# Convolutional autoencoder for the spatiotemporal latent representation of turbulence

arXiv: https://arxiv.org/abs/2301.13728 · HTML: https://mlsanity.com/paper/2301.13728/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 16 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 4 of 4)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Are extreme dissipation events predictable in turbulent fluid flows?](https://mlsanity.com/paper/1807.10263/) (2018)
- [Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network](https://mlsanity.com/paper/2211.11379/) (2022)

## Built on by (most cited first, 4 of 4)

- [Decoder Decomposition for the Analysis of the Latent Space of Nonlinear Autoencoders With Wind-Tunnel Experimental Data](https://mlsanity.com/paper/2404.19660/) (2024)
- [Fourier-Invertible Neural Encoder (FINE) for Homogeneous Flows](https://mlsanity.com/paper/2505.15329/) (2025)
- [Physically Interpretable Representation Learning with Gaussian Mixture Variational AutoEncoder (GM-VAE)](https://mlsanity.com/paper/2511.21883/) (2025)
- [Spectrally Regularized Latent Flow Matching for Turbulence Generation](https://mlsanity.com/paper/2606.11691/) (2026)

## Abstract (arXiv)

Turbulence is characterised by chaotic dynamics and a high-dimensional state space, which make this phenomenon challenging to predict. However, turbulent flows are often characterised by coherent spatiotemporal structures, such as vortices or large-scale modes, which can help obtain a latent description of turbulent flows. However, current approaches are often limited by either the need to use some form of thresholding on quantities defining the isosurfaces to which the flow structures are associated or the linearity of traditional modal flow decomposition approaches, such as those based on proper orthogonal decomposition. This problem is exacerbated in flows that exhibit extreme events, which are rare and sudden changes in a turbulent state. The goal of this paper is to obtain an efficient and accurate reduced-order latent representation of a turbulent flow that exhibits extreme events. Specifically, we employ a three-dimensional multiscale convolutional autoencoder (CAE) to obtain such latent representation. We apply it to a three-dimensional turbulent flow. We show that the Multiscale CAE is efficient, requiring less than 10% degrees of freedom than proper orthogonal decomposition for compressing the data and is able to accurately reconstruct flow states related to extreme events. The proposed deep learning architecture opens opportunities for nonlinear reduced-order modeling of turbulent flows from data.