GL-Coarsener: A Graph representation learning framework to construct coarse grid hierarchy for AMG solvers

11/19/2020
by   Reza Namazi, et al.
0

In many numerical schemes, the computational complexity scales non-linearly with the problem size. Solving a linear system of equations using direct methods or most iterative methods is a typical example. Algebraic multi-grid (AMG) methods are numerical methods used to solve large linear systems of equations efficiently. One of the main differences between AMG methods is how the coarser grid is constructed from a given fine grid. There are two main classes of AMG methods; graph and aggregation based coarsening methods. Here we propose an aggregation-based coarsening framework leveraging graph representation learning and clustering algorithms. Our method introduces the power of machine learning into the AMG research field and opens a new perspective for future researches. The proposed method uses graph representation learning techniques to learn latent features of the graph obtained from the underlying matrix of coefficients. Using these extracted features, we generated a coarser grid from the fine grid. The proposed method is highly capable of parallel computations. Our experiments show that the proposed method's efficiency in solving large systems is closely comparable with other aggregation-based methods, demonstrating the high capability of graph representation learning in designing multi-grid solvers.

READ FULL TEXT

Authors

page 7

05/06/2020

Two-Grid Deflated Krylov Methods for Linear Equations

An approach is given for solving large linear systems that combines Kryl...
04/29/2020

Deep Reinforcement Learning with Graph-based State Representations

Deep RL approaches build much of their success on the ability of the dee...
04/28/2021

Two-Grid Domain Decomposition Methods for the Coupled Stokes-Darcy System

In this paper, we propose two novel Robin-type domain decomposition meth...
07/24/2020

Convergence analysis of inexact two-grid methods: A theoretical framework

Multigrid methods are among the most efficient iterative techniques for ...
05/27/2021

Coarse-Grid Selection Using Simulated Annealing

Multilevel techniques are efficient approaches for solving the large lin...
06/03/2021

Optimization-Based Algebraic Multigrid Coarsening Using Reinforcement Learning

Large sparse linear systems of equations are ubiquitous in science and e...
10/10/2021

About one method of constructing Hermite trigonometric splines

The method of constructing trigonometric Hermite splines, which interpol...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.