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# Universal Simulation of Stable Dynamical Systems by Recurrent Neural Nets

*Proceedings of the 2nd Conference on Learning for Dynamics and Control*, PMLR 120:384-392, 2020.

#### 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.