Data-driven discovery of Fokker-Planck equation for the Earth's radiation belts electrons using Physics-Informed Neural Networks
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• Enrico Camporeale,
• George J Wilkie,
• Alexander Yurievich Drozdov,
• Jacob Bortnik
Enrico Camporeale

Corresponding Author:enrico.camporeale@noaa.gov

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George J Wilkie
Princeton Plasma Physics Laboratory
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Alexander Yurievich Drozdov
University of California Los Angeles
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Jacob Bortnik
University of California Los Angeles
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## Abstract

We use the framework of Physics-Informed Neural Network (PINN) to solve the inverse problem associated to the Fokker-Planck equation for radiation belts’ electron transport, using four years of Van Allen Probes data. Traditionally, reduced models have employed a diffusion equation based on the quasilinear approximation. We show that the dynamics of “killer electrons’ is described more accurately by a drift-diffusion equation, and that drift is as important as diffusion for nearly-equatorially trapped $\sim$1 MeV electrons in the inner part of the belt. Moreover, we present a recipe for gleaning physical insight from solving the ill-posed inverse problem of inferring model coefficients from data using PINNs.
Furthermore, we derive a parameterization for the diffusion and drift coefficients as a function of $L$ only, which is both simpler and more accurate than earlier models. Finally, we use the PINN technique to develop an automatic event identification method that allows to identify times at which the radial transport assumption is inadequate to describe all the physics of interest.