Machine-learning based discovery of missing physical processes in radiation belt modeling

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 quasi-linear approximation. Using a Physics-Informed Neutral Network (PINN) framework, we train and test a model based on four years of 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.