Deep Neural Networks for Data-Driven Turbulence Models

Abstract

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.

References in corpus (10)

• Adam: A Method for Stochastic Optimization
• Very Deep Convolutional Networks for Large-Scale Image Recognition
• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• Deep Learning in Neural Networks: An Overview
• End to End Learning for Self-Driving Cars
• AtomNet: A Deep Convolutional Neural Network for Bioactivity Prediction in Structure-based Drug Discovery
• Split Form Nodal Discontinuous Galerkin Schemes with Summation-By-Parts Property for the Compressible Euler Equations
• A neural network approach for the blind deconvolution of turbulent flows
• Quantifying model form uncertainty in Reynolds-averaged turbulence models with Bayesian deep neural networks
• On the use of kinetic energy preserving DG-schemes for large eddy simulation

Cited by in corpus (96)

• Machine learning accelerated computational fluid dynamics
• Deep Learning Methods for Reynolds-Averaged Navier-Stokes Simulations of Airfoil Flows
• Enhancing Computational Fluid Dynamics with Machine Learning
• Learning data driven discretizations for partial differential equations
• Sub-grid modelling for two-dimensional turbulence using neural networks
• A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries
• Unsupervised deep learning for super-resolution reconstruction of turbulence
• Perspectives on Machine Learning-augmented Reynolds-averaged and Large Eddy Simulation Models of Turbulence
• Robust active flow control over a range of Reynolds numbers using an artificial neural network trained through deep reinforcement learning
• Improving aircraft performance using machine learning: a review
• Scientific multi-agent reinforcement learning for wall-models of turbulent flows
• Recent advances in applying deep reinforcement learning for flow control: perspectives and future directions
• A Perspective on Machine Learning Methods in Turbulence Modelling
• Physics guided machine learning using simplified theories
• Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers
• JAX-FLUIDS: A fully-differentiable high-order computational fluid dynamics solver for compressible two-phase flows
• Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher Re via transfer learning
• Sub-grid scale model classification and blending through deep learning
• Deconvolutional artificial neural network models for large eddy simulation of turbulence
• Deep Reinforcement Learning for Turbulence Modeling in Large Eddy Simulations
• Long-term predictions of turbulence by implicit U-Net enhanced Fourier neural operator
• Multi-resolution partial differential equations preserved learning framework for spatiotemporal dynamics
• Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizons
• Embedded training of neural-network sub-grid-scale turbulence models
• A Neural Network based Shock Detection and Localization Approach for Discontinuous Galerkin Methods
• Data-driven subgrid-scale modeling of forced Burgers turbulence using deep learning with generalization to higher Reynolds numbers via transfer learning
• Attention-Enhanced Neural Network Models for Turbulence Simulation
• A posteriori learning for quasi-geostrophic turbulence parametrization
• Learning physics-constrained subgrid-scale closures in the small-data regime for stable and accurate LES
• Turbulence closure modeling with data-driven techniques: physical compatibility and consistency considerations
• Deep Reinforcement Learning for Computational Fluid Dynamics on HPC Systems
• Deep reinforcement learning for large-eddy simulation modeling in wall-bounded turbulence
• Physics-inspired architecture for neural network modeling of forces and torques in particle-laden flows
• Explaining the physics of transfer learning a data-driven subgrid-scale closure to a different turbulent flow
• A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
• Physical invariance in neural networks for subgrid-scale scalar flux modeling
• OpenFOAMGPT: a RAG-Augmented LLM Agent for OpenFOAM-Based Computational Fluid Dynamics
• Deep Learning Closure Models for Large-Eddy Simulation of Flows around Bluff Bodies
• Finite volume method network for acceleration of unsteady computational fluid dynamics: non-reacting and reacting flows
• Forecasting small scale dynamics of fluid turbulence using deep neural networks
• Interpreting neural network models of residual scalar flux
• Generative data-driven approaches for stochastic subgrid parameterizations in an idealized ocean model
• Deep learning of the spanwise-averaged Navier-Stokes equations
• Investigation of nonlocal data-driven methods for subgrid-scale stress modelling in large eddy simulation
• Toward Discretization-Consistent Closure Schemes for Large Eddy Simulation Using Reinforcement Learning
• Data-Driven Multi-Grid Solver for Accelerated Pressure Projection
• Convolutional-network models to predict wall-bounded turbulence from wall quantities
• Accelerating high order discontinuous Galerkin solvers using neural networks: 3D compressible Navier-Stokes equations
• Discovery of interpretable structural model errors by combining Bayesian sparse regression and data assimilation: A chaotic Kuramoto-Sivashinsky test case
• A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows
• Comparison of neural closure models for discretised PDEs
• Frame invariant neural network closures for Kraichnan turbulence
• Discretize first, filter next: learning divergence-consistent closure models for large-eddy simulation
• Consistent and symmetry preserving data-driven interface reconstruction for the level-set method
• Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations. Part II
• Inserting machine-learned virtual wall velocity for large-eddy simulation of turbulent channel flows
• A machine learning framework for LES closure terms
• Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations. Part I
• Automating Turbulence Modeling by Multi-Agent Reinforcement Learning
• Generalizability of reservoir computing for flux-driven two-dimensional convection
• Robust deep learning for emulating turbulent viscosities
• Ensemble data assimilation-based mixed subgrid-scale model for large-eddy simulations
• Predicting the wall-shear stress and wall pressure through convolutional neural networks
• Training neural networks under physical constraints using a stochastic augmented Lagrangian approach
• Dimension Reduced Turbulent Flow Data From Deep Vector Quantizers
• A recursive neural-network-based subgrid-scale model for large eddy simulation: application to homogeneous isotropic turbulence
• A Status Quo Investigation of Large Language Models towards Cost-Effective CFD Automation with OpenFOAMGPT: ChatGPT vs. Qwen vs. Deepseek
• Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning
• Explicit physics-informed neural networks for non-linear upscaling closure: the case of transport in tissues
• Data assimilation empowered neural network parameterizations for subgrid processes in geophysical flows
• Predicting the near-wall region of turbulence through convolutional neural networks
• Review of Physics-based and Data-driven Multiscale Simulation Methods for Computational Fluid Dynamics and Nuclear Thermal Hydraulics
• Godunov Loss Functions for Modelling of Hyperbolic Conservation Laws
• Data-driven dynamical coarse-graining for condensed matter systems
• Data-driven spectral turbulence modeling for Rayleigh-Bénard convection
• Adjoint-based variational optimal mixed models for large-eddy simulation of turbulence
• Improving accuracy of turbulence models by neural network
• Predicting the mechanical response of oligocrystals with deep learning
• Reduced Data-Driven Turbulence Closure for Capturing Long-Term Statistics
• Kinetic data-driven approach to turbulence subgrid modeling
• A Deep Neural Network Model of Particle Thermal Radiation in Packed Bed
• A unified understanding of scale-resolving simulations and near-wall modeling of turbulent flows using optimal finite element projections
• Defiltering turbulent flow fields for Lagrangian particle tracking using machine learning techniques
• Deep learning at scale for subgrid modeling in turbulent flows
• Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models
• Finding Closure Terms Directly from Coarse Data for 2D Turbulent Flow
• A turbulent eddy-viscosity surrogate modeling framework for Reynolds-Averaged Navier-Stokes simulations
• Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows
• Normalizing Flows as a Novel PDF Turbulence Model
• UCNN: A Convolutional Strategy on Unstructured Mesh
• Turbulence closure modeling with data-driven techniques: Investigation of generalizable deep neural networks
• Machine learning for adjoint vector in aerodynamic shape optimization
• Modelling of Flow Past Long Cylindrical Structures
• Addressing A Posteriori Performance Degradation in Neural Network Subgrid Stress Models
• Reynolds Stress Modeling Using Data Driven Machine Learning Algorithms
• Unsupervised Machine Learning to Teach Fluid Dynamicists to Think in 15 Dimensions