mlsanityData to 7 Oct 2026

Deep Neural Networks for Data-Driven Turbulence Models

arXiv 1806.04482 ↗First posted 10 Jun 2018cs.CE physics.flu-dyncited by 35

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Abstract (arXiv)

In this work, we present a novel data-based approach to turbulence modelling for Large Eddy Simulation (LES) by artificial neural networks. We define the exact closure terms including the discretization operators and generate training data from direct numerical simulations of decaying homogeneous isotropic turbulence. We design and train artificial neural networks based on local convolution filters to predict the underlying unknown non-linear mapping from the coarse grid quantities to the closure terms without a priori assumptions. All investigated networks are able to generalize from the data and learn approximations with a cross correlation of up to 47% and even 73% for the inner elements, leading to the conclusion that the current training success is data-bound. We further show that selecting both the coarse grid primitive variables as well as the coarse grid LES operator as input features significantly improves training results. Finally, we construct a stable and accurate LES model from the learned closure terms. Therefore, we translate the model predictions into a data-adaptive, pointwise eddy viscosity closure and show that the resulting LES scheme performs well compared to current state of the art approaches. This work represents the starting point for further research into data-driven, universal turbulence models.

Key facts. Cited by 35 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Jun 2018.

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Citing papers per year: 2021: 8; 2022: 12; 2023: 4; 2024: 3; 2025: 8.

35 papers.

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  1. 2021Machine learning accelerated computational fluid dynamicscited by 461
  2. 2021Scientific multi-agent reinforcement learning for wall-models of turbulent flowscited by 52
  3. 2022Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamicscited by 44
  4. 2022Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizonscited by 39
  5. 2022JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flowscited by 36
  6. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  7. 2022Improving aircraft performance using machine learning: a reviewcited by 19
  8. 2022Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation datacited by 18
  9. 2022Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulationscited by 16
  10. 2021Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolutioncited by 14
  11. 2021Embedded training of neural-network sub-grid-scale turbulence modelscited by 13
  12. 2023Learning About Structural Errors in Models of Complex Dynamical Systemscited by 13
23 more
  1. 2021Finite volume method network for acceleration of unsteady computational fluid dynamics: non-reacting and reacting flowscited by 12
  2. 2022Deep Learning Closure Models for Large-Eddy Simulation of Flows around Bluff Bodiescited by 11
  3. 2024JAX-Fluids 2.0: Towards HPC for Differentiable CFD of Compressible Two-phase Flowscited by 7
  4. 2021Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test casecited by 6
  5. 2022Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systemscited by 6
  6. 2022Comparison of neural closure models for discretised PDEscited by 6
  7. 2025EddyFormer: Accelerated Neural Simulations of Three-Dimensional Turbulence at Scalecited by 6
  8. 2021Consistent and symmetry preserving data-driven interface reconstruction for the level-set methodcited by 5
  9. 2022Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learningcited by 5
  10. 2023Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learningcited by 5
  11. 2025PICT -- A Differentiable, GPU-Accelerated Multi-Block PISO Solver for Simulation-Coupled Learning Tasks in Fluid Dynamicscited by 5
  12. 2024Additive-feature-attribution methods: a review on explainable artificial intelligence for fluid dynamics and heat transfercited by 4
  13. 2022Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulationscited by 3
  14. 2025Comparison of CNN-based deep learning architectures for unsteady CFD acceleration on small datasetscited by 3
  15. 2025A Status Quo Investigation of Large Language Models towards Cost-Effective CFD Automation with OpenFOAMGPT: ChatGPT vs. Qwen vs. Deepseekcited by 3
  16. 2025Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Modelscited by 3
  17. 2023Predicting the wall-shear stress and wall pressure through convolutional neural networkscited by 2
  18. 2025Optimal Lattice Boltzmann Closures through Multi-Agent Reinforcement Learningcited by 2
  19. 2021Machine Learning for Naval Architecture, Ocean and Marine Engineeringcited by 1
  20. 2024Learning WENO for entropy stable schemes to solve conservation lawscited by 1
  21. 2025Stabilizing PDE--ML coupled systemscited by 1
  22. 2023Improving Pseudo-Time Stepping Convergence for CFD Simulations With Neural Networkscited by 0
  23. 2025Addressing A Posteriori Performance Degradation in Neural Network Subgrid Stress Modelscited by 0