Autoregressive Surrogate Modeling of the Solar Wind with Spherical Fourier Neural Operator

TL;DR

This paper presents an autoregressive machine learning surrogate model using the Spherical Fourier Neural Operator to predict steady-state solar wind radial velocity, offering improved accuracy and efficiency over traditional models for space weather forecasting.

Contribution

It introduces the first autoregressive SFNO-based surrogate for solar wind modeling, enabling iterative prediction over radial distances and outperforming existing HUX models.

Findings

SFNO outperforms HUX in accuracy at distant regions

The autoregressive approach improves prediction fidelity

Model provides a flexible, data-driven alternative to MHD simulations

Abstract

The solar wind, a continuous outflow of charged particles from the Sun's corona, shapes the heliosphere and impacts space systems near Earth. Accurate prediction of features such as high-speed streams and coronal mass ejections is critical for space weather forecasting, but traditional three-dimensional magnetohydrodynamic (MHD) models are computationally expensive, limiting rapid exploration of boundary condition uncertainties. We introduce the first autoregressive machine learning surrogate for steady-state solar wind radial velocity using the Spherical Fourier Neural Operator (SFNO). By predicting a limited radial range and iteratively propagating the solution outward, the model improves accuracy in distant regions compared to a single-step approach. Compared with the numerical HUX surrogate, SFNO demonstrates superior or comparable performance while providing a flexible, trainable, and data-driven alternative, establishing a novel methodology for high-fidelity solar wind modeling. The source code and additional visual results are available at https://github.com/rezmansouri/solarwind-sfno-velocity-autoregressive.