7.0NAJul 5
Domain decomposition methods with Physics-informed neural networks for elliptic equations on manifoldsYufang Jiang, Lizhen Qin, Feng Wang
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 $10$.