Deep Learning of Solver-Aware Turbulence Closures from Nudged LES Dynamics

TL;DR

This paper introduces a novel deep learning approach for turbulence closure modeling in LES, inspired by continuous data assimilation, enabling stable, a-priori training without backpropagation through the solver.

Contribution

The work presents a new nudging-based deep learning method for turbulence closures that improves stability and generalization across different numerical schemes.

Findings

The proposed model captures ground-truth turbulence statistics effectively.

It maintains stability over long-term simulations without backpropagation.

The model adapts well to various numerical and temporal discretizations.

Abstract

Deep learning approaches have shown remarkable promise in turbulence closure modeling for large eddy simulations (LES). The differentiable physics paradigm uses the so-called a-posteriori approach for learning by embedding a neural network closure directly inside the solver and optimizing its learnable parameters against ground truth time-series data which may be observed sparsely. This addresses a key limitation of a-priori learning where direct numerical simulation (DNS) data is used to approximate the subgrid stress with the assumption of a filter. However, closures that are trained in this manner frequently lead to unstable deployments due to the mismatch between the assumed filter and the effect of numerical discretizations. However, a-posteriori learning incurs high computational costs due to the need to backpropagate gradients through an LES solver. Furthermore, a-posteriori methods are challenging to apply broadly since they require significant modification of existing solvers. Finally, these approaches have also been observed to be limited when generalization is desired across different numerical schemes. In this work, we discuss a novel approach for the deep learning of turbulence closure models motivated by the continuous data assimilation (CDA) approach (also known as nudging). Our approach enables a-priori training of closures for coarse-grid LES, treating DNS data as sparse observations. This approach enables the deep learning model to successfully learn the required forcing to capture the ground-truth statistics while maintaining long term stability without needing adjoints or backpropagation through the solver. We train and evaluate the model's ability to adapt to different numerical and temporal schemes. Additionally, we analyse the model behavior with varying numerical discretization errors and compare its predictions to traditional closure models.