用，这对于理解恒星和星系结构以及核聚变中的 plasma运动至关重要。解决这些超偏微分方程需要先进的数值方法，但由于复杂结构和高的计算成本，呈现了计算挑战。最近，引入了类似于傅立叶神经操作器（FNO）的神经元操作模型作为传统数值分析的替代模型。本研究探讨了修改的流量傅立叶神经操作器模型，用于近似理想MHD的数值流量，提供了一种在连续推理、扩展到非采样分布外推和与经典数值方案相比更快计算的新颖方法。
URL
https://arxiv.org/abs/2404.16015
