# Short note on the behavior of recurrent neural network for noisy dynamical system

arXiv: https://arxiv.org/abs/1904.05158 · HTML: https://mlsanity.com/paper/1904.05158/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2019.

## Built on by (most cited first, 2 of 2)

- [Deep Chaos Synchronization](https://mlsanity.com/paper/2104.08436/) (2021)
- [It's a super deal -- train recurrent network on noisy data and get smooth prediction free](https://mlsanity.com/paper/2206.04215/) (2022)

## Abstract (arXiv)

The behavior of recurrent neural network for the data-driven simulation of noisy dynamical systems is studied by training a set of Long Short-Term Memory Networks (LSTM) on the Mackey-Glass time series with a wide range of noise level. It is found that, as the training noise becomes larger, LSTM learns to depend more on its autonomous dynamics than the noisy input data. As a result, LSTM trained on noisy data becomes less susceptible to the perturbation in the data, but has a longer relaxation timescale. On the other hand, when trained on noiseless data, LSTM becomes extremely sensitive to a small perturbation, but is able to adjusts to the changes in the input data.