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

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 physics-agnostic CNNs trained in the big-data regime are accurate and stable, and outperform dynamic Smagorinsky (DSMAG) closures, their performances 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+EnsCon, 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. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

This study demonstrates 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. Three methods for incorporating physics were examined: data augmentation (DA), CNN with group convolutions (GCNN), and loss functions that enforce a global enstrophy-transfer conservation (EnsCon). The results show that DA, GCNN, and EnsCon can all produce accurate and stable data-driven closures in the small-data regime, with GCNN+EnsCon showing the best performance.