Relativistic Electron Flux Prediction at Geosynchronous Orbit Based on the Neural Network and the Quantile Regression Method

Geosynchronous satellites are exposed to the relativistic electrons, which may cause irreparable damage to the satellites. The prediction of the relativistic electron flux is therefore important for the safety of the satellites. Unlike previous works focusing on the single-value prediction of relativistic electron flux, we predict the relativistic electron flux in a probabilistic approach by using the neural network and the quantile regression method. In this study, a feedforward neural network is first designed to predict average daily flux of relativistic electrons (>2 MeV), or the expectation of the flux from the probabilistic perspective, at geosynchronous orbit 1 day in advance. The neural network performs well, with the average root mean squared error, the average prediction efficiency, and the average linear correlation coefficient between observations and predictions reaching 0.305, 0.832, and 0.916, respectively, during the periods of 2011-2017. We then combine the quantile regression method with the feedforward neural network to predict the quantiles of relativistic electron flux by applying a special loss function to the neural network. We use the multiple-quantiles prediction model to predict flux ranges of the relativistic electrons and the corresponding probabilities, which is an advantage over the single-value prediction. Moreover, it appears to be for the first time that the approximate shape of the probability density function of relativistic electron flux is predicted.