Model Reduction and Neural Networks
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Abstract
Abstract
We propose two numerical domain decomposition methods (DDMs) for elliptic equations on compact Riemannian manifolds, based on physics-informed neural networks (PINNs). Our approach incorporates the DDM technique for manifolds with the advantages of neural networks in high-dimensional settings. The proposed methods are validated through numerical experiments on various manifolds, both with and without boundary, in dimensions ranging from $5$ to $10$.
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@article{Jiang2026Domain,
title = {Domain decomposition methods with Physics-informed neural networks for elliptic equations on manifolds},
author = {Yufang Jiang and Lizhen Qin and Fang Wang},
journal = {arXiv (Cornell University)},
year = {2026},
doi = {10.48550/arxiv.2607.04285},
url = {https://doi.org/10.48550/arxiv.2607.04285}
}FAQ
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