Prediction of radiation belt relativistic electron phase space density using artificial neural networks

Relativistic electrons (>1 MeV) saturating Earth's outer radiation belt is widely regarded as a vital risk to human astronomical activities. In the present work, we construct an artificial neural network model to predict the relativistic electron phase space density (PSD) at μ = 1000 MeV/G (the first adiabatic invariant) with K = 0.08 G1/2RE and K = 0.17 G1/2RE (the second adiabatic invariant) at L* (the third adiabatic invariant) ranging from 2.0 to 5.5, based on Van Allen Probe-A observations from 2012 to 2019. The historical values of the solar wind, geomagnetic indices, and the last orbital observations of the electron PSD are all adopted as inputs. Within the core region of relativistic electrons (L* = 3.0–5.5), the model achieves good performance, with overall root mean square errors of 0.1328 and 0.1342, prediction efficiencies of 0.9918 and 0.9916, and Pearson correlation coefficients of 0.9959 and 0.9958 for K = 0.08 G1/2RE and K = 0.17 G1/2RE, respectively. Statistical analysis revealed that 99.9% of the samples present an observation-prediction difference of less than one order of magnitude, 99% present a difference of less than 0.5 order, and 90% present a difference of less than 0.2 order. Furthermore, predictions can accurately reproduce the temporal evolution of the electron PSD during both quiet times and active conditions with no noticeable errors. The current model will aid in further analyzing the competition between the sources and losses of radiation belt particles and contribute to developing a future space weather catastrophe warning system.