Subgrid modelling for two-dimensional turbulence using neural networks

Abstract

In this investigation, a data-driven turbulence closure framework is introduced and deployed for the sub-grid 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 gridresolved 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 sub-grid 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 sub-grid predictions. In the latter, we analyse the performance of our framework for flow evolution in a classical decaying twodimensional 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 sub-grid 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.

A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence

“…The CNN mapping, on the other hand, seems more suitable for applications where a large amount of training data is available in the form of snapshots. While intelligent SGS modeling frameworks can model true SGS stresses accurately, they are prone to numerically unstable prediction in the a posteriori deployment as shown in recent studies [37,52]. To exploit the potential of these black-box models in safety critical applications, we further investigate their robustness in predicting eddy viscosity coefficient.…”

“…One more advantage of this approach is that numerical stability during the a posteriori deployment will be enforced. Maulik et al [37] noted that clipping of vorticity source term is required to attain the numerical stability during the deployment of data-driven SGS model. The similar observation was also found by Beck et al [52] for the decaying homogeneous isotropic turbulence problem.…”

“…Several studies have been conducted to model the dynamics of chaotic fluid flow using ML algorithms [25][26][27][28][29][30][31]. Recently there is a growing interest in using the physics of the problem in combination with the data-driven algorithms [28,[32][33][34][35][36][37][38]. The physics can be incorporated into these learning algorithms by adding a regularization term (based on governing equations) in loss function or modifying the neural network architecture to enforce certain physical constraints.In addition to reduced order modeling and chaotic dynamical systems, the turbulence closure problem has also benefited from the application of ML algorithms and has led to reducing uncertainties in .…”

Feature engineering and symbolic regression methods for detecting hidden physics from sparse sensor observation data

“…We can observe that SR approaches satisfactorily identify the value of the modelling constant c s , which controls reasonably well the right amount of dissipation needed to account for the unresolved small scales. We also highlight that several deep learning frameworks such as ANNs have been exploited for subgrid scale modelling for 2D Kraichnan turbulence [126][127][128] . The importance of feature selection can be seen in these works where different invariant kernels, like those listed in the feature library given in Eq.…”

Enabling real-time multi-messenger astrophysics discoveries with deep learning

“…In the same way that numerical relativity simulations of BBH mergers have been critical for the detection and characterization of these sources with GW observations, numerical relativity simulations of BNS and NSBH mergers are critical to get insights into the physical processes that may lead to the production of electromagnetic and astro-particle counterparts, and to better interpret MMA observations 67 . These modeling efforts do not currently benefit from DL, but recent studies have suggested the possibility to improve the efficiency and robustness of simulations, enabling the inclusion of detailed microphysics [68][69][70][71][72] , and a significance increase in the speed with which partial different equations are solved 73,74 .…”