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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.02799 |
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| _version_ | 1866913087299256320 |
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| author | Zhuang, Qiao Wang, Taorui Wanjiku, Rita Bani-Yaghoub, Majid Zhang, Zhongqiang |
| author_facet | Zhuang, Qiao Wang, Taorui Wanjiku, Rita Bani-Yaghoub, Majid Zhang, Zhongqiang |
| contents | We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate multiple small parameters, we use a single effective scale parameter defined as the geometric mean of all parameters. We thus augment the network input with a scale-aware feature, enabling it to capture sharp solution transitions intrinsically. Numerical experiments across a range of dynamical systems demonstrate that the proposed framework can handle coupled systems with multiple and high-contrast small parameters and obtain satisfactory accuracy in capturing solution features induced by small parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02799 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters Zhuang, Qiao Wang, Taorui Wanjiku, Rita Bani-Yaghoub, Majid Zhang, Zhongqiang Numerical Analysis Computational Physics 65N35, 34E15 I.2.6 We extend our two-scale neural-network method for scalar singularly perturbed problems with one small parameter to dynamical systems with multiple small parameters. To accommodate multiple small parameters, we use a single effective scale parameter defined as the geometric mean of all parameters. We thus augment the network input with a scale-aware feature, enabling it to capture sharp solution transitions intrinsically. Numerical experiments across a range of dynamical systems demonstrate that the proposed framework can handle coupled systems with multiple and high-contrast small parameters and obtain satisfactory accuracy in capturing solution features induced by small parameters. |
| title | Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters |
| topic | Numerical Analysis Computational Physics 65N35, 34E15 I.2.6 |
| url | https://arxiv.org/abs/2605.02799 |