Scholarlink

<p>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.</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

Unsupervised method to solve the Poisson equation on unstructured grid

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月3日

查看全文
  • G. Vigot,
  • B. Cuenot

摘要

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.