TY - JOUR
T1 - Two-Scale Neural Networks for Partial Differential Equations with Small Parameters
AU - Zhuang , Qiao
AU - Yao , Chris Ziyi
AU - Zhang , Zhongqiang
AU - Karniadakis , George Em
JO - Communications in Computational Physics
VL - 3
SP - 603
EP - 629
PY - 2025
DA - 2025/08
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0040
UR - https://global-sci.org/intro/article_detail/cicp/24309.html
KW - Two-scale neural networks, partial differential equations, small parameters, successive training.
AB - <p style="text-align: justify;">We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks
(PINNs). We directly incorporate the small parameters into the architecture of neural
networks. The proposed method enables solving PDEs with small parameters in a simple fashion, without adding Fourier features or other computationally taxing searches
of truncation parameters. Various numerical examples demonstrate reasonable accuracy in capturing features of large derivatives in the solutions caused by small parameters.</p>