Physics-informed Neural Network for Force-free Magnetic Field Extrapolation

Abstract In this paper, we propose a physics-informed neural network extrapolation method that leverages machine learning techniques to reconstruct coronal magnetic fields. We enhance the classical neural network structure by introducing the concept of a quasi-output layer to address the challenge of preserving physical constraints during the neural network extrapolation process. Furthermore, we employ second-order optimization methods for training the neural network, which are more efficient compared to the first-order optimization methods commonly used in classical machine learning. Our approach is evaluated on the widely recognized semi-analytical model proposed by Low and Lou. The results demonstrate that the deep learning method achieves high accuracy in reconstructing the semi-analytical model across multiple evaluation metrics. In addition, we validate the effectiveness of our method on the observed magnetogram of active region.