Data-driven subgrid-scale modeling of forced Burgers turbulence using deep learning with generalization to higher Reynolds numbers via transfer learning

Subel, Adam; Chattopadhyay, Ashesh; Guan, Yifei; Hassanzadeh, Pedram

doi:10.1063/5.0040286

Cited by 65 publications

(37 citation statements)

References 53 publications

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“…Retraining an ANN on such a data set might strike a useful balance between the robustness of online training and the economy of offline training. Similar approaches have shown promise for comparable problems (Subel et al., 2021); our preliminary experiments using this approach have also been encouraging (Pusuluri, 2020).…”

Section: Toward Online Applicabilitymentioning

confidence: 59%

“…The example of data set enrichment presented here also offers encouragement to resolving instabilities that develop over several time steps. As it turned out to be overly optimistic to assume that an ANN trained on exact E F and E  combinations could handle erroneous E F in the early stages of a predictor-corrector scheme, it may also be too ambitious to expect that it will handle erroneous (Subel et al, 2021); our preliminary experiments using this approach have also been encouraging (Pusuluri, 2020).…”

Section: Toward Online Applicabilitymentioning

confidence: 95%

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Advancing Artificial Neural Network Parameterization for Atmospheric Turbulence Using a Variational Multiscale Model

Janssens

Hulshoff

2022

J Adv Model Earth Syst

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Intercomparison studies of existing atmospheric General Circulation Models (GCMs) exhibit a large spread in their predictions of atmospheric 2 CO E concentration at which a 2 K temperature rise with respect to preindustrial times is reached (Boucher et al., 2013). This uncertainty imposes a considerable cost on society (Hope, 2015).The largest contributor to this uncertainty concerns the response of low clouds to warming (Dufresne & Bony, 2008), as their impact is large (Boucher et al., 2013), but the turbulent phenomena that drive much of their evolution lie far below the resolutions that computational limits will allow GCMs to resolve in the coming decades . Such clouds are currently approximated by phenomenological unresolved scales models, "parameterizations", of considerably lower fidelity than the resolved simulation.

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Section: Toward Online Applicabilitymentioning

confidence: 59%

Section: Toward Online Applicabilitymentioning

confidence: 95%

Advancing Artificial Neural Network Parameterization for Atmospheric Turbulence Using a Variational Multiscale Model

Janssens

Hulshoff

2022

J Adv Model Earth Syst

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“…For example, Maulik et al [25,39] and Xie et al [40][41][42] have, respectively, developed local data-driven closures for 2D decaying homogeneous isotropic turbulence (2D-DHIT) and 3D incompressible and compressible turbulence using multilayer perceptron artificial neural networks (ANNs); also see [22,[43][44][45][46]. Zanna and Bolton [29,47], Beck and colleagues [26,48], Pawar et al [19], Guan et al [20], and Subel et al [49] developed non-local closures, e.g., using convolutional neural networks (CNNs), for ocean circulation, 3D-DHIT, 2D-DHIT, and forced 1D Burgers' turbulence, respectively. While finding outstanding results in a priori analyses, in many cases, these studies also reported instabilities in a posteriori analyses, requiring further modifications to the learnt closures for stabilization.…”

Section: Introductionmentioning

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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“…Large-eddy simulation (LES) is an effective approach which adopts the coarse mesh to merely resolve the large flow scales and model the effect of residual subgrid scales (SGS) on the resolved large scales [4,5,6,7]. Extensive SGS models are proposed to reconstruct the unclosed SGS stress in previous works, including the Smagorinsky model [8,9,10], the velocity-gradient model (VGM) [11], the scale-similarity model [12,13], the implicit LES (ILES) [14,15,16], the Reynolds-stress-constrained LES model [17], the datadriven models [18,19,20,21,22,23,24,25], etc. The Smagorinsky model is one of the commonly-used SGS models whose model coefficient for the original version is statically adjusted by the experimental and DNS data in the early stage.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Nonlinear Algebraic Models With Scale-Similarity Dynamic Procedure For Large-Eddy Simulation of Turbulence

Yuan

Wang

Xie

et al. 2021

Preprint

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A dynamic nonlinear algebraic model with scale-similarity dynamic procedure (DNAM-SSD) is proposed for subgrid-scale (SGS) stress in large-eddy simulation of turbulence. The model coefficients of the DNAM-SSD model are adaptively calculated through the scale-similarity relation, which greatly simplifies the conventional Germano-identity based dynamic procedure (GID). The a priori study shows that the DNAM-SSD model predicts the SGS stress considerably better than the conventional velocity gradient model (VGM), dynamic Smagorinsky model (DSM), dynamic mixed model (DMM) and DNAM-GID model at a variety of filter widths ranging from inertial to viscous ranges. The correlation coefficients of the SGS stress predicted by the DNAM-SSD model can be larger than 95% with the relative errors lower than 30%. In the a posteriori testings of LES, the DNAM-SSD model outperforms the implicit LES (ILES), DSM, DMM and DNAM-GID models without increasing computational costs, which only takes up half the time of the DNAM-GID model. The DNAM-SSD model accurately predicts plenty of turbulent statistics and instantaneous spatial structures in reasonable agreement with the filtered DNS data. These results indicate that the current DNAM-SSD model is attractive for the development of highly accurate SGS models for LES of turbulence.

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Data-driven subgrid-scale modeling of forced Burgers turbulence using deep learning with generalization to higher Reynolds numbers via transfer learning

Cited by 65 publications

References 53 publications

Advancing Artificial Neural Network Parameterization for Atmospheric Turbulence Using a Variational Multiscale Model

Advancing Artificial Neural Network Parameterization for Atmospheric Turbulence Using a Variational Multiscale Model

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

Dynamic Nonlinear Algebraic Models With Scale-Similarity Dynamic Procedure For Large-Eddy Simulation of Turbulence

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