OS-net: Orbitally Stable Neural Networks

Marieme Ngom, Carlo Graziani

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Keywords: neural networks, dynamical systems, chaotic systems, periodic attractor, stable attractors

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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 fully 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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Submission Number: 4014