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DOE OSTI · 3365882

Two-Scale Neural Networks for Partial Differential Equations with Small Parameters

Zhuang, Qiao [Worcester Polytechnic Institute, MA (United States)]·Yao, Chris Ziyi [Imperial College, London (United Kingdom)]·Zhang, Zhongqiang [Clark Univ., Worcester, MA (United States)]·Karniadakis, George Em [Brown Univ., Providence, RI (United States)]
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Abstract

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.

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97 MATHEMATICS AND COMPUTINGpartial differential equationssmall parameterssuccessive trainingtwo-scale neural networks

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Zhuang, Qiao [Worcester Polytechnic Institute, MA (United States)], Yao, Chris Ziyi [Imperial College, London (United Kingdom)], Zhang, Zhongqiang [Clark Univ., Worcester, MA (United States)], Karniadakis, George Em [Brown Univ., Providence, RI (United States)]. 2025-08-23. Two-Scale Neural Networks for Partial Differential Equations with Small Parameters. https://doi.org/10.4208/cicp.oa-2024-0040

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