OS-net: Orbitally Stable Neural Networks
This work addresses the challenge of stable neural network modeling for periodic dynamical systems, which is important for researchers in physics and engineering, but it appears incremental as it builds on existing Neural ODE frameworks.
The authors tackled the problem of modeling periodic dynamical data by introducing OS-net, a neural network architecture based on Neural ODEs with stability conditions derived from ODE theory, and demonstrated its efficacy by applying it to discover dynamics in Rössler and Sprott's systems, achieving accurate reconstructions with error reductions of up to 30% compared to baseline methods.
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 Rössler and Sprott's systems, two dynamical systems known for their period doubling attractors and chaotic behavior.