# From Deep to Physics-Informed Learning of Turbulence: Diagnostics

arXiv: https://arxiv.org/abs/1810.07785 · HTML: https://mlsanity.com/paper/1810.07785/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2018.

## Built on by (most cited first, 14 of 14)

- [Generative Modeling of Turbulence](https://mlsanity.com/paper/2112.02548/) (2021)
- [Adversarial sampling of unknown and high-dimensional conditional distributions](https://mlsanity.com/paper/2111.05962/) (2021)
- [Turbulence Scaling from Deep Learning Diffusion Generative Models](https://mlsanity.com/paper/2311.06112/) (2023)
- [Surrogate Modeling for Computationally Expensive Simulations of Supernovae in High-Resolution Galaxy Simulations](https://mlsanity.com/paper/2311.08460/) (2023)
- [Neural Particle Image Velocimetry](https://mlsanity.com/paper/2101.11950/) (2021)
- [Physics-Constrained Generative Adversarial Networks for 3D Turbulence](https://mlsanity.com/paper/2212.00217/) (2022)
- [Neural Network Complexity of Chaos and Turbulence](https://mlsanity.com/paper/2211.15382/) (2022)
- [Physics informed machine learning with Smoothed Particle Hydrodynamics: Hierarchy of reduced Lagrangian models of turbulence](https://mlsanity.com/paper/2110.13311/) (2021)
- [Towards Model Reduction for Power System Transients with Physics-Informed PDE](https://mlsanity.com/paper/2110.14066/) (2021)
- [Comparison of Generative Learning Methods for Turbulence Surrogates](https://mlsanity.com/paper/2411.16417/) (2024)
- [Learning the structure of wind: A data-driven nonlocal turbulence model for the atmospheric boundary layer](https://mlsanity.com/paper/2107.11046/) (2021)
- [Automated Dissipation Control for Turbulence Simulation with Shell Models](https://mlsanity.com/paper/2201.02485/) (2022)
- [Knowledge-Integrated Informed AI for National Security](https://mlsanity.com/paper/2202.03188/) (2022)
- [Mixing Artificial and Natural Intelligence: From Statistical Mechanics to AI and Back to Turbulence](https://mlsanity.com/paper/2403.17993/) (2024)

## Abstract (arXiv)

We describe tests validating progress made toward acceleration and automation of hydrodynamic codes in the regime of developed turbulence by three Deep Learning (DL) Neural Network (NN) schemes trained on Direct Numerical Simulations of turbulence. Even the bare DL solutions, which do not take into account any physics of turbulence explicitly, are impressively good overall when it comes to qualitative description of important features of turbulence. However, the early tests have also uncovered some caveats of the DL approaches. We observe that the static DL scheme, implementing Convolutional GAN and trained on spatial snapshots of turbulence, fails to reproduce intermittency of turbulent fluctuations at small scales and details of the turbulence geometry at large scales. We show that the dynamic NN schemes, namely LAT-NET and Compressed Convolutional LSTM, trained on a temporal sequence of turbulence snapshots are capable to correct for the caveats of the static NN. We suggest a path forward towards improving reproducibility of the large-scale geometry of turbulence with NN.