# Analysis of chaotic dynamical systems with autoencoders

arXiv: https://arxiv.org/abs/2109.13078 · HTML: https://mlsanity.com/paper/2109.13078/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 34 references that are in the map.
- First posted on arXiv 22 Sep 2021.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)

## Built on by (most cited first, 1 of 1)

- [Reconstruction of neuromorphic dynamics from a single scalar time series using variational autoencoder and neural network map](https://mlsanity.com/paper/2411.07055/) (2024)

## Abstract (arXiv)

We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space dimension of each system and thus determines the minimal number of nodes necessary to capture the essential information contained in the chaotic time series. The constructed chaotic autoencoders generate similar maximal Lyapunov exponents as the original chaotic systems and thus encompass their essential dynamical information.