# Predicting the temporal dynamics of turbulent channels through deep learning

arXiv: https://arxiv.org/abs/2203.00974 · HTML: https://mlsanity.com/paper/2203.00974/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 2 Mar 2022.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [The role of artificial intelligence in achieving the Sustainable Development Goals](https://mlsanity.com/paper/1905.00501/) (2019)
- [Physics-informed neural networks for solving Reynolds-averaged Navierunicodex2013Stokes equations](https://mlsanity.com/paper/2107.10711/) (2021)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [Towards extraction of orthogonal and parsimonious non-linear modes from turbulent flows](https://mlsanity.com/paper/2109.01514/) (2021)
- [Interpretable deep-learning models to help achieve the Sustainable Development Goals](https://mlsanity.com/paper/2108.10744/) (2021)
- [Recurrent neural networks and Koopman-based frameworks for temporal predictions in a low-order model of turbulence](https://mlsanity.com/paper/2005.02762/) (2020)

## Built on by (most cited first, 10 of 10)

- [β-Variational autoencoders and transformers for reduced-order modelling of fluid flows](https://mlsanity.com/paper/2304.03571/) (2023)
- [Physics-Informed Computer Vision: A Review and Perspectives](https://mlsanity.com/paper/2305.18035/) (2023)
- [Improving aircraft performance using machine learning: a review](https://mlsanity.com/paper/2210.11481/) (2022)
- [Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow](https://mlsanity.com/paper/2301.04638/) (2023)
- [Stability analysis of chaotic systems in latent spaces](https://mlsanity.com/paper/2410.00480/) (2024)
- [A predictive physics-aware hybrid reduced order model for reacting flows](https://mlsanity.com/paper/2301.09860/) (2023)
- [Predicting the wall-shear stress and wall pressure through convolutional neural networks](https://mlsanity.com/paper/2303.00706/) (2023)
- [Generalization capabilities and robustness of hybrid models grounded in physics compared to purely deep learning models](https://mlsanity.com/paper/2404.17884/) (2024)
- [Differentiable Physics-Neural Models enable Learning of Non-Markovian Closures for Accelerated Coarse-Grained Physics Simulations](https://mlsanity.com/paper/2511.21369/) (2025)
- [Machine learning for advancing low-temperature plasma modeling and simulation](https://mlsanity.com/paper/2307.00131/) (2023)

## Abstract (arXiv)

The success of recurrent neural networks (RNNs) has been demonstrated in many applications related to turbulence, including flow control, optimization, turbulent features reproduction as well as turbulence prediction and modeling. With this study we aim to assess the capability of these networks to reproduce the temporal evolution of a minimal turbulent channel flow. We first obtain a data-driven model based on a modal decomposition in the Fourier domain (which we denote as FFT-POD) of the time series sampled from the flow. This particular case of turbulent flow allows us to accurately simulate the most relevant coherent structures close to the wall. Long-short-term-memory (LSTM) networks and a Koopman-based framework (KNF) are trained to predict the temporal dynamics of the minimal-channel-flow modes. Tests with different configurations highlight the limits of the KNF method compared to the LSTM, given the complexity of the flow under study. Long-term prediction for LSTM show excellent agreement from the statistical point of view, with errors below 2% for the best models with respect to the reference. Furthermore, the analysis of the chaotic behaviour through the use of the Lyapunov exponents and of the dynamic behaviour through Poincar'e maps emphasizes the ability of the LSTM to reproduce the temporal dynamics of turbulence. Alternative reduced-order models (ROMs), based on the identification of different turbulent structures, are explored and they continue to show a good potential in predicting the temporal dynamics of the minimal channel.