# A Physics-Informed Vector Quantized Autoencoder for Data Compression of Turbulent Flow

arXiv: https://arxiv.org/abs/2201.03617 · HTML: https://mlsanity.com/paper/2201.03617/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 10 Jan 2022.

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

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Generating Diverse High-Fidelity Images with VQ-VAE-2](https://mlsanity.com/paper/1906.00446/) (2019)
- [Theory and Experiments on Vector Quantized Autoencoders](https://mlsanity.com/paper/1805.11063/) (2018)

## Built on by (most cited first, 5 of 5)

- [Statistical Deep Learning for Spatial and Spatio-Temporal Data](https://mlsanity.com/paper/2206.02218/) (2022)
- [QuadConv: Quadrature-Based Convolutions with Applications to Non-Uniform PDE Data Compression](https://mlsanity.com/paper/2211.05151/) (2022)
- [Capturing Extreme Events in Turbulence using an Extreme Variational Autoencoder (xVAE)](https://mlsanity.com/paper/2502.04685/) (2025)
- [A Geometric Lens on Physics-Aligned Data Compression](https://mlsanity.com/paper/2606.03279/) (2026)
- [Coupled Diffusion-Encoder Models for Reconstruction of Flow Fields](https://mlsanity.com/paper/2601.07946/) (2026)

## Abstract (arXiv)

Analyzing large-scale data from simulations of turbulent flows is memory intensive, requiring significant resources. This major challenge highlights the need for data compression techniques. In this study, we apply a physics-informed Deep Learning technique based on vector quantization to generate a discrete, low-dimensional representation of data from simulations of three-dimensional turbulent flows. The deep learning framework is composed of convolutional layers and incorporates physical constraints on the flow, such as preserving incompressibility and global statistical characteristics of the velocity gradients. The accuracy of the model is assessed using statistical, comparison-based similarity and physics-based metrics. The training data set is produced from Direct Numerical Simulation of an incompressible, statistically stationary, isotropic turbulent flow. The performance of this lossy data compression scheme is evaluated not only with unseen data from the stationary, isotropic turbulent flow, but also with data from decaying isotropic turbulence, and a Taylor-Green vortex flow. Defining the compression ratio (CR) as the ratio of original data size to the compressed one, the results show that our model based on vector quantization can offer CR =85 with a mean square error (MSE) of O(10-3), and predictions that faithfully reproduce the statistics of the flow, except at the very smallest scales where there is some loss. Compared to the recent study based on a conventional autoencoder where compression is performed in a continuous space, our model improves the CR by more than 30 percent, and reduces the MSE by an order of magnitude. Our compression model is an attractive solution for situations where fast, high quality and low-overhead encoding and decoding of large data are required.