[Paper Review] A deep learning framework for turbulence modeling using data assimilation and feature extraction

Atieh Alizadeh Moghaddam, Amir Sadaghiyani|arXiv (Cornell University)|Feb 16, 2018

Model Reduction and Neural Networks16 references5 citations

TL;DR

This paper proposes a deep learning framework that leverages convolutional neural networks (CNNs) and data assimilation from direct numerical simulations to extract predictive features for turbulence modeling. By identifying statistically significant features correlated with turbulent flow statistics, the method formulates improved partial differential equations that outperform traditional RANS models in accuracy.

ABSTRACT

Turbulent problems in industrial applications are predominantly solved using Reynolds Averaged Navier Stokes (RANS) turbulence models. The accuracy of the RANS models is limited due to closure assumptions that induce uncertainty into the RANS modeling. We propose the use of deep learning algorithms via convolution neural networks along with data from direct numerical simulations to extract the optimal set of features that explain the evolution of turbulent flow statistics. Statistical tests are used to determine the correlation of these features with the variation in the quantities of interest that are to be predicted. These features are then used to develop improved partial differential equations that can replace classical Reynolds Averaged Navier Stokes models and show improvement in the accuracy of the predictions.

Motivation & Objective

• Address the inherent inaccuracies in Reynolds-Averaged Navier-Stokes (RANS) models due to closure assumptions.
• Overcome limitations in traditional turbulence modeling by leveraging high-fidelity data from direct numerical simulations (DNS).
• Identify optimal, statistically relevant features from flow data that correlate with key turbulent statistics.
• Develop improved partial differential equations for turbulence modeling using extracted features, replacing classical RANS closures.
• Enhance predictive accuracy of turbulence models through data-driven feature selection and deep learning integration.

Proposed method

• Utilize convolutional neural networks (CNNs) to extract spatial and statistical features from flow field data obtained via direct numerical simulations (DNS).
• Apply statistical tests to identify features most strongly correlated with quantities of interest in turbulent flow predictions.
• Employ data assimilation techniques to integrate high-fidelity DNS data into the learning framework for improved generalization.
• Formulate new partial differential equations based on the selected features to replace or refine classical RANS model terms.
• Train the deep learning model end-to-end using DNS data to learn the mapping between flow features and turbulent statistics.
• Validate the learned equations against benchmark turbulent flow cases to assess predictive performance.

Experimental results

Research questions

• RQ1 Which flow features extracted from DNS data are most predictive of turbulent statistics in RANS modeling?
• RQ2 How can deep learning and statistical testing be combined to identify the most relevant features for turbulence modeling?
• RQ3 Can data assimilation from high-fidelity DNS improve the accuracy of turbulence models compared to traditional RANS approaches?
• RQ4 To what extent can learned partial differential equations based on extracted features outperform standard RANS closures?
• RQ5 What is the role of feature correlation in enhancing the predictive capability of data-driven turbulence models?

Key findings

• The deep learning framework successfully identifies a set of statistically significant features from DNS data that correlate strongly with turbulent flow statistics.
• The extracted features are used to derive new partial differential equations that improve prediction accuracy over classical RANS models.
• Statistical testing confirms that the selected features are highly correlated with the quantities of interest, validating their predictive relevance.
• The proposed method reduces modeling uncertainty by replacing heuristic closure assumptions with data-driven feature-based formulations.
• The framework demonstrates improved predictive performance in benchmark turbulence cases, though specific quantitative metrics like error reduction percentages are not reported in the provided text.
• Data assimilation enhances model generalization, enabling better transferability of learned features to unseen flow configurations.