Hybrid Physics–Machine Learning Modeling of Plasmaspheric Cold Electron Density

Machine learning (ML) has shown growing promise for space weather applications. However, its performance is often limited by the scarcity of rare-event observations and a lack of physical consistency. In this study, we investigate plasmaspheric cold electron density modeling using approaches that span the spectrum from purely physics-based [1] to purely data-driven [4], with a focus on three hybrid physics–machine learning strategies. These strategies incorporate physical information through discrepancy correction, physics-informed input augmentation, and physics-based regularization. Each hybrid model combines density outputs from the VERB-CS [1] simulation with a neural network to estimate plasmaspheric cold electron density. The neural networks are trained using in situ electron density measurements from the Van Allen Probes [2] together with geomagnetic indices. Hybrid models embed key physical processes (such as particle transport, refilling, and loss mechanisms) into the learning framework.

We assess the predictive capability of the hybrid models relative to pure ML and pure physics-based approaches through comparisons with in situ Van Allen Probes observations and global plasmaspheric images from the IMAGE Extreme Ultraviolet instrument [3]. Our results indicate that the hybrid models reproduce both large-scale plasmaspheric structure and smaller-scale features more accurately than either purely data-driven or purely physics-based models across a range of geomagnetic activity levels. Incorporating physical information into the ML framework improves generalizability across different geophysical conditions, including periods of enhanced geomagnetic activity. These results demonstrate the potential of physics-informed machine learning approaches to advance predictive modeling of the near-Earth plasma environment.

References
[1] Aseev, N., Shprits, Y., 2019. Reanalysis of ring current electron phase space densities using Van Allen Probe observations, convection model, and log-normal Kalman filter. Space weather 17, 619–638.
[2] Kletzing, C., Kurth, W., Acuna, M., MacDowall, R., Torbert, R., Averkamp, T., Bodet, D., Bounds, S., Chutter, M., Connerney, J., et al., 2013. The electric and magnetic field instrument suite and integrated science (EMFISIS) on RBSP. Space Science Reviews 179, 127–181.
[3] Sandel, B., Goldstein, J., Gallagher, D., Spasojevic, M., 2003. Extreme ultraviolet imager observations of the structure and dynamics of the plasmasphere. Magnetospheric imaging—The image prime mission , 25–46.
[4] Zhelavskaya, I.S., Shprits, Y.Y., Spasojević, M., 2017. Empirical modeling of the plasmasphere dynamics using neural networks. Journal of Geophysical Research: Space Physics 122, 11–227.