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.

翻译：本文提出了一种双尺度神经网络方法，用于利用物理信息神经网络求解含小参数的偏微分方程。该方法将小参数直接纳入神经网络架构中。所提出的方法能够以简洁的方式求解含小参数的偏微分方程，无需添加傅里叶特征或其他计算成本高昂的截断参数搜索。多种数值算例表明，该方法在捕捉小参数导致的解中大导数特征方面具有合理的精度。