Machine learning-based predictions of source, seed, and relativistic electron phase space density in the outer radiation belt Available to Purchase

Based on the in situ measurements of the Earth's radiation belt electrons as well as the historical solar wind and geomagnetic activity indices during the Van Allen Probe era (from 2012 to 2019), we constructed a prediction model of electron phase space density (PSD) using a machine learning method, i.e., the artificial neural network. Compared with previous study, the present model broadens the predicted energies to 31 channels (μ = 10¹–10⁴ MeV/G, μ is the first adiabatic invariant), with K = 0.08 G^1/2R_E and K = 0.17 G^1/2R_E (the second adiabatic invariant) at L^* (the third adiabatic invariant) ranging from 2.0 to 5.5. In the central part of the outer belt (L^* = 3.0–5.5), the model achieves outstanding performance for source, seed, and relativistic electrons at μ = 10²–10^3.5MeV/G, with overall root mean square errors <0.155, prediction efficiencies >0.982, and Pearson correlation coefficients >0.981 for both K = 0.08 G^1/2R_E and K = 0.17 G^1/2R_E, respectively. Moreover, 90.23% of samples present an observation–prediction difference of less than 0.2 order of magnitude, 98.76% present a difference of less than 0.5 order, and 99.71% present a difference of less than one order. Furthermore, it can well reproduce the energy spectral distributions of the electron PSD during different stages of a typical geomagnetic storm event. The present model provides a critical foundation for establishing an advanced predictive framework for space weather extreme events.