Application of a Grid-constrained U-shaped Neural Operator in Real-time Solar Corona Magnetic Field Extrapolation

In this study, we propose a neural network framework, called the Grid-constrained U-shaped Neural Operator (GC-UNO), for real-time extrapolation of the coronal magnetic fields of active regions (ARs). The framework first employs a U-shaped neural operator (U-NO) trained on nonlinear force-free field data to learn the mapping between horizontal magnetic field slices, allowing it to generate the next slice from an input slice. It then acquires the full coronal magnetic field through an iterative approach and uses a grid-based finite difference scheme to enforce physical constraints to fine-tune the trained U-NO for enhanced physical consistency. The GC-UNO can perform coronal magnetic field modeling for any AR in around 20 s, and excels in quantitative, qualitative, and temporal generalization tests. Additionally, the framework enables accurate and efficient extrapolation with fewer training-data samples, which makes it suitable for the study of solar eruption events and space-weather monitoring.