Neural Operators Learn the Local Physics of Magnetohydrodynamics
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 18 of its 63 references that are in the map. First posted on arXiv 24 Apr 2024.
Builds on
18 of 63 references.
References · 18
- 2020Fourier Neural Operator for Parametric Partial Differential Equationscited by 2,806
- 2019DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operatorscited by 1,965
- 2022FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operatorscited by 748
- 2020Neural Operator: Graph Kernel Network for Partial Differential Equationscited by 722
- 2015An Introduction to Convolutional Neural Networkscited by 510
- 2021Neural Operator: Learning Maps Between Function Spacescited by 413
- 2021U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flowcited by 292
- 2021Multiwavelet-based Operator Learning for Differential Equationscited by 229
- 2020Learning to Control PDEs with Differentiable Physicscited by 131
- 2018Generalization Error in Deep Learningcited by 46
- 2023Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equationcited by 32
- 2023HyperDeepONet: learning operator with complex target function space using the limited resources via hypernetworkcited by 25
6 more
- 2022Bounding the Rademacher Complexity of Fourier neural operatorscited by 16
- 2019Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learningcited by 15
- 2019Constraint-Aware Neural Networks for Riemann Problemscited by 14
- 2024Approximating Numerical Fluxes Using Fourier Neural Operators for Hyperbolic Conservation Lawscited by 10
- 2021Scale-invariant Learning by Physics Inversioncited by 6
- 2023Magnetohydrodynamics with Physics Informed Neural Operatorscited by 6
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Citing papers per year: 2026: 2.
2 papers.