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\begin{document}

\title{Data-driven discovery of Fokker-Planck equation for the Earth's
radiation belts electrons using Physics-Informed Neural Networks}



\author[1]{Enrico Camporeale}%
\author[2]{George J Wilkie}%
\author[3]{Alexander Yurievich Drozdov}%
\author[3]{Jacob Bortnik}%
\affil[1]{University of Colorado}%
\affil[2]{Princeton Plasma Physics Laboratory}%
\affil[3]{University of California Los Angeles}%


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  \date{June 15, 2024}


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\begin{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 \$\textbackslash{}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.%
\end{abstract}%



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