TY - JOUR
T1 - Convergence Analysis of PINNs with Over-Parameterization
AU - Chen , Mo
AU - Ding , Zhao
AU - Jiao , Yuling
AU - Lu , Xiliang
AU - Wu , Peiying
AU - Yang , Jerry Zhijian
JO - Communications in Computational Physics
VL - 4
SP - 942
EP - 974
PY - 2025
DA - 2025/04
SN - 37
DO - http://doi.org/10.4208/cicp.OA-2023-0101
UR - https://global-sci.org/intro/article_detail/cicp/24028.html
KW - PINNs, over-parameterization, convergence rate, deep approximation with norm control.
AB - <p style="text-align: justify;">Recently, physics-informed neural networks (PINNs) have been shown to
be a simple and efficient method for solving PDEs empirically. However, the numerical analysis of PINNs is still incomplete, especially why over-parameterized PINNs
work remains unknown. This paper presents the first convergence analysis of the over-parameterized PINNs for the Laplace equations with Dirichlet boundary conditions.
We demonstrate that the convergence rate can be controlled by the weight norm, regardless of the number of parameters in the network.</p>