Searching for turbulence models by artificial neural network

Gamahara, Masataka; Hattori, Yuji

doi:10.1103/physrevfluids.2.054604

Cited by 237 publications

(187 citation statements)

References 30 publications

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“…In terms of computational performance, point-to-point mapping requires less training time for learning SGS stresses from resolved flow variables. This approach is particularly attractive for complex or unstructured mesh and has been applied in many studies [35,36,49,50,72]. As illustrated in these works, our analysis with simple input features like resolved velocities and their derivatives also shows that the input features are critical for effective learning of SGS stresses for point-to-point mapping approach.…”

Section: Point-to-point Mappingmentioning

confidence: 67%

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

Pawar

San

Rasheed

et al. 2020

Theor. Comput. Fluid Dyn.

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In the present study, we investigate different data-driven parameterizations for large eddy simulation of two-dimensional turbulence in the a priori settings. These models utilize resolved flow field variables on the coarser grid to estimate the subgrid-scale stresses. We use data-driven closure models based on localized learning that employs multilayer feedforward artificial neural network (ANN) with point-to-point mapping and neighboring stencil data mapping, and convolutional neural network (CNN) fed by data snapshots of the whole domain. The performance of these data-driven closure models is measured through a probability density function and is compared with the dynamic Smagorinksy model (DSM). The quantitative performance is evaluated using the cross-correlation coefficient between the true and predicted stresses. We analyze different frameworks in terms of the amount of training data, selection of input and output features, their characteristics in modeling with accuracy, and training and deployment computational time. We also demonstrate computational gain that can be achieved using the intelligent eddy viscosity model that learns eddy viscosity computed by the DSM instead of subgrid-scale stresses. We detail the hyperparameters optimization of these models using the grid search algorithm.Keywords Turbulence closure · Deep learning · Neural networks · Subgrid scale modeling · Large eddy simulation 1 Introduction Direct numerical simulation (DNS) of complex fluid flows encountered in many engineering and geophysical applications is computationally unmanageable because of the need to resolve a wide range of spatiotemporal scales. Large eddy simulation (LES) and Reynolds Averaged Navier-Stokes (RANS) modeling are two most commonly used mathematical modeling frameworks that give accurate predictions by considering the interaction between the unresolved and grid-resolved scales. The development of these models is termed as the turbulence closure problem and has been a long-standing challenge in fluid mechanics community [1][2][3][4].In LES, we filter the Navier-Stokes equations using a low-pass filtering operator that separates the motion into small and large scales, and in turn, produces modified equations which are computationally faster to solve than actual Navier-Stokes equations [5][6][7]. The interaction between grid-resolved and unresolved scales is then taken into account by introducing subgrid-scale stress (SGS) term in the modified equation. The main task of the SGS model is to provide mean dissipation that corresponds to the transfer of energy from resolved scales to unresolved scales (the production of energy at large scales is balanced by the dissipation of energy at small scales based on Kolmogorov's theory of turbulence). The dissipation effect of unresolved scales can be included utilizing an eddy viscosity parameterization obtained through grid-resolved quantities. These approaches are called as functional approaches which assume isotropy of small scales to present the average dissipation of t...

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Section: Point-to-point Mappingmentioning

confidence: 67%

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

Pawar

San

Rasheed

et al. 2020

Theor. Comput. Fluid Dyn.

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“…ANNs have been also implemented in Parish & Duraisamy (2016) to correct errors in RANS turbulence models after the formulation of a field-inversion step. Gamahara & Hattori (2017) detailed the application of ANNs for identifying quantities of interest for sub-grid modelling in a turbulent channel flow through the measurement of Pearson correlation coefficients. Milano & Koumoutsakos (2002) also implemented these techniques for turbulent channel flow but for the generation of low-order wall models while Sarghini et al (2003) deployed ANNs for the prediction of the Smagorinsky coefficient (and thus the sub-grid contribution) in a mixed sub-grid model.…”

Section: Introductionmentioning

confidence: 99%

Subgrid modelling for two-dimensional turbulence using neural networks

Maulik

San

Rasheed³

et al. 2018

J. Fluid Mech.

267

235

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In this investigation, a data-driven turbulence closure framework is introduced and deployed for the sub-grid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized gridresolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the sub-grid vorticity forcing in a temporally and spatially dynamic fashion. Our study is both a-priori and a-posteriori in nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability density function based validation of sub-grid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying twodimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for sub-grid quantity inference. In addition, it is also observed that some measure of a-posteriori error must be considered during optimal model selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data.

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“…However, it can be easily applied to other types of neural networks (as demonstrated for data-driven forecasting of dynamical systems 110,113 ) or more traditional time series forecasting tools 114 . The neural networks are capable of approximating the nonlinear functions and have been successfully used in turbulence modeling [115][116][117] , solving differential equation 118,119 . We learn the dynamics of the reduced order model directly from the output of the full order model projected on the low-dimension space using a supervised learning task.…”

Section: Introductionmentioning

confidence: 99%

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

et al. 2019

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In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict evolution of dynamical systems by learning from either using discrete state or slope information of the system. Our approach has been demonstrated using both residual formula and backward difference scheme formulas. However, it can be easily generalized into many different numerical schemes as well. We give a demonstration of our framework for three examples: (i) Kraichnan-Orszag system, an illustrative coupled nonlinear ordinary differential equations, (ii) Lorenz system exhibiting chaotic behavior, and (iii) a non-intrusive model order reduction framework for the two-dimensional Boussinesq equations with a differentially heated cavity flow setup at various Rayleigh numbers. Using only snapshots of state variables at discrete time instances, our data-driven approach can be considered truly non-intrusive, since any prior information about the underlying governing equations is not required for generating the reduced order model. Our a posteriori analysis shows that the proposed data-driven approach is remarkably accurate, and can be used as a robust predictive tool for non-intrusive model order reduction of complex fluid flows.

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Searching for turbulence models by artificial neural network

Cited by 237 publications

References 30 publications

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

Subgrid modelling for two-dimensional turbulence using neural networks

A deep learning enabler for nonintrusive reduced order modeling of fluid flows

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