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arXiv · 2605.02799

Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters

Qiao Zhuang·Taorui Wang·Rita Wanjiku·Majid Bani-Yaghoub·Zhongqiang Zhang
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Abstract

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.

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BibTeXRIS

Qiao Zhuang, Taorui Wang, Rita Wanjiku, Majid Bani-Yaghoub, Zhongqiang Zhang. 2026-05-04. Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters. https://arxiv.org/abs/2605.02799

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