aiqbench analysis
This research introduces a solver-aware deep learning framework that trains turbulence closure models a-priori using sparse DNS data, effectively bypassing the high computational costs and solver modification requirements of traditional a-posteriori methods. By explicitly conditioning the model on numerical schemes, the approach maintains deployment stability while systematically tracking discretization errors across different solvers. This advancement offers a practical pathway for integrating neural networks into fluid dynamics simulations without compromising the robustness required for real-world applications.
Deep Learning of Solver-Aware Turbulence Closures from Nudged LES Dynamics
arXiv:2604.23874v3 Announce Type: replace-cross Abstract: The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data. 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 low-pass filter. Closures trained in this a-priori manner frequently lead to unstable deployments due to the mismatch between the assumed filter and the effect of numerical discretizations and coarse-graining. In comparison, while typically stable during deployment, a-posteriori learning incurs high computational costs due to the need to backpropagate through a large eddy simulation (LES) solver. Furthermore, a-posteriori methods are challenging to apply broadly since they require significant modification of existing solvers. Finally, both approaches are limited when generalization is desired across different numerical schemes with their implicit filtering characteristics. In this work, we present a deep-learning approach for turbulence closure modeling built on the continuous data assimilation framework. Our approach enables the a-priori training of closures using sparsely observed DNS data without modifying or differentiating through the LES solver, while preserving stability during deployment for the recovery of invariant statistics. We focus on the model's ability to adapt to different discretizations by explicitly conditioning it on the numerical scheme. We use two- and three-dimensional canonical cases to test our framework and show that the learned correction systematically tracks the discretization error of the coarse solver.
Abstract:The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data. 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 low-pass filter. Closures trained in this a-priori manner frequently lead to unstable deployments due to the mismatch between the assumed filter and the effect of numerical discretizations and coarse-graining. In comparison, while typically stable during deployment, a-posteriori learning incurs high computational costs due to the need to backpropagate through a large eddy simulation (LES) solver. Furthermore, a-posteriori methods are challenging to apply broadly since they require significant modification of existing solvers. Finally, both approaches are limited when generalization is desired across different numerical schemes with their implicit filtering characteristics. In this work, we present a deep-learning approach for turbulence closure modeling built on the continuous data assimilation framework. Our approach enables the a-priori training of closures using sparsely observed DNS data without modifying or differentiating through the LES solver, while preserving stability during deployment for the recovery of invariant statistics. We focus on the model's ability to adapt to different discretizations by explicitly conditioning it on the numerical scheme. We use two- and three-dimensional canonical cases to test our framework and show that the learned correction systematically tracks the discretization error of the coarse solver.
Fluid Dynamics (physics.flu-dyn); Machine Learning (cs.LG); Dynamical Systems (math.DS); Computational Physics (physics.comp-ph); Geophysics (physics.geo-ph)
arXiv:2604.23874 [physics.flu-dyn]
(or arXiv:2604.23874v3 [physics.flu-dyn] for this version)
Full text under the publisher's open licence · 267 words
Related coverage
Uncertainty-aware Multi-fidelity Closure via Conditional Normalizing Flows
arXiv · Jun 10, 2026
Uncertainty-aware Multi-fidelity Closure via Conditional Normalizing Flows
arXiv · Aug 24, 2026
Online learning of subgrid-scale models for quasi-geostrophic turbulence in planetary interiors
arXiv · Jul 29, 2026
Towards Deep Learning Surrogate for the Forward Problem in Electrocardiology: A Scalable Alternative to Physics-Based Models
arXiv · Jun 12, 2026