  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.
