Extending PINE for High-Kp Plasmaspheric Density Modeling Using Physics-Informed Neural Networks

Reliable modeling of plasmaspheric density during geomagnetically disturbed periods is limited by sparse in-situ observations at high geomagnetic activity. In this study, we extend the PINE (Plasma density in the Inner magnetosphere Neural network-based Empirical) model using a Physics-Informed Neural Network (PINN) framework to improve performance during extreme conditions (Kp > 6). Density predictions from the physics-based VERB-CS model are incorporated to augment training data for high-Kp events, addressing a key limitation of previous empirical approaches. We develop and evaluate two PINN-based models: one trained exclusively on high-Kp data and another trained on a combined data set including electron density measurements from the Van Allen Probes and Arase missions together with VERB-CS density outputs. The performance of these models is directly compared across geomagnetic activity levels, enabling a systematic assessment of the impact of physics-based data integration on plasmaspheric density predictions in terms of accuracy and error variance. Model outputs are also compared with independent IMAGE EUV observations to evaluate each model’s ability to reconstruct global plasmaspheric structures under disturbed conditions.