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ISSN  2096-3955

CN  10-1502/P

Citation: QingHua Zhou, YunXiang Chen, FuLiang Xiao, Sai Zhang, Si Liu, Chang Yang, YiHua He, ZhongLei Gao, 2022: A machine learning-based electron density (MLED) model in the inner magnetosphere, Earth and Planetary Physics.

doi: 10.26464/epp2022036

A machine learning-based electron density (MLED) model in the inner magnetosphere

1 School of Physics and Electronic Sciences, Changsha University of Science and Technology, Changsha, China;

2 Hunan Provincial Key Laboratory of Flexible Electronic Materials Genome Engineering, Changsha University of Science and Technology, Changsha, China

Fund Project: This work is supported by the National Natural Science Foundation of China grants 42074198, 41774194, 41974212 and 42004141, Natural Science Foundation of Hunan Province 2021JJ20010, Science and Technology Innovation Program of Hunan Province 2021RC3098, and Foundation of Education Bureau of Hunan Province for Distinguished Young Scientists 20B004. All the Van Allen Probes data are publicly available at The OMNI data are obtained online (

The plasma density is an important factor in determining wave-particle interaction in the magnetosphere. We develop a machine learning-based electron density (MLED) model in the inner magnetosphere using a data set of electron density from Van Allen Probes between September 25, 2012 and August 30, 2019. This MLED model is a physics-based nonlinear network that employs fundamental physical principles to represent the variation of electron density. It predicts the plasmapause location under different geomagnetic activities and models the electron density of the plasmasphere and trough separately. We train the model using gradient descent and backpropagation algorithms, which can be widely used to deal effectively with nonlinear relationships among physical quantities in space plasma environments. The model gives explicit expressions with few parameters and describes the association of electron density with geomagnetic activity, solar cycle, and seasonal effects. Under various geomagnetic conditions, the electron densities calculated by this model agree well with the observation and provide a good description of the plasmapause movement. This MLED model, which can be easily incorporated into the previously developed radiation belt model, would be very helpful in modeling and forecasting the radiation belt electron dynamics.

Key words: background electron density, inner magnetosphere, machine learning, Van Allen Probes observation

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A machine learning-based electron density (MLED) model in the inner magnetosphere

QingHua Zhou, YunXiang Chen, FuLiang Xiao, Sai Zhang, Si Liu, Chang Yang, YiHua He, ZhongLei Gao