A Novel Way for Extrapolating the Solar Magnetic Field with PRO-GAN

Abstract The magnetic field in the solar corona cannot be observed routinely at present. Nonlinear force-free field (NLFFF) extrapolation serves as a crucial method for modeling the coronal magnetic configuration. We present a novel physics- reinforced generative adversarial network (PRO-GAN), an integrated deep learning framework designed to efficiently transform solar potential fields into corresponding NLFFFs while enforcing physical constraints to improve the result. This dual-phase framework synthesizes multifaceted integration, including the data-driven mapping relation acquisition, the constraint of physics equations, and supervision by a numerical solver. On the other hand, by incorporating a gradient penalty reinforced by a numerical method during the physics reinforcement training process, this approach resolves the inherent gradient conflicts in physics-informed neural networks from a novel perspective. The validity and efficiency of PRO-GAN have also been verified on the dataset and two analytic models.