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

TL;DR

This work tackles the computational bottleneck of coronal magnetic-field modeling by learning a solution operator for Bifrost-based MHD data. It introduces the global-local Fourier Neural Operator (GL-FNO), a dual-branch architecture that captures global structure and local details, with Tucker-decomposed kernels for efficiency. Through extensive AI/ML and physics-based evaluations, GL-FNO achieves superior predictive accuracy (e.g., MSE ≈ 0.033, R^2 ≈ 0.966) and strong physical fidelity, while delivering predictions in seconds rather than days. The method, data, and code enable faster, more scalable space-weather forecasting and exploration of solar magnetic-field dynamics; the approach also outperforms other neural operators and deep learning baselines across multiple metrics.

Abstract

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 \times 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

Figures (7)

• Figure 1: (a) The architecture of the global-local fourier neural operators; (b) local fourier layer; (c) tucker decomposition.
• Figure 2: Training and test error curves for different epochs of GL-FNO, ViT, CNN-RNN, and CNN-LSTM.
• Figure 3: The visualization of prediction from GL-FNO, ViT, CNN-RNN, and CNN-LSTM, compared with ground truth at different heights: (a) $B_x$; (b) $B_y$; (c) $B_z$.
• Figure 4: The visualization of error maps from GL-FNO, ViT, CNN-RNN, and CNN-LSTM at different heights: (a) $B_x$; (b) $B_y$; (c) $B_z$.
• Figure 5: 2D histogram of GL-FNO, ViT, CNN-RNN, and CNN-LSTM to the ground truth, at height = 2.0 Mm, 7.0 Mm, and 11.0 Mm. Color gradient denotes the number of data points.