Subgrid modelling for two-dimensional turbulence using neural networks

By Romit Maulik, Omer San, Adil Rasheed, Prakash Vedula. Journal of Fluid Mechanics, 2018

341 citations recorded by the source corpus.

In this investigation, a data-driven turbulence closure framework is introduced and deployed for the subgrid modelling of Kraichnan turbulence. The novelty of the proposed method lies in the fact that snapshots from high-fidelity numerical data are used to inform artificial neural networks for predicting the turbulence source term through localized grid-resolved information. In particular, our proposed methodology successfully establishes a map between inputs given by stencils of the vorticity and the streamfunction along with information from two well-known eddy-viscosity kernels. Through this we predict the subgrid vorticity forcing in a temporally and spatially dynamic fashion. Our study is both a priori and a posteriori in nature. In the former, we present an extensive hyper-parameter optimization analysis in addition to learning quantification through probability-density-function-based validation of subgrid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying two-dimensional turbulence test case in the presence of errors related to temporal and spatial discretization. Statistical assessments in the form of angle-averaged kinetic energy spectra demonstrate the promise of the proposed methodology for subgrid quantity inference. In addition, it is also observed that some measure of a posteriori error must be considered during optimal model selection for greater accuracy. The results in this article thus represent a promising development in the formalization of a framework for generation of heuristic-free turbulence closures from data.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7310355d4a5041930db8f6ba210ddaf5deb44e81

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Citations in the corpus

Unsupervised deep learning for super-resolution reconstruction of turbulence (2020, background): “It was then extended to other flows, such as 2D turbulence (Maulik et al. 2019) and homogeneous isotropic turbulence (Beck et al. 2019; Xie et al. 2019).”
Resolving and Parameterising the Ocean Mesoscale in Earth System Models (2020, background): “Different classes of submesoscale parameterisations, those specifically designed for use as subgrid schemes to carry forward cascades of energy, enstrophy, and tracer variance in mesoscale-resolving models, are in development [41, 161, 175, 176] and being prototyped in realistic simulations where th”
Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows (2020, methodology): “For instance, Murata et al. (2020) proposed a nonlinear mode decomposition technique using an autoencoder (Hinton & Salakhutdinov 2006) based on convolutional neural networks (CNN; LeCun et al.”
Machine learning–accelerated computational fluid dynamics (2021, neutral): “Including the numerical solver in the training loss ensures fully “modelconsistent” training where the model sees its own outputs as inputs (23, 34, 41), unlike typical “a priori” training where simulation is only performed offline.”
Enhancing computational fluid dynamics with machine learning (2021, methodology): “Maulik et al. [77] employed a multilayer perceptron (MLP) to predict the SGS model in an LES using high-ﬁdelity numerical data to train the model.”
Reynolds-averaged Navier–Stokes equations with explicit data-driven Reynolds stress closure can be ill-conditioned (2018, neutral): “2018) and subgrid-scale models (e.g., Vollant et al. 2017; Maulik & San 2017; Maulik et al. 2019; King et al. 2016) for turbulent flows, the conditioning in such models must be closely examined along with their a priori predictive performances.”
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective (2019, methodology): “A better approach on the integration ofML to physical processes has been demonstrated intuitively in [336] where the known physics is modeled using the established governing equations while the unknown physics is modeled using blackboxDNNor LSTMnetworks.”