# Neural Operator based Multi-Field Reconstruction of Inner Solar Boundary State

arXiv: https://arxiv.org/abs/2608.22782 · HTML: https://mlsanity.com/paper/2608.22782/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Builds on (most cited first, 18 of 18)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs](https://mlsanity.com/paper/2310.00120/) (2023)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Physics guided machine learning using simplified theories](https://mlsanity.com/paper/2012.13343/) (2020)
- [Physics guided neural networks for modelling of non-linear dynamics](https://mlsanity.com/paper/2205.06858/) (2022)
- [Data-driven approaches for predicting spread of infectious diseases through DINNs: Disease Informed Neural Networks](https://mlsanity.com/paper/2110.05445/) (2021)
- [Hard Encoding of Physics for Learning Spatiotemporal Dynamics](https://mlsanity.com/paper/2105.00557/) (2021)
- [Surya: Foundation Model for Heliophysics](https://mlsanity.com/paper/2508.14112/) (2025)
- [Global-local Fourier Neural Operator for Accelerating Coronal Magnetic Field Model](https://mlsanity.com/paper/2405.12754/) (2024)
- [Solar image denoising with convolutional neural networks](https://mlsanity.com/paper/1908.02815/) (2019)
- [Solar Image Deconvolution by Generative Adversarial Network](https://mlsanity.com/paper/2001.03850/) (2020)
- [Toward Data-Driven Surrogates of the Solar Wind with Spherical Fourier Neural Operator](https://mlsanity.com/paper/2511.22112/) (2025)
- [Autoregressive Surrogate Modeling of the Solar Wind with Spherical Fourier Neural Operator](https://mlsanity.com/paper/2511.20830/) (2025)

## Abstract (arXiv)

The Solar wind is a continuous flow of charged particles emanating from the solar surface and governed by complex, interacting magnetohydrodynamic processes. Accurate specification of inner-boundary conditions is essential for heliospheric modeling and solar-wind prediction. In many practical applications, only a subset of interacting multi-field variables is directly available, but for a comprehensive view of solar wind prediction and downstream magnetohydrodynamic simulations, a more complete boundary state is required. In this work, we study the problem of learning the multi-field multi-scale solar magnetohydrodynamic state at 30 solar radii (R_odot) using operator learning. Specifically, given the radial velocity and radial magnetic field, we aim to reconstruct the non-radial velocity and magnetic field components, radial and non-radial current density, thermodynamic density, and pressure components. This mapping is highly nonlinear, spatially coupled, and multi-scale, making it a challenging task for data-driven scientific machine learning. To address this problem, we employ a Local Neural Operator (LocalNO) that learns mappings between input and output function spaces while retaining locality and resolution-awareness. Unlike conventional regression models and autoencoder models, neural operators are better suited for learning structured field-to-field transformations arising from physical systems. The resulting predictions along with inputs are intended to serve as boundary condition variables for future inner-heliospheric modeling pipelines.