Two-scale Neural Networks for Partial Differential Equations with Small Parameters
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910647335256064 |
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| author | Zhuang, Qiao Yao, Chris Ziyi Zhang, Zhongqiang Karniadakis, George Em |
| author_facet | Zhuang, Qiao Yao, Chris Ziyi Zhang, Zhongqiang Karniadakis, George Em |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_17232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Two-scale Neural Networks for Partial Differential Equations with Small Parameters Zhuang, Qiao Yao, Chris Ziyi Zhang, Zhongqiang Karniadakis, George Em Numerical Analysis Machine Learning Computational Physics 65N35, 35B25 I.2.6 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. |
| title | Two-scale Neural Networks for Partial Differential Equations with Small Parameters |
| topic | Numerical Analysis Machine Learning Computational Physics 65N35, 35B25 I.2.6 |
| url | https://arxiv.org/abs/2402.17232 |