OS-net: Orbitally Stable Neural Networks
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Abstract (arXiv)
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"ossler and Sprott's systems, two dynamical systems known for their period doubling attractors and chaotic behavior.
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References · 12
- 2018Neural Ordinary Differential Equationscited by 3,733
- 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
- 2019Augmented Neural ODEscited by 396
- 2017Stable Architectures for Deep Neural Networkscited by 340
- 2018Deep Neural Networks Motivated by Partial Differential Equationscited by 187
- 2020Neural Networks Fail to Learn Periodic Functions and How to Fix Itcited by 97
- 2019On Robustness of Neural Ordinary Differential Equationscited by 83
- 2020Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODEcited by 76
- 2020ResNet After All? Neural ODEs and Their Numerical Solutioncited by 20
- 2019Fourier Neural Networks: A Comparative Studycited by 14
- 2020Data-Driven Stabilization of Periodic Orbitscited by 7
- 2022A memory-efficient neural ODE framework based on high-level adjoint differentiationcited by 3
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