Development of a large-eddy simulation subgrid model based on artificial neural networks: a case study of turbulent channel flow

Stoffer, Robin; Leeuwen, Caspar M. van; Podareanu, Damian; Codreanu, Valeriu; Veerman, Menno; Janssens, Martin; Hartogensis, Oscar; Heerwaarden, Chiel C. van

doi:10.5194/gmd-14-3769-2021

Cited by 15 publications

(9 citation statements)

References 51 publications

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“…One approach is to train ML models to predict subgrid forcing (e.g., S q ) but incorporate a numerical divergence operation into their architectures (e.g., as the final layer of a neural network, see Zanna and Bolton [2020]). Another is to diagnose a different quantity whose divergence equals the subgrid forcing (Pawar et al., 2020; Stoffer et al., 2021; Yuval et al., 2021), train ML models to predict this quantity (i.e., the subgrid flux) directly, and compute divergences outside the learned model as part of the implementation of parameterization.…”

Section: Diagnosing Subgrid Forcingmentioning

confidence: 99%

Benchmarking of Machine Learning Ocean Subgrid Parameterizations in an Idealized Model

Ross

Perezhogin

Fernandez‐Granda

et al. 2023

J Adv Model Earth Syst

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Current state-of-the-art climate models solve geophysical fluid equations on horizontal grids of size 25 km and coarser. Models at this resolution are not able to accurately and sufficiently resolve processes with physical length scales smaller than the model grid, for example, convection in the atmosphere and mesoscale eddies in the ocean. Since increases in computational power will likely not enable climate models to resolve these processes before the effects of climate change ensue (Fox-Kemper et al., 2014;Schneider et al., 2017), we must represent subgrid-scale (SGS) processes with closure models, also known as parameterizations. Yet, these SGS models are some of the largest sources of bias and uncertainties in climate simulations: for example, insufficient representations of transient eddies cause biases in modeled currents and sea surface temperature in the ocean (Griffies et al., 2015;Hewitt et al., 2020), and the precipitation pattern is strongly sensitive to the different subgrid cloud closures, thereby causing significant errors in climate projections (Stevens & Bony, 2013). Therefore, developing robust parameterizations remains an important task toward reliable climate projections.

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Section: Diagnosing Subgrid Forcingmentioning

confidence: 99%

Benchmarking of Machine Learning Ocean Subgrid Parameterizations in an Idealized Model

Ross

Perezhogin

Fernandez‐Granda

et al. 2023

J Adv Model Earth Syst

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“…The performance of neural network-based SGS models is compared with the widely used dynamic Smagorinsky model (DSM) [61,62]. The a posteriori deployment is a rigorous task for any data-driven SGS model due to the presence of numerical instabilities, and the challenges and remedies have been highlighted in many studies [12,15,22,23,[86][87][88]. For example, Maulik et al [15] and Zhou et al [88] achieved the stable LES results by truncating SGS source term corresponding to negative eddy viscosity.…”

Section: B a Posteriori Deploymentmentioning

confidence: 99%

“…Guan et al [22] provided sufficient amount of data during training to obtain a stable a posteriori results. While the exact reason for this behavior is unknown, several issues such as error accumulation, aliasing errors, numerical instability, extrapolation beyond the training data, chaotic nature of turbulence, presence of multiple attractors might be responsible for unstable a posteriori simulation [6,23,38,87].…”

Section: B a Posteriori Deploymentmentioning

confidence: 99%

“…For example, Maulik et al [15] and Zhou et al [88] achieved the stable LES results by truncating SGS source term corresponding to negative eddy viscosity. Stoffer et al [87] attained stable a posteriori results by resorting to artificially introducing additional dissipation (via eddy-viscosity models). Guan et al [22] provided sufficient amount of data during training to obtain a stable a posteriori results.…”

Section: B a Posteriori Deploymentmentioning

confidence: 99%

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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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“…In a priori (offline) tests, in which the accuracy of the SGS model in estimating the SGS term as a function of the resolved flow is evaluated, some of these studies have found the data-driven SGS models to accurately account for inter-scale transfers (including backscattering) and outperform physics-based models such as SMAG and DSMAG [7,56,75,120,122]. However, most of the same studies have also found that in a posteriori (online) tests, in which the data-driven SGS model is coupled with a coarse-resolution numerical solver, the LES model is unstable, leading to numerical blow-up or physically unrealistic flows [4,5,44,56,98,115,120,122]. While the reason(s) for these instabilities remain unclear, a number of remedies have been proposed, e.g., post-processing of the trained SGS model to remove backscattering or to attenuate the SGS feedback into the numerical solver, or combining the data-driven model with an eddy viscosity model [4,56,120,122] (also, see the excellent review by Beck and Kurz [5]).…”

Section: Introductionmentioning

confidence: 99%

Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher Re via transfer learning

Guan,

Chattopadhyay,

Subel

et al. 2021

Preprint

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There is a growing interest in developing data-driven subgrid-scale (SGS) models for largeeddy simulation (LES) using machine learning (ML). In a priori (offline) tests, some recent studies have found ML-based data-driven SGS models that are trained on high-fidelity data (e.g., from direct numerical simulation, DNS) to outperform baseline physics-based models and accurately capture the inter-scale transfers, both forward (diffusion) and backscatter. While promising, instabilities in a posteriori (online) tests and inabilities to generalize to a different flow (e.g., with a higher Reynolds number, Re) remain as major obstacles in broadening the applications of such data-driven SGS models. For example, many of the same aforementioned studies have found instabilities that required often ad-hoc remedies to stabilize the LES at the expense of reducing accuracy. Here, using 2D decaying turbulence as the testbed, we show that deep fully convolutional neural networks (CNNs) can accurately predict the SGS forcing terms and the inter-scale transfers in a priori tests, and if trained with enough samples, lead to stable and accurate a posteriori LES-CNN. Further analysis attributes these instabilities to the disproportionally lower accuracy of the CNNs in capturing backscattering when the training set is small. We also show that transfer learning, which involves re-training the CNN with a small amount of data (e.g., 1%) from the new flow, enables accurate and stable a posteriori LES-CNN for flows with 16× higher Re (as well as higher grid resolution if needed). These results show the promise of CNNs with transfer learning to provide stable, accurate, and generalizable LES for practical use.

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Development of a large-eddy simulation subgrid model based on artificial neural networks: a case study of turbulent channel flow

Cited by 15 publications

References 51 publications

Benchmarking of Machine Learning Ocean Subgrid Parameterizations in an Idealized Model

Benchmarking of Machine Learning Ocean Subgrid Parameterizations in an Idealized Model

Frame invariant neural network closures for Kraichnan turbulence

Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher Re via transfer learning

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