# OS-net: Orbitally Stable Neural Networks

arXiv: https://arxiv.org/abs/2309.14822 · HTML: https://mlsanity.com/paper/2309.14822/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 26 Sep 2023.

## Builds on (most cited first, 12 of 12)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Deep Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/1804.04272/) (2018)
- [Neural Networks Fail to Learn Periodic Functions and How to Fix It](https://mlsanity.com/paper/2006.08195/) (2020)
- [On Robustness of Neural Ordinary Differential Equations](https://mlsanity.com/paper/1910.05513/) (2019)
- [Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE](https://mlsanity.com/paper/2006.02493/) (2020)
- [ResNet After All? Neural ODEs and Their Numerical Solution](https://mlsanity.com/paper/2007.15386/) (2020)
- [Fourier Neural Networks: A Comparative Study](https://mlsanity.com/paper/1902.03011/) (2019)
- [Data-Driven Stabilization of Periodic Orbits](https://mlsanity.com/paper/2010.13896/) (2020)
- [A memory-efficient neural ODE framework based on high-level adjoint differentiation](https://mlsanity.com/paper/2206.01298/) (2022)

## 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.