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

2026-04-26

AI Summary

This work addresses the challenges of deploying turbulence closure models in traditional large-eddy simulation (LES), where mismatch between filtering assumptions and numerical discretization often leads to instability, while a posteriori learning approaches suffer from high computational cost and poor generalization. The authors propose a novel prior-learning deep learning framework based on continuous data assimilation (nudging), which leverages sparse, high-fidelity direct numerical simulation (DNS) observations to train coarse-grid LES models. Crucially, this approach achieves long-term stable neural closures without requiring backpropagation through solver gradients or modifications to existing solvers. By introducing nudging into turbulence modeling for the first time, the method circumvents adjoint-based sensitivity analysis and enables generalization across different numerical schemes. Experiments demonstrate that the model accurately reproduces target statistical quantities across multiple discretization strategies, outperforms conventional closures, and exhibits strong robustness to discretization errors.

Technology Category

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• Machine Learning: Neuro-Symbolic Learning

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• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
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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.

Problem

• turbulence closure
• large eddy simulation
• deep learning
• numerical discretization
• generalization

Innovation

• continuous data assimilation
• turbulence closure
• deep learning
• large eddy simulation
• nudging