Universal Simulation of Stable Dynamical Systems by Recurrent Neural Nets
Abstract
It is well-known that continuous-time recurrent neural nets are universal approximators for continuous-time dynamical systems. However, existing results provide approximation guarantees only for finite-time trajectories. In this work, we show that infinite-time trajectories generated by dynamical systems that are stable in a certain sense can be reproduced arbitrarily accurately by recurrent neural nets. For a subclass of these stable systems, we provide quantitative estimates on the sufficient number of neurons needed to achieve a specified error tolerance.
Cite
Text
Hanson and Raginsky. "Universal Simulation of Stable Dynamical Systems by Recurrent Neural Nets." Proceedings of the 2nd Conference on Learning for Dynamics and Control, 2020.Markdown
[Hanson and Raginsky. "Universal Simulation of Stable Dynamical Systems by Recurrent Neural Nets." Proceedings of the 2nd Conference on Learning for Dynamics and Control, 2020.](https://mlanthology.org/l4dc/2020/hanson2020l4dc-universal/)BibTeX
@inproceedings{hanson2020l4dc-universal,
title = {{Universal Simulation of Stable Dynamical Systems by Recurrent Neural Nets}},
author = {Hanson, Joshua and Raginsky, Maxim},
booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control},
year = {2020},
pages = {384-392},
volume = {120},
url = {https://mlanthology.org/l4dc/2020/hanson2020l4dc-universal/}
}