Physics-informed neural network for three-dimensional ionospheric electron density modeling

Purely data-driven machine learning models have been widely applied in ionospheric modeling. However, these models rely heavily on the availability of training data and generally exhibit performance degradation in extrapolation tasks. In this study, we propose a physics-informed neural network (PINN) framework that incorporates the electron continuity equation in the training process for three-dimensional electron density modeling. The continuity equation is introduced as a physics-informed loss to constrain the gradients of predicted electron density during training. The effectiveness of the physics-informed loss is evaluated using both self-consistent SAMI3 simulations and real COSMIC-2 electron density observations. In both experiments, incorporating the physics-informed loss improves both the physical consistency and predictive performance. In particular, the systematic prediction bias is reduced by 35.6% and 45.2% for the SAMI3 and COSMIC-2 experiments, respectively. The standard deviations of prediction errors show only modest reductions of 4.4% and 2.2%. The improvements in prediction accuracy are more evident during extrapolation periods and under active solar conditions.