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

Yufang Jiang; Lizhen Qin; Feng Wang

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

Numerical Analysis 2026-07-05 v1 Differential Geometry

Authors: Yufang Jiang , Lizhen Qin , Feng Wang

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 $10$ .

Keywords

domain decomposition methods physics-informed neural networks elliptic equations manifolds high-dimensional

Cite

@article{arxiv.2607.04285,
  title  = {Domain decomposition methods with Physics-informed neural networks for elliptic equations on manifolds},
  author = {Yufang Jiang and Lizhen Qin and Feng Wang},
  journal= {arXiv preprint arXiv:2607.04285},
  year   = {2026}
}

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