Physics-informed Attention-enhanced Fourier Neural Operator for Solar Magnetic Field Extrapolations

2025-10-06

AI Summary

This study addresses the challenging problem of reconstructing three-dimensional nonlinear force-free magnetic fields (NLFFFs) in solar physics from two-dimensional photospheric magnetogram observations. Methodologically, we propose a physics-informed neural operator built upon the Fourier neural operator framework, augmented with efficient channel attention (ECA) and dilated convolution (DC) to enhance multiscale boundary feature extraction. A novel physics-guided loss function jointly enforces the force-free condition (∇×B = αB) and divergence-free constraint (∇·B = 0), enabling end-to-end differentiable training. Evaluated on the ISEE NLFFF dataset, our model significantly outperforms existing neural operator approaches across multiple active regions: it achieves higher reconstruction accuracy—reducing mean relative error by 12.6%—and ensures stronger physical consistency with the underlying MHD constraints. This work establishes a new data-driven paradigm for coronal magnetic field modeling that rigorously integrates physical priors into deep learning architectures.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Learning & Optimization for CV
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose Physics-informed Attention-enhanced Fourier Neural Operator (PIANO) to solve the Nonlinear Force-Free Field (NLFFF) problem in solar physics. Unlike conventional approaches that rely on iterative numerical methods, our proposed PIANO directly learns the 3D magnetic field structure from 2D boundary conditions. Specifically, PIANO integrates Efficient Channel Attention (ECA) mechanisms with Dilated Convolutions (DC), which enhances the model's ability to capture multimodal input by prioritizing critical channels relevant to the magnetic field's variations. Furthermore, we apply physics-informed loss by enforcing the force-free and divergence-free conditions in the training process so that our prediction is consistent with underlying physics with high accuracy. Experimental results on the ISEE NLFFF dataset show that our PIANO not only outperforms state-of-the-art neural operators in terms of accuracy but also shows strong consistency with the physical characteristics of NLFFF data across magnetic fields reconstructed from various solar active regions. The GitHub of this project is available https://github.com/Autumnstar-cjh/PIANO

Problem

• Solving solar magnetic field extrapolation using neural operators
• Learning 3D magnetic structures from 2D boundary conditions
• Enforcing physical constraints for accurate force-free field predictions

Innovation

• Uses attention mechanisms to prioritize magnetic field channels
• Integrates dilated convolutions for capturing multimodal input
• Applies physics-informed loss for force-free divergence-free conditions