Domain decomposition methods with Physics-informed neural networks for elliptic equations on manifolds

Yufang Jiang; Lizhen Qin; Feng Wang

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arXiv · 2607.04285

Domain decomposition methods with Physics-informed neural networks for elliptic equations on manifolds

Yufang Jiang·Lizhen Qin·Feng Wang

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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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Yufang Jiang, Lizhen Qin, Feng Wang. 2026-07-05. Domain decomposition methods with Physics-informed neural networks for elliptic equations on manifolds. https://arxiv.org/abs/2607.04285

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