UCLA

This brief technique paper presents a method of reconstructing the global, time-varying distribution of some physical quantity Q that has been sparsely sampled at various locations within the magnetosphere and at different times. The quantity Q can be essentially any measurement taken on the satellite including a variety of waves (chorus, hiss, magnetosonic, and ion cyclotron), electrons of various energies ranging from cold to relativistic, and ions of various species and energies. As an illustrative example, we chose Q to be the electron number density (inferred from spacecraft potential) measured by three Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes between 2008 and 2014 and use the SYM-H index, taken at a 5 min cadence for the 5 h preceding each observed data point as the main regressor, although the predictor can also be any suitable geomagnetic index or solar wind parameter. Results show that the equatorial electron number density can be accurately reconstructed throughout the whole of the inner magnetosphere as a function of space and time, even capturing the dynamics of elementary plasmaspheric plume formation and corotation, suggesting that the dynamics of various other physical quantities could be similarly captured. For our main model, we use a simple, fully connected feedforward neural network with two hidden layers having sigmoidal activation functions and an output layer with a linear activation function to perform the reconstruction. The training is performed using the Levenberg-Marquardt algorithm and gives typical RMS errors of ~1.7 and regression of >0.93, which is considered excellent. We also present a discussion on the different applications and future extensions of the present model, for modeling various physical quantities.