A mutually embedded perception model for solar corona

This paper proposes a new mutually embedded perception model (MEPM) based on the 3D magnetohydrodynamic (MHD) equations of the solar wind plasma to reconstruct the structure of the solar corona. The goal is to embed the physics-based information and gradient into solar wind parameters data through the neural network and leverage the adaptive procedures to improve solution accuracy. The loss term proportional to the divergence is directly introduced to force a divergence-free solution. The established MEPM displays almost the same results as the exact solution for an artificial 3D analytic problem and the Parker solar wind for 1D steady Parker flow with the corresponding boundary conditions. The MEPM can well capture the solar coronal leading structures, recover the results of the traditional numerical schemes, and be consistent with the observations with CR 2068 as an example. When supplementary data (from the results of the MHD simulation or empirical models) are used, the modeled results improve. This implies that in situ satellite observations as supplementary data can be incorporated into the model in the same way.