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

arXiv: https://arxiv.org/abs/2511.20830 · HTML: https://mlsanity.com/paper/2511.20830/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 33 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Builds on (most cited first, 10 of 10)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Professor Forcing: A New Algorithm for Training Recurrent Networks](https://mlsanity.com/paper/1610.09038/) (2016)
- [Operator Learning: Algorithms and Analysis](https://mlsanity.com/paper/2402.15715/) (2024)
- [Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration](https://mlsanity.com/paper/2303.04778/) (2023)
- [A Library for Learning Neural Operators](https://mlsanity.com/paper/2412.10354/) (2024)
- [Global-local Fourier Neural Operator for Accelerating Coronal Magnetic Field Model](https://mlsanity.com/paper/2405.12754/) (2024)

## Built on by (most cited first, 1 of 1)

- [Neural Operator based Multi-Field Reconstruction of Inner Solar Boundary State](https://mlsanity.com/paper/2608.22782/) (2026)

## Abstract (arXiv)

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.