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.

翻译：磁流体动力学（MHD）在描述等离子体与导电流体动力学中具有核心作用，对理解恒星与星系的结构演化等天体物理现象，以及通过理想MHD方程实现核聚变中等离子体运动的控制至关重要。求解这些双曲型偏微分方程需借助复杂的数值方法，因其复杂结构与高昂计算成本带来了计算挑战。最新进展引入傅里叶神经算子（FNO）等神经算子作为传统数值分析的替代模型。本研究探索了一种改进的通量傅里叶神经算子模型，用于逼近理想MHD的数值通量，该模型通过实现连续推断、对采样分布外数据的泛化能力及相较经典数值方案更快的计算速度，提供了一种优于现有神经算子模型的新方法。