# A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numbers

arXiv: https://arxiv.org/abs/2211.00601 · HTML: https://mlsanity.com/paper/2211.00601/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 59 references that are in the map.
- First posted on arXiv 1 Nov 2022.

## Builds on (most cited first, 5 of 5)

- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Ensemble Kalman Inversion: A Derivative-Free Technique For Machine Learning Tasks](https://mlsanity.com/paper/1808.03620/) (2018)
- [Machine Learning-augmented Predictive Modeling of Turbulent Separated Flows over Airfoils](https://mlsanity.com/paper/1608.03990/) (2016)
- [A regularizing iterative ensemble Kalman method for PDE-constrained inverse problems](https://mlsanity.com/paper/1505.03876/) (2015)
- [Adaptive regularisation for ensemble Kalman inversion](https://mlsanity.com/paper/2006.14980/) (2020)

## Built on by (most cited first, 1 of 1)

- [Distributed physics-informed neural networks via domain decomposition for fast flow reconstruction](https://mlsanity.com/paper/2602.15883/) (2026)

## Abstract (arXiv)

In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of high-fidelity data and the convergence and stability problem in the coupling process of turbulence models and the RANS solvers. In this paper, we propose an improved ensemble kalman inversion method as a unified approach of data assimilation and turbulence modeling for separated flows at high Reynolds numbers. The trainable parameters of the DNN are optimized according to the given experimental surface pressure coefficients in the framework of mutual coupling between the RANS equations and DNN eddy-viscosity models. In this way, data assimilation and model training are combined into one step to get the high-fidelity turbulence models agree well with experiments efficiently. The effectiveness of the method is verified by cases of separated flows around airfoils(S809) at high Reynolds numbers. The results show that through joint assimilation of vary few experimental states, we can get turbulence models generalizing well to both attached and separated flows at different angles of attack. The errors of lift coefficients at high angles of attack are significantly reduced by more than three times compared with the traditional SA model. The models obtained also perform well in stability and robustness.