# Auto-Encoded Reservoir Computing for Turbulence Learning

arXiv: https://arxiv.org/abs/2012.10968 · HTML: https://mlsanity.com/paper/2012.10968/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2020.

## Built on by (most cited first, 7 of 7)

- [Data-driven low-dimensional dynamic model of Kolmogorov flow](https://mlsanity.com/paper/2210.16708/) (2022)
- [Frame-independent vector-cloud neural network for nonlocal constitutive modeling on arbitrary grids](https://mlsanity.com/paper/2103.06685/) (2021)
- [Decoder Decomposition for the Analysis of the Latent Space of Nonlinear Autoencoders With Wind-Tunnel Experimental Data](https://mlsanity.com/paper/2404.19660/) (2024)
- [Statistical prediction of extreme events from small datasets](https://mlsanity.com/paper/2201.08294/) (2022)
- [Building symmetries into data-driven manifold dynamics models for complex flows: application to two-dimensional Kolmogorov flow](https://mlsanity.com/paper/2312.10235/) (2023)
- [Online model learning with data-assimilated reservoir computers](https://mlsanity.com/paper/2504.16767/) (2025)
- [Spectrally Regularized Latent Flow Matching for Turbulence Generation](https://mlsanity.com/paper/2606.11691/) (2026)

## Abstract (arXiv)

We present an Auto-Encoded Reservoir-Computing (AE-RC) approach to learn the dynamics of a 2D turbulent flow. The AE-RC consists of an Autoencoder, which discovers an efficient manifold representation of the flow state, and an Echo State Network, which learns the time evolution of the flow in the manifold. The AE-RC is able to both learn the time-accurate dynamics of the flow and predict its first-order statistical moments. The AE-RC approach opens up new possibilities for the spatio-temporal prediction of turbulence with machine learning.