@Article{CiCP-33-2,
author = {Wu, Sidi and Zhu, Aiqing and Yifa, Tang and Lu, Benzhuo},
title = {Convergence of Physics-Informed Neural Networks Applied to Linear Second-Order Elliptic Interface Problems},
journal = {Communications in Computational Physics},
year = {2023},
volume = {33},
number = {2},
pages = {596--627},
abstract = {<p style="text-align: justify;">With the remarkable empirical success of neural networks across diverse
scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. However, there has been little theoretical work focusing on neural networks in solving interface problems. In this paper, we perform a convergence
analysis of physics-informed neural networks (PINNs) for solving second-order elliptic interface problems. Specifically, we consider PINNs with domain decomposition
technologies and introduce gradient-enhanced strategies on the interfaces to deal with
boundary and interface jump conditions. It is shown that the neural network sequence
obtained by minimizing a Lipschitz regularized loss function converges to the unique
solution to the interface problem in $H^2$ as the number of samples increases. Numerical
experiments are provided to demonstrate our theoretical analysis.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2022-0218},
url = {https://global-sci.com/article/79427/convergence-of-physics-informed-neural-networks-applied-to-linear-second-order-elliptic-interface-problems}
}