Discovery of Sparse Invariant Subgrid-Scale Closures via Dissipation-Controlled Training for Large Eddy Simulation on Anisotropic Grids

TL;DR

This paper introduces a sparse regression framework for turbulence SGS modeling that enforces invariance, incorporates anisotropy, and explicitly constrains energy dissipation, achieving accurate and computationally efficient closures.

Contribution

It develops a polynomial-based, sparsity-promoting SGS closure method that maintains physical invariance and generalizes well across flow regimes.

Findings

Sparse regression closures match neural network accuracy

Closures are simpler and computationally cheaper than neural networks

Explicit dissipation constraints improve stability and performance

Abstract

Neural networks offer highly expressive turbulence closures, yet their complexity obscures the physical mechanisms they aim to model, and their computational cost can limit their tractability. To address these limitations, we introduce a sparsity-promoting subgrid-scale (SGS) stress closure modeling framework that identifies explicit polynomial model forms using sparse regression. Candidate models are constructed through scaling a minimal tensor basis by a truncated polynomial expansion of invariant scalars, thereby enforcing fundamental invariance properties while regulating the highest order of admissible terms. Arbitrary filter anisotropy is incorporated to enable consistent representation of turbulent structures across computational grids with anisotropic scales and resolutions. We also explicitly constrain SGS energy dissipation during training to improve functional performance and promote numerical stability. The framework is trained on a small dataset of idealized turbulence and evaluated through a series of a priori and a posteriori tests. Sensitivity studies examine the effects of variations in model order and optimization penalties for regularization and dissipation across a range of canonical flow configurations. We also evaluate on a separated flow benchmark to assess generalizability to a more complex turbulent regime. In many cases, the sparse regression closures achieve predictive accuracy comparable to an invariance-preserving neural network while retaining markedly simpler parametric forms. Moreover, we demonstrate that the sparse closures can be trained and evaluated at a fraction of the cost of the neural network model.