Invariant Data-Driven Subgrid Stress Modeling in the Strain-Rate Eigenframe for Large Eddy Simulation

Prakash, Aviral; Jansen, Kenneth E.; Evans, John A.

doi:10.48550/arxiv.2106.13410

Cited by 3 publications

(5 citation statements)

References 49 publications

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“…Although all results shown here were attained with Clark's gradient model as the base structural SGS model, optimal clipping can be applied to other structural SGS models such as Bardina's scale-similarity model, approximate deconvolution models, and data-driven models without modification. In fact, optimal clipping was also tested with the Bardina's scale-similarity [6] and the data-driven model presented in [22], and similar trends to those reported here were also observed for these models. The significant improvement in turbulent channel flow predictions observed here is a motivation for testing optimal clipping for other complicated wall-bounded flows such as a developing turbulent boundary layer, a boundary layer subject to favorable and/or adverse pressure gradients, or even a separating boundary layer.…”

Section: Discussionsupporting

confidence: 73%

“…In this article, we will demonstrate the applicability of optimal clipping by using it in conjunction with Clark's gradient model [5]. However, it must be highlighted that the optimal clipping formulation can be easily used with other models: 𝜏 𝑀 𝑖 𝑗 can be defined by Bardina's scale-similarity model [6], the approximate deconvolution model [7] or even a data-driven SGS model [22].…”

Section: 𝑖 𝑗mentioning

confidence: 99%

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Optimal Clipping of Structural Subgrid Stress Closures for Large Eddy Simulation

Prakash¹,

Jansen²,

Evans³

2022

Preprint

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Structural subgrid stress models for large eddy simulation often allow for backscatter of energy from unresolved to resolved turbulent scales, but excessive model backscatter can eventually result in numerical instability. A commonly employed strategy to overcome this issue is to set predicted subgrid stresses to zero in regions of model backscatter. This clipping procedure improves the stability of structural models, however, at the cost of reduced correlation between the predicted subgrid stresses and the exact subgrid stresses. In this article, we propose an alternative strategy that removes model backscatter from model predictions through the solution of a constrained minimization problem. This procedure, which we refer to as optimal clipping, results in a parameter-free mixed model, and it yields predicted subgrid stresses in higher correlation with the exact subgrid stresses as compared with those attained with the traditional clipping procedure. We perform a series of a priori and a posteriori tests to investigate the impact of applying the traditional and optimal clipping procedures to Clark's gradient subgrid stress model, and we observe that optimal clipping leads to a significant improvement in model predictions as compared to the traditional clipping procedure.

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Section: Discussionsupporting

confidence: 73%

Section: 𝑖 𝑗mentioning

confidence: 99%

Optimal Clipping of Structural Subgrid Stress Closures for Large Eddy Simulation

Prakash¹,

Jansen²,

Evans³

2022

Preprint

Self Cite

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“…In the context of SGS modeling, there are many ways to embed physical constraints into the ML model. One such method for constructing a robust and generalizable SGS model is through the selection of suitable non-dimensionalized input and output quantities of the ML model to ensure that the known symmetries are respected [41]. Another class of methods pertains to the customized neural network architectures that encode the prior physical or mathematical knowledge as hard constraints.…”

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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“…While translation equivariance is already achieved in a regular CNN by weight sharing [92], rotational equivariance is not guaranteed. Recent studies show that rotational equivariance can actually be critical in data-driven SGS modeling [27,66,69,74]. To capture the rotational equivariance in the small-data regime, we propose two separate approaches: (1) DA, by including 3 additional rotated (by 90 • , 180 • , and 270 • ) counterparts of each original FDNS snapshot in the training set [74] and (2) by using a GCNN architecture, which enforces rotational equivariance by construction [92,93].…”

Section: Physics-constraint Cnns: Incorporating Rotational Equivarian...mentioning

confidence: 99%

“…Past studies have shown that embedding physical insights or constraints can enhance the performance of data-driven models, e.g., in reduced-order models [e.g., [50][51][52][53][54][55][56][57] and in neural networks [e.g., 38,49,[58][59][60][61][62][63][64][65][66][67][68][69]. There are various ways to incorporate physics in neural networks (e.g., see the reviews by Kashinath et al [70], Balaji [71], and Karniadakis et al [72]).…”

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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Invariant Data-Driven Subgrid Stress Modeling in the Strain-Rate Eigenframe for Large Eddy Simulation

Cited by 3 publications

References 49 publications

Optimal Clipping of Structural Subgrid Stress Closures for Large Eddy Simulation

Optimal Clipping of Structural Subgrid Stress Closures for Large Eddy Simulation

Frame invariant neural network closures for Kraichnan turbulence

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

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