A perspective on machine learning methods in turbulence modeling

Beck, Andrea; Kurz, Marius

doi:10.1002/gamm.202100002

Cited by 98 publications

(52 citation statements)

References 71 publications

(72 reference statements)

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“…The development of SGS models has largely been driven by physical insights, mathematical considerations, and often problem-specific intuition. More recently, the availability of data from observations and high-resolution simulation along with advances in hardware and algorithms has fuelled interest in the development of data-driven turbulence models [5][6][7][8]. * osan@okstate.edu…”

Section: Introductionmentioning

confidence: 99%

Frame invariant neural network closures for Kraichnan turbulence

Pawar,

San,

Rasheed

et al. 2022

Preprint

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Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperfect and can lead to inaccurate predictions. In recent years, machine learning has been successful in extracting complex patterns from high-resolution spatio-temporal data, leading to improved parameterization models, and ultimately better coarse grid prediction. However, the inability to satisfy known physics and poor generalization hinders the application of these models for real-world problems. In this work, we propose a frame invariant closure approach to improve the accuracy and generalizability of deep learning-based subgrid scale closure models by embedding physical symmetries directly into the structure of the neural network. Specifically, we utilized specialized layers within the convolutional neural network in such a way that desired constraints are theoretically guaranteed without the need for any regularization terms. We demonstrate our framework for a two-dimensional decaying turbulence test case mostly characterized by the forward enstrophy cascade. We show that our frame invariant SGS model (i) accurately predicts the subgrid scale source term, (ii) respects the physical symmetries such as translation, Galilean, and rotation invariance, and (iii) is numerically stable when implemented in coarse-grid simulation with generalization to different initial conditions and Reynolds number. This work builds a bridge between extensive physics-based theories and data-driven modeling paradigms, and thus represents a promising step towards the development of physically consistent data-driven turbulence closure models.

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Section: Introductionmentioning

confidence: 99%

Frame invariant neural network closures for Kraichnan turbulence

Pawar,

San,

Rasheed

et al. 2022

Preprint

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“…Therefore, increasing focus is laid upon finding this mapping M from data by leveraging the recent advances in machine learning. See [2] for an extensive review. In that reference, machine learning is used to directly recover the unknown flux term R(F (U )) = f (U ) without positing any prior assumptions on the functional form of the underlying mapping f (•).…”

Section: Turbulence Closure Problemmentioning

confidence: 99%

Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows

Wenzel¹,

Kurz²,

Beck³

et al. 2021

Preprint

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Standard kernel methods for machine learning usually struggle when dealing with large datasets. We review a recently introduced Structured Deep Kernel Network (SDKN) approach that is capable of dealing with high-dimensional and huge datasets -and enjoys typical standard machine learning approximation properties. We extend the SDKN to combine it with standard machine learning modules and compare it with Neural Networks on the scientific challenge of data-driven prediction of closure terms of turbulent flows. We show experimentally that the SDKNs are capable of dealing with large datasets and achieve near-perfect accuracy on the given application.

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“…In recent years, there has been a rapidly growing interest in using machine learning (ML) methods to learn data-driven SGS closure models from filtered direct numerical simulation (DNS) data [e.g., 19,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Different approaches applied to a variety of canonical fluid systems have been investigated in these studies.…”

Section: Introductionmentioning

confidence: 99%

Learning physics-constrained subgrid-scale closures in the small-data regime for stable and accurate LES

Guan,

Subel,

Chattopadhyay

et al. 2022

Preprint

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We demonstrate how incorporating physics constraints into convolutional neural networks (CNNs) enables learning subgrid-scale (SGS) closures for stable and accurate large-eddy simulations (LES) in the small-data regime (i.e., when the availability of high-quality training data is limited). Using several setups of forced 2D turbulence as the testbeds, we examine the a priori and a posteriori performance of three methods for incorporating physics: 1) data augmentation (DA), 2) CNN with group convolutions (GCNN), and 3) loss functions that enforce a global enstrophy-transfer conservation (EnsCon). While the data-driven closures from physicsagnostic CNNs trained in the big-data regime are accurate and stable, and outperform dynamic Smagorinsky (DSMAG) closures, their performance substantially deteriorate when these CNNs are trained with 40x fewer samples (the small-data regime). An example based on a vortex dipole demonstrates that the physics-agnostic CNN cannot account for never-seen-before samples ′ rotational equivariance (symmetry), an important property of the SGS term. This shows a major shortcoming of the physics-agnostic CNN in the small-data regime. We show that CNN with DA and GCNN address this issue and each produce accurate and stable data-driven closures in the small-data regime. Despite its simplicity, DA, which adds appropriately rotated samples to the training set, performs as well or in some cases even better than GCNN, which uses a sophisticated equivariance-preserving architecture. EnsCon, which combines structural modeling with aspect of functional modeling, also produces accurate and stable closures in the small-data regime. Overall, GCNN+EnCon, which combines these two physics constraints, shows the best a posteriori performance in this regime. These results illustrate the power of physics-constrained learning in the small-data regime for accurate and stable LES.

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A perspective on machine learning methods in turbulence modeling

Cited by 98 publications

References 71 publications

Frame invariant neural network closures for Kraichnan turbulence

Frame invariant neural network closures for Kraichnan turbulence

Structured Deep Kernel Networks for Data-Driven Closure Terms of Turbulent Flows

Learning physics-constrained subgrid-scale closures in the small-data regime for stable and accurate LES

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