Disentangled and interpretable feature extraction of the Earth electron radiation belt: a first step towards the development of a reduced order model

The radiation belts are populations of energetic particles, such as electrons and protons, trapped in the near-Earth space vicinity by the geomagnetic field. Because they cover the great majority of existing orbits and because the particles’ dynamics, highly coupled with solar activity, can strongly affect spacecraft components and mission, the accurate modeling of these regions is of uttermost importance for the monitoring of the near-Earth space dynamics.

Traditionally, the radiation belts are modeled by solving a three‑dimensional diffusion equation with numerical solvers. While a single 3D simulation can easily be run in real time, as done routinely in many space weather forecasting pipelines, the computational burden can become significant when the model is used in ensemble‑based data assimilation that potentially requires hundreds of runs, over very long periods, such as those needed for space‑climate studies.

Within this context, machine learning based Reduced Order models (ROMs) offer an interesting solution to approach the solutions of traditional high-fidelity physics-based models with a reasonable accuracy and at a reduced computational cost. This is achieved by projecting project highly non-linear features onto a disentangled, interpretable latent space of reduced dimension which dynamics could be driven by external variables.

In this work, we take a first step towards the development of a ROM for the Earth electron radiation belts. Using a Distance regularized Siamese twin autoencoder (DIRESA) on long-term simulations we manage to reduce electron fluxes on a refined grid to a small subset of latent variables. We then show that these variables that can all be linked with external geomagnetic parameters. This allows them to be at the core of a ROM of the Earth electron radiation belts driven by those external parameters.

This work was supported by both the "Event-Based Electron Belt Radiation Storm Environments Modelling" Activity led by the Space Applications & Research Consultancy (SPARC) under ESA Contract 4000141351/23/UK/EG and ONERA internal fundings, through the federated research project PRF-FIRSTS.