A Perspective on Machine Learning Methods in Turbulence Modelling
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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.
Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). First posted on arXiv 23 Oct 2020.
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Citing papers per year: 2021: 1; 2022: 4; 2023: 6; 2024: 4; 2025: 4; 2026: 4.
23 papers.
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- 2022Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulationscited by 16
- 2023Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equationscited by 13
- 2022Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systemscited by 7
- 2023CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boostingcited by 7
- 2023Solving the Discretised Neutron Diffusion Equations using Neural Networkscited by 5
- 2025Harnessing Equivariance: Modeling Turbulence with Graph Neural Networkscited by 5
- 2024Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamicscited by 4
- 2022Neural Network Complexity of Chaos and Turbulencecited by 3
- 2024Mean flow data assimilation using physics-constrained Graph Neural Networkscited by 3
- 2022A Numerical Proof of Shell Model Turbulence Closurecited by 2
- 2023A multiscale and multicriteria Generative Adversarial Network to synthesize 1-dimensional turbulent fieldscited by 2
- 2026PSTNet: Physically-Structured Turbulence Networkcited by 2
11 more
- 2021Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flowscited by 1
- 2023Differentiable Turbulence: Closure as a partial differential equation constrained optimizationcited by 1
- 2023Generative convective parametrization of dry atmospheric boundary layercited by 1
- 2025Capturing Extreme Events in Turbulence using an Extreme Variational Autoencoder (xVAE)cited by 1
- 2024MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Datacited by 0
- 2024Upstream flow geometries can be uniquely learnt from single-point turbulence signaturescited by 0
- 2025Intelligent Sampling of Extreme-Scale Turbulence Datasets for Accurate and Efficient Spatiotemporal Model Trainingcited by 0
- 2025Addressing A Posteriori Performance Degradation in Neural Network Subgrid Stress Modelscited by 0
- 2026Long-horizon prediction of three-dimensional wall-bounded turbulence with CTA-Swin-UNet and resolvent analysiscited by 0
- 2026Improving Reduced-Order Rotating Detonation Engine Models with Data Assimilation and Machine Learningcited by 0
- 2026PDE-PFN: Prior-Data Fitted Neural PDE Solvercited by 0
- 2026PDE-PFN: Prior-Data Fitted Neural PDE Solver9 Oct 2026
- 2026Improving Reduced-Order Rotating Detonation Engine Models with Data Assimilation and Machine Learning14 Sep 2026
- 2026Long-horizon prediction of three-dimensional wall-bounded turbulence with CTA-Swin-UNet and resolvent analysis18 May 2026
- 2026PSTNet: Physically-Structured Turbulence Network9 Mar 2026
- 2025Addressing A Posteriori Performance Degradation in Neural Network Subgrid Stress Models21 Nov 2025
- 2025Intelligent Sampling of Extreme-Scale Turbulence Datasets for Accurate and Efficient Spatiotemporal Model Training5 Aug 2025
- 2025Harnessing Equivariance: Modeling Turbulence with Graph Neural Networks10 Apr 2025
- 2025Capturing Extreme Events in Turbulence using an Extreme Variational Autoencoder (xVAE)7 Feb 2025
- 2024Upstream flow geometries can be uniquely learnt from single-point turbulence signatures14 Dec 2024
- 2024Mean flow data assimilation using physics-constrained Graph Neural Networks14 Nov 2024
- 2024MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data9 Oct 2024
- 2024Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics27 Feb 2024
11 more
- 2023A multiscale and multicriteria Generative Adversarial Network to synthesize 1-dimensional turbulent fields31 Jul 2023
- 2023Generative convective parametrization of dry atmospheric boundary layer27 Jul 2023
- 2023Differentiable Turbulence: Closure as a partial differential equation constrained optimization7 Jul 2023
- 2023Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equations1 Jun 2023
- 2023CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boosting16 Apr 2023
- 2023Solving the Discretised Neutron Diffusion Equations using Neural Networks24 Jan 2023
- 2022Neural Network Complexity of Chaos and Turbulence24 Nov 2022
- 2022Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations21 Jun 2022
- 2022Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systems13 May 2022
- 2022A Numerical Proof of Shell Model Turbulence Closure18 Feb 2022
- 2021Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows25 Mar 2021
- 2022Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulationscited by 16
- 2023Neural Ideal Large Eddy Simulation: Modeling Turbulence with Neural Stochastic Differential Equationscited by 13
- 2022Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systemscited by 7
- 2023CEBoosting: Online Sparse Identification of Dynamical Systems with Regime Switching by Causation Entropy Boostingcited by 7
- 2023Solving the Discretised Neutron Diffusion Equations using Neural Networkscited by 5
- 2025Harnessing Equivariance: Modeling Turbulence with Graph Neural Networkscited by 5
- 2024Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamicscited by 4
- 2022Neural Network Complexity of Chaos and Turbulencecited by 3
- 2024Mean flow data assimilation using physics-constrained Graph Neural Networkscited by 3
- 2022A Numerical Proof of Shell Model Turbulence Closurecited by 2
- 2023A multiscale and multicriteria Generative Adversarial Network to synthesize 1-dimensional turbulent fieldscited by 2
- 2026PSTNet: Physically-Structured Turbulence Networkcited by 2
12 most cited of 23 All 23 (JSON)
- 2026PDE-PFN: Prior-Data Fitted Neural PDE Solver9 Oct 2026
- 2026Improving Reduced-Order Rotating Detonation Engine Models with Data Assimilation and Machine Learning14 Sep 2026
- 2026Long-horizon prediction of three-dimensional wall-bounded turbulence with CTA-Swin-UNet and resolvent analysis18 May 2026
- 2026PSTNet: Physically-Structured Turbulence Network9 Mar 2026
- 2025Addressing A Posteriori Performance Degradation in Neural Network Subgrid Stress Models21 Nov 2025
- 2025Intelligent Sampling of Extreme-Scale Turbulence Datasets for Accurate and Efficient Spatiotemporal Model Training5 Aug 2025
- 2025Harnessing Equivariance: Modeling Turbulence with Graph Neural Networks10 Apr 2025
- 2025Capturing Extreme Events in Turbulence using an Extreme Variational Autoencoder (xVAE)7 Feb 2025
- 2024Upstream flow geometries can be uniquely learnt from single-point turbulence signatures14 Dec 2024
- 2024Mean flow data assimilation using physics-constrained Graph Neural Networks14 Nov 2024
- 2024MaD-Scientist: AI-based Scientist solving Convection-Diffusion-Reaction Equations Using Massive PINN-Based Prior Data9 Oct 2024
- 2024Neural Physics: Using AI Libraries to Develop Physics-Based Solvers for Incompressible Computational Fluid Dynamics27 Feb 2024
12 newest of 23 All 23 (JSON)