# Multi-scale data reconstruction of turbulent rotating flows with Gappy POD, Extended POD and Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2210.11921 · HTML: https://mlsanity.com/paper/2210.11921/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 85 references that are in the map.
- First posted on arXiv 21 Oct 2022.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [Missing Data Reconstruction in Remote Sensing image with a Unified Spatial-Temporal-Spectral Deep Convolutional Neural Network](https://mlsanity.com/paper/1802.08369/) (2018)
- [Turbulence Enrichment using Physics-informed Generative Adversarial Networks](https://mlsanity.com/paper/2003.01907/) (2020)
- [Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database](https://mlsanity.com/paper/2006.09179/) (2020)
- [TURB-Rot. A large database of 3d and 2d snapshots from turbulent rotating flows](https://mlsanity.com/paper/2006.07469/) (2020)

## Built on by (most cited first, 8 of 8)

- [Scientific Machine Learning Based Reduced-Order Models for Plasma Turbulence Simulations](https://mlsanity.com/paper/2401.05972/) (2024)
- [Reconstructing unsteady flows from sparse, noisy measurements with a physics-constrained convolutional neural network](https://mlsanity.com/paper/2409.00260/) (2024)
- [EngineBench: Flow Reconstruction in the Transparent Combustion Chamber III Optical Engine](https://mlsanity.com/paper/2406.03325/) (2024)
- [Spatiotemporal wall pressure forecast of a rectangular cylinder with physics-aware DeepU-Fourier neural network](https://mlsanity.com/paper/2508.03183/) (2025)
- [Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning framework](https://mlsanity.com/paper/2311.03776/) (2023)
- [Stochastic Reconstruction of Gappy Lagrangian Turbulent Signals by Conditional Diffusion Models](https://mlsanity.com/paper/2410.23971/) (2024)
- [Comparison of Generative Learning Methods for Turbulence Surrogates](https://mlsanity.com/paper/2411.16417/) (2024)
- [Vector-based loss functions for turbulent flow field inpainting](https://mlsanity.com/paper/2509.05787/) (2025)

## Abstract (arXiv)

Data reconstruction of rotating turbulent snapshots is investigated utilizing data-driven tools. This problem is crucial for numerous geophysical applications and fundamental aspects, given the concurrent effects of direct and inverse energy cascades, which lead to non-Gaussian statistics at both large and small scales. Data assimilation also serves as a tool to rank physical features within turbulence, by evaluating the performance of reconstruction in terms of the quality and quantity of the information used. Additionally, benchmarking various reconstruction techniques is essential to assess the trade-off between quantitative supremacy, implementation complexity, and explicability. In this study, we use linear and non-linear tools based on the Proper Orthogonal Decomposition (POD) and Generative Adversarial Network (GAN) for reconstructing rotating turbulence snapshots with spatial damages (inpainting). We focus on accurately reproducing both statistical properties and instantaneous velocity fields. Different gap sizes and gap geometries are investigated in order to assess the importance of coherency and multi-scale properties of the missing information. Surprisingly enough, concerning point-wise reconstruction, the non-linear GAN does not outperform one of the linear POD techniques. On the other hand, supremacy of the GAN approach is shown when the statistical multi-scale properties are compared. Similarly, extreme events in the gap region are better predicted when using GAN. The balance between point-wise error and statistical properties is controlled by the adversarial ratio, which determines the relative importance of the generator and the discriminator in the GAN training. Robustness against the measurement noise is also discussed.