Two-level deep domain decomposition method Article Swipe
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Victorita Dolean
,
Serge Gratton
,
Alexander Heinlein
,
Valentin Mercier
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2408.12198
· OA: W4401717165
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2408.12198
· OA: W4401717165
This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural networks (PINNs). The addition of the coarse level network improves scalability and convergence rates compared to the single level method. Tested on a Poisson equation with Dirichlet boundary conditions, the two-level deep DDM demonstrates superior performance, maintaining efficient convergence regardless of the number of subdomains. This advance provides a more scalable and effective approach to solving complex partial differential equations with machine learning.
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