OS-net: Orbitally Stable Neural Networks

• URL: http://arxiv.org/abs/2309.14822v1
• Date: Tue, 26 Sep 2023 10:40:04 GMT
• Title: OS-net: Orbitally Stable Neural Networks
• Authors: Marieme Ngom and Carlo Graziani
• Abstract summary: We introduce OS-net, a new family of neural network architectures specifically designed for periodic dynamical data. 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"ossler and Sprott's systems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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.

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