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.
@article{arxiv.2605.02799,
title = {Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters},
author = {Qiao Zhuang and Taorui Wang and Rita Wanjiku and Majid Bani-Yaghoub and Zhongqiang Zhang},
journal= {arXiv preprint arXiv:2605.02799},
year = {2026}
}