🎓Gabriel VIGOT thesis defense
Friday 14 March 2025 at 15h00
JCA room, Cerfacs, Toulouse
Graph Neural Networks for Hall Effect Thrusters modeling
ED MEGEP – [Subject to defense authorization]

Solving a sparse linear system can represent one of the most critical bottlenecks of computational cost for a numerical simulation. In plasma physics, when we need to model a Hall-Effect Thruster numerically, computing the electric field is necessary to understand the plasma dynamics. To get the value of the electric field over time, we need to solve the Poisson equation directly derived from the Gauss law from the Maxwell equations. On a numerical approach, the Poisson equation is discretized over a computational domain and then reduced into a linear system where powerful algorithms such as iterative solvers are employed to solve this problem. The problem of solving linear systems in plasma simulation becomes stiff when the computational domain is based on an unstructured mesh, even more so when the domain is so large that it cannot be held in a single processor’s memory.
This thesis proposes machine learning methods based on Graph Neural Networks to accelerate plasma physics simulation by solving the linear system that results from the discretization of the Poisson equation. Multiple methods are proposed. Some of the proposed methods rely on coupling with classical iterative solvers to enhance the convergence rate, while others are simply standalone implementations to solve linear systems. The final purpose of this work is to propose different strategies that can reduce the computational cost of solving linear systems with reasonable accuracy on any computational domain, whether a structured or unstructured grid, regular or irregular grid, or small or large grid. In the end, the proposed methods aim to generalize the solving process of any linear system on any kind of geometry. A partitioning technique is also proposed for node embedding on large grids. This approach aims to maximize the prediction’s accuracy while ensuring as few operations as possible.
The thesis will present different neural network architectures and their implementation into a partitioning technique. For unstructured data, Graph Neural Networks are used for node embedding and will be assessed on small or large graphs. Different approaches are made, such as choosing different Graph Neural Network architectures, objective functions, and training methods to find the right approach to solve linear systems with less computational time than classical linear system solvers and closer to their precision level. These approaches will also help us to better understand the existing Graph Neural Networks implementations, their current possibilities and limitations, and their perspectives of improvement in the future, not only for Graph Neural Networks but also for any neural network in general.
Jury
Josiane Mothe | IRIT-Toulouse | Examiner |
Sylvain Laizet | Imperial College London | Reviewer |
Kentaro Hara | Stanford University | Examiner |
James Polk | Jet Propulsion Laboratory – NASA | Reviewer |
Bénédicte Cuenot | Safran Aircraft Engine | Invited member |
Ulysse Weller | CNES | Invited member |