2D turbulence closures for the barotropic jet instability simulation

Perezhogin, Pavel

doi:10.1515/rnam-2020-0003

Cited by 2 publications

(1 citation statement)

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“…( 8)), we can also modify the loss function to combine structural and functional modeling approaches to enhance the performance of CNN in the small-data regime. For example, in 2D turbulence, the SGS enstrophy transfer is critical in maintaining the accuracy and stability of LES [20,39,95]. Therefore, capturing the correct SGS enstrophy transfer ωΠ in a CNN can be important for its performance.…”

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

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

confidence: 99%