# Global-local Fourier Neural Operator for Accelerating Coronal Magnetic Field Model

arXiv: https://arxiv.org/abs/2405.12754 · HTML: https://mlsanity.com/paper/2405.12754/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 55 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Can Spatiotemporal 3D CNNs Retrace the History of 2D CNNs and ImageNet?](https://mlsanity.com/paper/1711.09577/) (2017)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [CNN-RNN: A Unified Framework for Multi-label Image Classification](https://mlsanity.com/paper/1604.04573/) (2016)
- [A unified deep artificial neural network approach to partial differential equations in complex geometries](https://mlsanity.com/paper/1711.06464/) (2017)
- [Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs](https://mlsanity.com/paper/2310.00120/) (2023)
- [Smooth Robust Tensor Completion for Background/Foreground Separation with Missing Pixels: Novel Algorithm with Convergence Guarantee](https://mlsanity.com/paper/2203.16328/) (2022)

## Built on by (most cited first, 4 of 4)

- [F-Adapter: Frequency-Adaptive Parameter-Efficient Fine-Tuning in Scientific Machine Learning](https://mlsanity.com/paper/2509.23173/) (2025)
- [Physics-informed Attention-enhanced Fourier Neural Operator for Solar Magnetic Field Extrapolations](https://mlsanity.com/paper/2510.05351/) (2025)
- [Autoregressive Surrogate Modeling of the Solar Wind with Spherical Fourier Neural Operator](https://mlsanity.com/paper/2511.20830/) (2025)
- [Neural Operator based Multi-Field Reconstruction of Inner Solar Boundary State](https://mlsanity.com/paper/2608.22782/) (2026)

## Abstract (arXiv)

Exploring the outer atmosphere of the sun has remained a significant bottleneck in astrophysics, given the intricate magnetic formations that significantly influence diverse solar events. Magnetohydrodynamics (MHD) simulations allow us to model the complex interactions between the sun's plasma, magnetic fields, and the surrounding environment. However, MHD simulation is extremely time-consuming, taking days or weeks for simulation. The goal of this study is to accelerate coronal magnetic field simulation using deep learning, specifically, the Fourier Neural Operator (FNO). FNO has been proven to be an ideal tool for scientific computing and discovery in the literature. In this paper, we proposed a global-local Fourier Neural Operator (GL-FNO) that contains two branches of FNOs: the global FNO branch takes downsampled input to reconstruct global features while the local FNO branch takes original resolution input to capture fine details. The performance of the GLFNO is compared with state-of-the-art deep learning methods, including FNO, U-NO, U-FNO, Vision Transformer, CNN-RNN, and CNN-LSTM, to demonstrate its accuracy, computational efficiency, and scalability. Furthermore, physics analysis from domain experts is also performed to demonstrate the reliability of GL-FNO. The results demonstrate that GL-FNO not only accelerates the MHD simulation (a few seconds for prediction, more than × 20,000 speed up) but also provides reliable prediction capabilities, thus greatly contributing to the understanding of space weather dynamics. Our code implementation is available at https://github.com/Yutao-0718/GL-FNO