Authors: Vladimir Fanaskov

Published on: February 08, 2024

Impact Score: 8.22

Arxiv code: Arxiv:2402.05563

Summary

• What is new: A matrix-free neural architecture for the multigrid method that can handle problems with millions of unknowns.
• Why this is important: Existing neural networks with dense layers are inefficient for iterative methods used in solving large linear problems.
• What the research proposes: Introducing a simplified architecture utilizing parameter sharing and serialization of layers, avoiding dense layers.
• Results: Achieved a 2 to 5 times smaller spectral radius of the error propagation matrix compared to traditional linear multigrid solvers.

Technical Details

Technological frameworks used: Matrix-free neural architecture

Models used: Multigrid solvers

Data used: Second-order elliptic equations

Potential Impact

Numerical computing, software companies specializing in simulations, and computational fluid dynamics markets.

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