Bénédicte Cuenot

This work introduces a novel unsupervised method for solving sparse linear systems related to a Poisson equation problem in plasma physics simulations. The approach leverages recurrent Graph Neural Networks (GNNs) trained iteratively in an online unsupervised manner to generate an initial guess, which is designed to lower the computational cost of traditional iterative solvers in terms of the number of iterations and execution time. By employing recurrent GNNs, we aim to model arbitrary simulation domains, accommodating computational meshes that are structured or unstructured, small or large, in 2D or 3D. The proposed unsupervised method seeks to improve previous works in solving the Poisson equation with GNNs by using a supervised, data-driven approach. Particular emphasis is placed on the interaction between the GNN-generated initial guess and the Flexible Generalized Minimal RESidual (FGMRES) solver. Through this hybridization, the method evaluates whether the unsupervised method can accelerate the convergence rate of the FGMRES solver. Ultimately, the proposed method will demonstrate whether a hybridization between a recurrent GNN and FGMRES solver can accelerate the solving process for the Poisson equation, which has been discretized into a linear system.

Low-temperature plasmas are essential to both fundamental scientific research and critical industrial applications. As in many areas of science, numerical simulations have become a vital tool for uncovering new physical phenomena and guiding technological development. Code benchmarking remains crucial for verifying implementations and evaluating performance. This work continues the Landmark benchmark initiative, a series specifically designed to support the verification of low-temperature plasma codes. In this study, seventeen simulation codes from a collaborative community of nineteen international institutions modeled a partially magnetized E×B Penning discharge. The emergence of large scale coherent structures, or rotating plasma spokes, endows this configuration with an enormous range of time scales, making it particularly challenging to simulate. The codes showed excellent agreement on the rotation frequency of the spoke as well as key plasma properties, including time-averaged ion density, plasma potential, and electron temperature profiles. Achieving this level of agreement came with challenges, and we share lessons learned on how to conduct future benchmarking campaigns. Comparing code implementations, computational hardware, and simulation runtimes also revealed interesting trends, which are summarized with the aim of guiding future plasma simulation software development.

The following work presents a supervised method for approximating the solution of the discretized Poisson equation as a linear system using graph neural networks (GNNs). The neural network aims to find the solution to the Poisson equation for each time step in a 3D plasma numerical simulation, which is modeled using a large, unstructured grid. The plasma physics simulation is designed to model a Hall-Effect thruster where the electric field must be calculated with good precision. The Poisson equation is an elliptic problem that represents one of the most significant computational costs associated with plasma simulations. As a preliminary study, we propose a Graph Neural Network trained using a supervised approach. This network will provide an estimation of the initial guess update for each simulation time step. Given the size of the original unstructured mesh for the 3D plasma simulation, a partitioning technique is proposed to manage the memory requirements of the original unstructured grid. This article primarily focuses on demonstrating the feasibility of estimating the solution of a linear system for a large unstructured problem before applying this supervised method in a real simulation. To demonstrate the validity of approximating the solution of linear systems on a large unstructured grid, we will also showcase the generalization capacity of the neural network model. The GNN will be trained on a specific partition configuration and tested using a different partitioning configuration. The GNN is expected to approximate the solution of linear systems at each time step, independent of the geometric arrangement of the partitioning process.

Surrogate models of turbulent diffusive flames could play a strategic role in the design of liquid rocket engine combustion chambers. The present article introduces a method to obtain data-driven surrogate models for coaxial injectors, by leveraging an inductive transfer learning strategy over a U-Net with available multifidelity Large Eddy Simulations (LES) data. The resulting models preserve reasonable accuracy while reducing the offline computational cost of data-generation. First, a database of about 100 low-fidelity LES simulations of shear-coaxial injectors, operating with gaseous oxygen and gaseous methane as propellants, has been created. The design of experiments explores three variables: the chamber radius, the recess-length of the oxidizer post, and the mixture ratio. Subsequently, U-Nets were trained upon this dataset to provide reasonable approximations of the temporal-averaged two-dimensional flow field. Despite the fact that neural networks are efficient non-linear data emulators, in purely data-driven approaches their quality is directly impacted by the precision of the data they are trained upon. Thus, a high-fidelity (HF) dataset has been created, made of about 10 simulations, to a much greater cost per sample. The amalgamation of low and HF data during the the transfer-learning process enables the improvement of the surrogate model’s fidelity without excessive additional cost.