We introduce OS-net (Orbitally Stable neural NETworks), a new family of
neural network architectures specifically designed for periodic dynamical data.
OS-net is a special case of Neural Ordinary Differential Equations (NODEs) and
takes full advantage of the adjoint method based backpropagation method.
Utilizing ODE theory, we derive conditions on the network weights to ensure
stability of the resulting dynamics. We demonstrate the efficacy of our
approach by applying OS-net to discover the dynamics underlying the R\"{o}ssler
and Sprott's systems, two dynamical systems known for their period doubling
attractors and chaotic behavior.

介绍了一种名为 OS-net（轨道稳定神经网络）的神经网络架构，专门用于周期动力数据。OS-net 是神经常微分方程 (NODEs) 的一种特殊情况，并充分利用了基于伴随方法的反向传播方法。通过利用常微分方程理论，我们推导出保证结果动力学稳定性的网络权重条件。通过将 OS-net 应用于发现 Rössler 和 Sprott 系统的动力学，这是两种以吸引子周期倍增和混沌行为而闻名的动力学系统，我们证明了我们方法的功效。