Interpreting neural network models of residual scalar flux

Portwood, Gavin; Nadiga, Balasubramanya T.; Sáenz, Juan A.; Livescu, Daniel

doi:10.1017/jfm.2020.861

Cited by 33 publications

(20 citation statements)

References 36 publications

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“…2020; Portwood et al. 2020; Vela-Martín & Jiménez 2021). Here, the definition of the filter width, , is chosen such that its gradient, , is maximum at .…”

Section: Energy Cascade In Terms Of Filtered Velocity Gradientsmentioning

confidence: 99%

On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade

Johnson

2021

J. Fluid Mech.

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“…2020; Portwood et al. 2020; Vela-Martín & Jiménez 2021). Here, the definition of the filter width, , is chosen such that its gradient, , is maximum at .…”

Section: Energy Cascade In Terms Of Filtered Velocity Gradientsmentioning

confidence: 99%

On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade

Johnson

2021

J. Fluid Mech.

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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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“…While LES may be practiced in isolation from specific concerns of a consistent framework, a specific definition of that which an LES aspires to accurately reproduce is required for advanced techniques such as data-driven closure (Sarghini, de Felice & Santini 2003;Moreau, Teytaud & Bertoglio 2006;Gamahara & Hattori 2017;Vollant, Balarac & Corre 2017;Wang et al 2018;Beck, Flad & Munz 2019;Cheng et al 2019;Yang et al 2019;Zhou et al 2019;Sirignano, MacArt & Freund 2020;Xie, Wang & Weinan 2020a;Xie, Yuan & Wang 2020b;Yuan, Xie & Wang 2020;Bode et al 2021;Duraisamy 2021;Freund & Ferrante 2021;Park & Choi 2021;Portwood et al 2021;Prakash, Jansen & Evans 2021;Stoffer et al 2021;Wang et al 2021) and super-resolution enrichment (Domaradzki & Loh 1999;Scotti & Meneveau 1999;Stolz & Adams 1999;Milano & Koumoutsakos 2002;Leonard 2016;Ghate & Lele 2017;Maulik & San 2017;Bassenne et al 2019;Wang, Zhao & Ihme 2019;Ghate & Lele 2020;Liu et al 2020;Kim et al 2021). For example, without a clear definition of what an LES solution should represent, one cannot train a neural network to serve as a sub-grid closure in a robust way.…”

Section: Introductionmentioning

confidence: 99%

A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows

Johnson

2022

J. Fluid Mech.

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Large-eddy simulations (LES) are widely used for computing high Reynolds number turbulent flows. Spatial filtering theory for LES is not without its shortcomings, including how to define filtering for wall-bounded flows, commutation errors for non-uniform filters and extensibility to flows with additional complexity, such as multiphase flows. In this paper, the theory for LES is reimagined using a coarsening procedure that imitates nature. This physics-inspired coarsening approach is equivalent to Gaussian filtering for single-phase wall-free flows but opens up new insights for both physical understanding and modelling even in that simple case. For example, an alternative to the Germano identity is introduced and used to define a dynamic procedure without the need for a test filter. Non-uniform resolution can be represented in this framework without commutation errors, and the divergence-free condition is retained for incompressible flows. Potential extensions of the theory to more complex physics such as multiphase flows are briefly discussed.

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Interpreting neural network models of residual scalar flux

Abstract: Abstract

Cited by 33 publications

References 36 publications

On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade

On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade

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

A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows

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