The Earth's radiation belts, a highly dynamic natural radiation environment, remain a challenge for physical modeling. However, their accurate simulation and reproduction is crucial for protecting satellites and understanding space phenomena. The Salammbô 3D electrons code, developed at ONERA/DPHY, is an international reference for modeling these belts and is based on solving a diffusion equation with an implicit, finite volume numerical scheme. However, its computational cost limits its use for refined, very long-term simulations, which are used to better characterize the behavior of radiation belts from a climatological perspective, but also for the rapid generation of forecast ensembles, an essential requirement for space weather forecasting. Reduced modeling offers a solution by constructing surrogates (“simplified” models) capable of reproducing the dynamics of the system while drastically reducing computation time. The main objective of this thesis is to study the feasibility of developing such a model for Salammbô. Underlying this will be the exploration of innovative data-driven modeling methods, complementary to purely physical modeling, and the analysis of the limitations and benefits of such methods.

This thesis focuses on three main issues that combine digital and physical considerations. The first axis concerns dimensionality reduction: the aim is to identify a compact latent representation capable of preserving the physical characteristics of the system, while allowing efficient compression of the phase space density maps produced by Salammbô. The second area explores the construction of a dynamic model in this latent space: we will study classical approaches (polynomial regressions, Gaussian processes) and deep learning techniques such as recurrent models capable of capturing the temporal evolution of state variables. 

One potential avenue will be to integrate external parameters (solar activity, geomagnetic conditions) to dynamically adapt the model. These parameters could be those already used to calculate the various coefficients for the current Salammbô model (Kp, Ca, etc.), but also other physical parameters of interest that are more difficult to exploit in purely physical modeling. The third area aims to quantify the impact of the dimensionality reduction on the accuracy and robustness of the surrogate. This will involve analyzing the ability of the model(s) to reproduce critical events and understanding the physical interactions taken into account (or not) by the reduced models, in order to evaluate performance in terms of the balance between physical credibility and computational performance gains.

Beyond these areas of focus, this thesis will open up new avenues for studying and understanding Earth's radiation belts, some of which may be explored during the course of the thesis depending on progress.  For example, using sensitivity analysis methods coupled with reduced models, it will be possible to highlight the coupling mechanisms between solar activity and belt dynamics and to quantify the influence of geomagnetic parameters on belt dynamics. This can be supported by comparison with measurements from scientific missions in order to validate the advances made. 

This work also opens the door to an initial exploration of the assimilation of observational data in latent space. The work and studies proposed in this thesis are therefore highly innovative but also multidisciplinary, at the frontier of numerical modeling, physics, and artificial intelligence.

In terms of prospects, this study will pave the way for operational applications, such as the integration of surrogates into real-time forecasting chains. It will also contribute to the improvement of specification models for space missions by providing statistically richer long-term climatological simulations.

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For more Information about the topics and the co-financial partner (found by the lab!); contact Directeur de thèse - vincent.maget@onera.fr

Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering school director and you will be ready to apply online  before March 13th, 2026 Midnight Paris time!