Reconstruction of Two‐Dimensional Magnetohydrodynamic and Hall Magnetohydrodynamic Equilibria in Space Using Physics‐Informed Neural Networks

Abstract We present a novel data analysis technique based on physics‐informed neural networks (PINNs) to reconstruct two‐dimensional (2D) magnetohydrodynamic (MHD) and Hall MHD equilibria in a space plasma from in situ spacecraft measurements. Our method incorporates the steady‐state MHD or Hall MHD equations—a set of partial differential equations (PDEs) as physical constraints—into a deep learning framework. In contrast to traditional reconstruction techniques relying on explicit spatial integration of the PDEs from spacecraft trajectories, the PINN approach allows us to obtain a physically consistent equilibrium by minimizing a composite loss function that includes both prediction errors and PDE residuals. We validate the method through benchmark tests using exact solutions of axially symmetric MHD and Hall MHD equilibria, and further demonstrate its utility through application to an extensively investigated magnetotail reconnection event observed by the Magnetospheric Multiscale mission. The resulting reconstruction reproduces key structural features, including the X‐type current sheet geometry and quadrupolar Hall magnetic field, consistent with prior results and numerical simulations. We also present empirical estimates of the reconnection rate and spatially varying resistivity based on the reconstructed fields. Our results demonstrate that the PINN‐based method provides a flexible and powerful new tool for revealing plasma structures around observing spacecraft, particularly in regions where model assumptions may be only approximately valid.