Two-scale Neural Networks for Partial Differential Equations with Small
  Parameters
Qiao Zhuang Chris Ziyi Yao Zhongqiang Zhang George Em Karniadakis
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.