Scholarlink

<p>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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Graph neural networks for computational plasma physics on unstructured grids: application to approximate the Poisson equation for Hall-Effect Thrusters modeling

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年6月24日

查看全文
  • G. Vigot,
  • B. Cuenot,
  • O. Vermorel,
  • M. Bauerheim

摘要

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.