Data-driven discovery of the governing equations describing radiation belt dynamics

Radiation belt dynamics are typically modeled by numerically solving the Fokker-Planck diffusion equation. However, this traditional mode of analysis is heuristic and requires a priori physical understanding and a number assumptions regarding the form and variation of the diffusion coefficients that determine the rate of transport. With the rapid development of satellites, sensors, computational power and data storage in the past decade, vast quantities of data accumulated the explosive growth rate now offer new opportunities for data-driven discovery of the underlying physics, directly from the data itself. We report the initial results of data-driven Partial Differential Equation discovery, where the data is taken directly from a Fokker Planck simulation with diffusion coefficients varying in both space and time. We achieve this discovery by using optimized group-sparsity model-discovery techniques and demonstrate the potential of this approach in discovering PDEs from in-situ measurements. Our findings reveal the data requirements necessary for PDE discovery from real observational data in the radiation belts and offer new directions to understanding radiation belt dynamics.