Machine Learning for Fluid Mechanics

Brunton, Steven L.; Noack, Bernd R.; Koumoutsakos, Petros

doi:10.1146/annurev-fluid-010719-060214

Cited by 1,629 publications

(672 citation statements)

References 217 publications

(257 reference statements)

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“…Interested readers are directed to Refs. [66][67][68][69][70] for more on the influence of ML on fluid mechanics, specifically turbulence modeling.…”

Section: Introductionmentioning

confidence: 99%

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

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In this study, we present a non-intrusive reduced order modeling (ROM) framework for largescale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that: (i) in the training phase, the LSTM model is trained on the modal coefficients extracted from the highresolution data snapshots using proper orthogonal decomposition (POD) transform, and (ii) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. Hence, no prior information about the underlying governing equations is required to generate the ROM. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first illustrate that the conventional Galerkin projection based reduced order modeling of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-GP does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed non-intrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasi-periodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time-window in this paper. Throughout the paper, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed fully non-intrusive ROM framework is robust and capable of predicting noisy nonlinear fluid flows in an extremely efficient way compared to the conventional projection based ROM framework.

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“…Interested readers are directed to Refs. [66][67][68][69][70] for more on the influence of ML on fluid mechanics, specifically turbulence modeling.…”

Section: Introductionmentioning

confidence: 99%

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

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“…Hence, there is a constant effort to develop a subgrid-scale model that is free from heuristics and can predict the SGS stresses accurately.In the past decade, the unprecedented amount of data collected from experiments, high-fidelity simulations has facilitated using machine learning (ML) algorithms in fluid mechanics. ML algorithms are now used for flow control, flow optimization, reduce order modeling, flow reconstruction, super-resolution, and flow cleansing [19,20]. One of the first applications of deep learning in fluid mechanics was by Milano & Koumoutsakos [21] who implemented neural network methodology to reconstruct near-wall turbulence and showed an improvement in prediction capability of velocity fields.…”

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confidence: 99%

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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“…Therefore, more complicated processes can be modeled without the need to formulate them with mathematical expressions [17]. Machine learning (ML) tools have shown substantial success in the fluid community identifying the underlying structures and mimicking their dynamics [18][19][20][21][22][23]. However, end-to-end modeling with ML, especially deep learning, has been facing stiff opposition, both in academia and industry, because of their black-box nature, lack of interpretability and generalizability which might produce nonphysical results [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics

et al. 2020

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In this paper, we put forth an evolve-then-correct reduced order modeling approach that combines intrusive and nonintrusive models to take hidden physical processes into account. Specifically, we split the underlying dynamics into known and unknown components. In the known part, we first utilize an intrusive Galerkin method projected on a set of basis functions obtained by proper orthogonal decomposition. We then formulate a recurrent neural network emulator based on the assumption that observed data is a manifestation of all relevant processes. We further enhance our approach by using an orthonormality conforming basis interpolation approach on a Grassmannian manifold to address off-design conditions. The proposed framework is illustrated here with the application of two-dimensional co-rotating vortex simulations under modeling uncertainty. The results demonstrate highly accurate predictions underlining the effectiveness of the evolve-thencorrect approach toward realtime simulations, where the full process model is not known a priori.

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Machine Learning for Fluid Mechanics

Cited by 1,629 publications

References 217 publications

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

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

An Evolve-Then-Correct Reduced Order Model for Hidden Fluid Dynamics

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