  Real-time prediction of the dynamics of energetic electrons in Earth's
radiation belts incorporating incomplete observation data is important to
protect valuable artificial satellites and to understand their physical
processes. Traditionally, reduced models have employed a diffusion equation
based on the quasilinear approximation. Using a Physics-Informed Neural Network
(PINN) framework, we train and test a model based on Van Allen Probe data. We
present a recipe for gleaning physical insight from solving the ill-posed
inverse problem of inferring model coefficients from data using PINNs. With
this, it is discovered that the dynamics of "killer electrons" is described
more accurately instead by a drift-diffusion equation. A parameterization for
the diffusion and drift coefficients, which is both simpler and more accurate
than existing models, is presented.
