Machine-Learning-Based Numerical Solution for Low and Lou’s Nonlinear Force-Free Field Equilibria

Low and Lou (Astrophys. J. 352, 343, 1990) presented a family of nonlinear force-free magnetic fields that have established themselves as the gold standard for extrapolating force-free magnetic fields in solar physics. Building upon this important work, our study introduces a novel grid-free machine-learning-based method to effectively solve the equilibria proposed by Low and Lou. Through extensive numerical experiments, our results unequivocally demonstrate the efficient capability of the machine-learning algorithm in deriving numerical solutions for Low and Lou’s equilibria. Furthermore, we explore the opportunities and challenges of applying artificial-intelligence technology to real observed solar active regions.