Open access
Date
2022-10Type
- Journal Article
Abstract
Solving linear system of equations stemming from Laplacian operators is at the heart of a wide range of applications. Due to the sparsity of the linear systems, iterative solvers such as Conjugate Gradient and Multigrid are usually employed when the solution has a large number of degrees of freedom. These iterative solvers can be seen as sparse approximations of the Green's function for the Laplacian operator. In this paper we propose a machine learning approach that regresses a Green's function from boundary conditions. This is enabled by a Green's function that can be effectively represented in a multi-scale fashion, drastically reducing the cost associated with a dense matrix representation. Additionally, since the Green's function is solely dependent on boundary conditions, training the proposed neural network does not require sampling the right-hand side of the linear system. We show results that our method outperforms state of the art Conjugate Gradient and Multigrid methods. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000566910Publication status
publishedExternal links
Journal / series
Computers & GraphicsVolume
Pages / Article No.
Publisher
ElsevierSubject
Machine learning; Modeling and simulation; Poisson equation; Green’s functionOrganisational unit
03420 - Gross, Markus / Gross, Markus
Funding
ETH-08 18-1 - A technical foundation for deep learning based physics simulations (ETHZ)
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