# Patch-Based 3D Variational Autoencoder for Super-Resolution of Turbulent Channel Flow

arXiv: https://arxiv.org/abs/2507.22082 · HTML: https://mlsanity.com/paper/2507.22082/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 26 Jul 2025.

## Builds on (most cited first, 14 of 14)

- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Accelerating the Super-Resolution Convolutional Neural Network](https://mlsanity.com/paper/1608.00367/) (2016)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [Enhancing Computational Fluid Dynamics with Machine Learning](https://mlsanity.com/paper/2110.02085/) (2021)
- [Super-Resolution Analysis via Machine Learning: A Survey for Fluid Flows](https://mlsanity.com/paper/2301.10937/) (2023)
- [Turbulence Enrichment using Physics-informed Generative Adversarial Networks](https://mlsanity.com/paper/2003.01907/) (2020)
- [Adversarial sampling of unknown and high-dimensional conditional distributions](https://mlsanity.com/paper/2111.05962/) (2021)
- [PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction](https://mlsanity.com/paper/2404.08412/) (2024)
- [Single-snapshot machine learning for super-resolution of turbulence](https://mlsanity.com/paper/2409.04923/) (2024)
- [SURFNet: Super-resolution of Turbulent Flows with Transfer Learning using Small Datasets](https://mlsanity.com/paper/2108.07667/) (2021)

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

- [Guiding diffusion models to reconstruct flow fields from sparse data](https://mlsanity.com/paper/2510.19971/) (2025)

## Abstract (arXiv)

Direct numerical simulation (DNS) accurately resolves all spatio-temporal scales of wall-bounded turbulence but becomes prohibitively expensive as the Reynolds number increases. Super-resolution (SR) provides a practical alternative by reconstructing fine-scale flow structures from coarse fields. Most existing SR methods focus on two-dimensional data, where vortex stretching is absent, and extend poorly to three dimensions because model complexity increases with the reconstructed volume. We propose a patch-based three-dimensional variational autoencoder (3D-VAE) that reconstructs a local (163) high-resolution block from a larger coarse neighbourhood. The learned operator is then applied convolutionally across the domain with overlap averaging, making the parameter count dependent only on patch size rather than domain size. The model is trained using the streamwise velocity from a single DNS snapshot of turbulent channel flow at (Reτ ≈ 1000) from the Johns Hopkins Turbulence Database and evaluated on a held-out snapshot. Compared with DNS, the proposed method achieves a mean absolute error of 0.055, outperforming tricubic (0.075) and Lanczos (0.076) interpolation. In spectral space, it reduces the mean absolute error of the two-dimensional Fourier amplitude from 2.63 and 2.85 to 0.91, an improvement of about threefold. Applied to coarse finite-element simulations, the model reconstructs spectral content absent from the input, demonstrating transfer beyond filtered DNS. A conditional 3D-GAN trained on the same data failed to converge under Wasserstein training and is reported as a negative result. The main limitations are attenuation of the smallest resolved scales, periodic artefacts caused by the patch stride, and under-prediction of extreme velocity values.