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🔗 Source: peterchencyc.com
📊 Size: 3.98 MB
👤 Author: Yichen Li, Peter Yichen Chen, Tao Du, Wojciech Matusik
⬇️ Downloads: 591

Summary

Researchers propose a learning-based method for preconditioning conjugate gradient (CG) solvers, which are used to solve large sparse linear systems originating from partial differential equations (PDEs). The method involves training a graph neural network to obtain an approximate decomposition of the system matrix, used as a preconditioner. This approach introduces inductive bias to preconditioning techniques and has several benefits, including adapting to data distributions from target PDE applications and being applicable to various problems. Experiments demonstrate the efficacy and generalizability of the proposed method, outperforming classical preconditioners and existing learning-based methods in speed. The approach guarantees positive definiteness by design, works with irregular geometric domains, and is generic, applicable to many different problems, including elliptic, parabolic, and hyperbolic PDEs.

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Researchers propose a learning-based method for preconditioning conjugate gradient (CG) solvers, which are used to solve large sparse linear systems...

Technical Information

  • File Format: PDF
  • File Size: 3.98 MB
  • Pages: 16
  • Language: EN
  • Author: Yichen Li, Peter Yichen Chen, Tao Du, Wojciech Matusik
  • Total Downloads: 591
  • Last Updated: 9 hours ago

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