June 20, 2024Open Access

Multilevel domain decomposition-based architectures for physics-informed neural networks

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Resumen

We propose a method for solving differential equations.• Our method combines PINNs with multilevel domain decomposition.• Our approach significantly outperforms PINNs when solving multiscale problems.• Multilevel modeling improves accuracy by aiding communication between subdomains.

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Dolean et al. (Thu,) studied this question.

synapsesocial.com/papers/68e63e25b6db6435875d0060 https://doi.org/https://doi.org/10.1016/j.cma.2024.117116

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations2023 · 302 citations
2On the limited memory BFGS method for large scale optimization1989 · 8,551 citations
3Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains2020 · 1,219 citations
4First International Symposium on Domain Decomposition Methods for Partial Differential Equations.1989 · 198 citations
5Artificial neural networks for solving ordinary and partial differential equations1998 · 2,246 citations

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