# A multiscale and multicriteria Generative Adversarial Network to synthesize 1-dimensional turbulent fields

arXiv: https://arxiv.org/abs/2307.16580 · HTML: https://mlsanity.com/paper/2307.16580/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 84 references that are in the map.
- First posted on arXiv 31 Jul 2023.

## Builds on (most cited first, 17 of 17)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Towards Physics-informed Deep Learning for Turbulent Flow Prediction](https://mlsanity.com/paper/1911.08655/) (2019)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Models](https://mlsanity.com/paper/2106.10121/) (2021)
- [Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems](https://mlsanity.com/paper/1905.06841/) (2019)
- [Synthetic Lagrangian Turbulence by Generative Diffusion Models](https://mlsanity.com/paper/2307.08529/) (2023)
- [Generative Modeling of Turbulence](https://mlsanity.com/paper/2112.02548/) (2021)
- [A Perspective on Machine Learning Methods in Turbulence Modelling](https://mlsanity.com/paper/2010.12226/) (2020)
- [Multi-fidelity Generative Deep Learning Turbulent Flows](https://mlsanity.com/paper/2006.04731/) (2020)
- [Explaining the physics of transfer learning a data-driven subgrid-scale closure to a different turbulent flow](https://mlsanity.com/paper/2206.03198/) (2022)
- [Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database](https://mlsanity.com/paper/2006.09179/) (2020)
- [Perceptual Generative Autoencoders](https://mlsanity.com/paper/1906.10335/) (2019)
- [Generative Adversarial Networks to infer velocity components in rotating turbulent flows](https://mlsanity.com/paper/2301.07541/) (2023)
- [Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics](https://mlsanity.com/paper/2211.11580/) (2022)

## Built on by (most cited first, 2 of 2)

- [Machine Learning Visualization Tool for Exploring Parameterized Hydrodynamics](https://mlsanity.com/paper/2406.15509/) (2024)
- [Spectrally Regularized Latent Flow Matching for Turbulence Generation](https://mlsanity.com/paper/2606.11691/) (2026)

## Abstract (arXiv)

This article introduces a new Neural Network stochastic model to generate a 1-dimensional stochastic field with turbulent velocity statistics. Both the model architecture and training procedure ground on the Kolmogorov and Obukhov statistical theories of fully developed turbulence, so guaranteeing descriptions of 1) energy distribution, 2) energy cascade and 3) intermittency across scales in agreement with experimental observations. The model is a Generative Adversarial Network with multiple multiscale optimization criteria. First, we use three physics-based criteria: the variance, skewness and flatness of the increments of the generated field that retrieve respectively the turbulent energy distribution, energy cascade and intermittency across scales. Second, the Generative Adversarial Network criterion, based on reproducing statistical distributions, is used on segments of different length of the generated field. Furthermore, to mimic multiscale decompositions frequently used in turbulence's studies, the model architecture is fully convolutional with kernel sizes varying along the multiple layers of the model. To train our model we use turbulent velocity signals from grid turbulence at Modane wind tunnel.