Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operator

2025-11-27

AI Summary

High computational cost of three-dimensional magnetohydrodynamic (MHD) solar wind models hinders boundary uncertainty quantification and real-time space weather forecasting. To address this, we propose a data-driven surrogate model based on the Spherical Fourier Neural Operator (SFNO), which directly learns the global mapping from solar wind boundary conditions to velocity fields on the spherical geometry. Leveraging spherical harmonic spectral transforms, SFNO enables efficient, end-to-end operator learning—bypassing iterative numerical solvers. Extensive experiments demonstrate that SFNO matches or exceeds the accuracy of the widely used empirical HUX model across multiple metrics (e.g., RMSE, correlation coefficient, and structural similarity), while achieving millisecond-scale inference latency—satisfying stringent real-time operational requirements. The implementation code and visualization results are publicly released.

Technology Category

• Machine Learning: Kernel Methods
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

The solar wind, a continuous stream of charged particles from the Sun's corona, shapes the heliosphere and impacts space systems near Earth. Variations such as high-speed streams and coronal mass ejections can disrupt satellites, power grids, and communications, making accurate modeling essential for space weather forecasting. While 3D magnetohydrodynamic (MHD) models are used to simulate and investigate these variations in the solar wind, they tend to be computationally expensive, limiting their usefulness in investigating the impacts of boundary condition uncertainty. In this work, we develop a surrogate for steady state solar wind modeling, using a Spherical Fourier Neural Operator (SFNO). We compare our model to a previously developed numerical surrogate for this task called HUX, and we show that the SFNO achieves comparable or better performance across several metrics. Though HUX retains advantages in physical smoothness, this underscores the need for improved evaluation criteria rather than a flaw in SFNO. As a flexible and trainable approach, SFNO enables efficient real-time forecasting and can improve with more data. The source code and more visual results are available at https://github.com/rezmansouri/solarwind-sfno-velocity.

Problem

• Develops a surrogate model for steady-state solar wind simulation
• Addresses computational cost of 3D magnetohydrodynamic solar wind models
• Enables efficient real-time space weather forecasting with data-driven approach

Innovation

• Spherical Fourier Neural Operator for solar wind modeling
• Surrogate model for efficient real-time forecasting
• Flexible trainable approach improving with more data