Deep Learning Approach for Turbulence Closure Models Using Data Assimilation
Researchers have developed a deep learning approach for turbulence closure modeling that uses continuous data assimilation to train neural networks on sparse DNS data without requiring modification or differentiation through the LES solver. The method addresses longstanding trade-offs between a-priori learning, which is computationally cheap but often produces unstable deployments, and a-posteriori learning, which is stable but computationally expensive and solver-invasive. The framework could broaden the applicability of data-driven turbulence models across different numerical schemes and discretizations.
A team of researchers has proposed a turbulence closure modeling framework that combines deep learning with continuous data assimilation, aiming to overcome key limitations of existing a-priori and a-posteriori training paradigms. Traditional a-priori methods train neural networks directly on direct numerical simulation (DNS) data but frequently produce unstable models when deployed, because the assumed low-pass filter does not match the implicit filtering introduced by numerical discretizations. A-posteriori methods improve stability by embedding the neural network inside the solver during training, but require backpropagation through the full large eddy simulation (LES) solver, incurring high computational costs and demanding significant solver modification. The new approach allows a-priori-style training using sparsely observed DNS data while maintaining deployment stability and recovering correct invariant statistics. A distinctive feature is explicit conditioning of the model on the numerical scheme, enabling generalization across different discretizations. The framework was validated on two- and three-dimensional canonical fluid dynamics cases, where the learned correction was shown to systematically track the discretization error of the coarse solver.
What's missing
Generalization to more complex, industrially relevant geometries and flow regimes beyond canonical test cases has not yet been demonstrated. Long-term stability over extended simulation horizons and sensitivity to the sparsity level of the DNS observations are open questions not fully addressed in the abstract.
What different sources said
- arXiv cs.LGCenter
Deep Learning of Solver-Aware Turbulence Closures from Nudged LES Dynamics
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