Data-driven discovery of Fokker-Planck equation for radiation belt electrons using physics-informed neural networks

Abstract:

We solve the one-dimensional Fokker-Planck equation for radiation belt electrons under the assumption of the conservation of the first and second adiabatic invariants.

We use a physics-informed neural network to discover the optimal drift and diffusion coefficients that, once used in the Fokker-Planck equation, yield the solution with smaller discrepancy with respect to Van Allen Probes observations. Further, we train a machine learning algorithm that generalizes such coefficients for any radiation belt condition (boundary conditions and initial values). Interestingly, a feature selection analysis shows that the drift and diffusion coefficients are weakly dependent on the value of the geomagnetic index Kp, in contrast with all previous parameterizations presented in the literature.

This approach, although well rooted in our physical understanding of the process in play, seeks to extract the largest amount of information from the data with minimal assumptions, and we believe it promises to shed light on the physics of resonant and non-resonant wave-particle interactions in the radiation belts.