# A Perspective on Machine Learning Methods in Turbulence Modelling

arXiv: https://arxiv.org/abs/2010.12226 · HTML: https://mlsanity.com/paper/2010.12226/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 23 of 23)

- [Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations](https://mlsanity.com/paper/2206.11038/) (2022)
- [Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equations](https://mlsanity.com/paper/2306.01174/) (2023)
- [Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systems](https://mlsanity.com/paper/2205.06502/) (2022)
- [CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting](https://mlsanity.com/paper/2304.07863/) (2023)
- [Solving the Discretised Neutron Diffusion Equations using Neural Networks](https://mlsanity.com/paper/2301.09939/) (2023)
- [Harnessing Equivariance: Modeling Turbulence with Graph Neural Networks](https://mlsanity.com/paper/2504.07741/) (2025)
- [Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics](https://mlsanity.com/paper/2402.17913/) (2024)
- [Neural Network Complexity of Chaos and Turbulence](https://mlsanity.com/paper/2211.15382/) (2022)
- [Mean flow data assimilation using physics-constrained Graph Neural Networks](https://mlsanity.com/paper/2411.09476/) (2024)
- [A Numerical Proof of Shell Model Turbulence Closure](https://mlsanity.com/paper/2202.09289/) (2022)
- [A multiscale and multicriteria Generative Adversarial Network to synthesize 1-dimensional turbulent fields](https://mlsanity.com/paper/2307.16580/) (2023)
- [PSTNet: Physically-Structured Turbulence Network](https://mlsanity.com/paper/2603.07957/) (2026)
- [Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows](https://mlsanity.com/paper/2103.13655/) (2021)
- [Differentiable Turbulence: Closure as a partial differential equation constrained optimization](https://mlsanity.com/paper/2307.03683/) (2023)
- [Generative convective parametrization of dry atmospheric boundary layer](https://mlsanity.com/paper/2307.14857/) (2023)
- [Capturing Extreme Events in Turbulence using an Extreme Variational Autoencoder (xVAE)](https://mlsanity.com/paper/2502.04685/) (2025)
- [MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data](https://mlsanity.com/paper/2410.06442/) (2024)
- [Upstream flow geometries can be uniquely learnt from single-point turbulence signatures](https://mlsanity.com/paper/2412.10630/) (2024)
- [Intelligent Sampling of Extreme-Scale Turbulence Datasets for Accurate and Efficient Spatiotemporal Model Training](https://mlsanity.com/paper/2508.03872/) (2025)
- [Addressing A Posteriori Performance Degradation in Neural Network Subgrid Stress Models](https://mlsanity.com/paper/2511.17475/) (2025)
- [Long-horizon prediction of three-dimensional wall-bounded turbulence with CTA-Swin-UNet and resolvent analysis](https://mlsanity.com/paper/2605.17888/) (2026)
- [Improving Reduced-Order Rotating Detonation Engine Models with Data Assimilation and Machine Learning](https://mlsanity.com/paper/2609.16237/) (2026)
- [PDE-PFN: Prior-Data Fitted Neural PDE Solver](https://mlsanity.com/paper/2610.13334/) (2026)

## Abstract (arXiv)

This work presents a review of the current state of research in data-driven turbulence closure modeling. It offers a perspective on the challenges and open issues, but also on the advantages and promises of machine learning methods applied to parameter estimation, model identification, closure term reconstruction and beyond, mostly from the perspective of Large Eddy Simulation and related techniques. We stress that consistency of the training data, the model, the underlying physics and the discretization is a key issue that needs to be considered for a successful ML-augmented modeling strategy. In order to make the discussion useful for non-experts in either field, we introduce both the modeling problem in turbulence as well as the prominent ML paradigms and methods in a concise and self-consistent manner. Following, we present a survey of the current data-driven model concepts and methods, highlight important developments and put them into the context of the discussed challenges.