[Paper Review] Convolutional-network models to predict wall-bounded turbulence from wall quantities

Luca Guastoni, Alejandro Güemes+5 more|arXiv (Cornell University)|Jun 22, 2020

Fluid Dynamics and Turbulent Flows70 references22 citations

TL;DR

This study develops two convolutional neural network (CNN) models—FCN and FCN-POD—that predict two-dimensional velocity-fluctuation fields in turbulent channel flow using only wall-shear stress and wall pressure as inputs. The models outperform linear methods like EPOD, with FCN excelling near the wall and FCN-POD performing better at higher wall-normal distances, while transfer learning enables high performance with reduced training data.

ABSTRACT

Two models based on convolutional neural networks are trained to predict the two-dimensional velocity-fluctuation fields at different wall-normal locations in a turbulent open channel flow, using the wall-shear-stress components and the wall pressure as inputs. The first model is a fully-convolutional neural network (FCN) which directly predicts the fluctuations, while the second one reconstructs the flow fields using a linear combination of orthonormal basis functions, obtained through proper orthogonal decomposition (POD), hence named FCN-POD. Both models are trained using data from two direct numerical simulations (DNS) at friction Reynolds numbers $Re_τ = 180$ and $550$. Thanks to their ability to predict the nonlinear interactions in the flow, both models show a better prediction performance than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between input and output fields. The performance of the various models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. The FCN exhibits the best predictions closer to the wall, whereas the FCN-POD model provides better predictions at larger wall-normal distances. We also assessed the feasibility of performing transfer learning for the FCN model, using the weights from $Re_τ=180$ to initialize those of the $Re_τ=550$ case. Our results indicate that it is possible to obtain a performance similar to that of the reference model up to $y^{+}=50$, with $50\%$ and $25\%$ of the original training data. These non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence.

Motivation & Objective

• To develop data-driven, non-intrusive models that predict full turbulent velocity-fluctuation fields from minimal wall measurements.
• To overcome limitations of linear models like EPOD in capturing nonlinear interactions in wall-bounded turbulence.
• To evaluate the performance of deep learning models in reconstructing instantaneous flow fields, statistics, and spectral content.
• To investigate transfer learning feasibility for reducing training data and time requirements across Reynolds numbers.
• To enable real-time, low-cost flow sensing for closed-loop control applications in turbulent flows.

Proposed method

• A fully-convolutional neural network (FCN) is trained to directly predict two-dimensional velocity-fluctuation fields from wall-shear-stress and wall-pressure inputs.
• A second model, FCN-POD, reconstructs the flow fields by combining learned coefficients with orthonormal basis functions derived from proper orthogonal decomposition (POD).
• Both models are trained on direct numerical simulation (DNS) data at Reτ = 180 and 550, using a loss function based on instantaneous error in the predicted fields.
• The models are evaluated using instantaneous field predictions, turbulence statistics (RMS, Reynolds stresses), and power-spectral densities.
• Transfer learning is applied by initializing the FCN model at Reτ = 550 using pre-trained weights from Reτ = 180 to reduce data and training time.
• Model efficiency is enhanced via pruning, enabling deployment on low-power hardware for real-time applications.

Experimental results

Research questions

• RQ1 Can convolutional neural networks accurately predict the full two-dimensional velocity-fluctuation fields in wall-bounded turbulence using only wall-shear stress and wall pressure as inputs?
• RQ2 How do the performance of the FCN and FCN-POD models compare to the extended proper orthogonal decomposition (EPOD) method in predicting flow structures, statistics, and spectra?
• RQ3 Does transfer learning from a lower Reynolds number (Reτ = 180) to a higher one (Reτ = 550) enable high prediction accuracy with significantly reduced training data?
• RQ4 Where are the FCN and FCN-POD models most accurate in the wall-normal direction, and what explains the difference in performance across y⁺ locations?
• RQ5 Can the trained models be made computationally efficient enough for real-time deployment in control systems?

Key findings

• The FCN model achieves superior prediction accuracy near the wall (up to y⁺ = 50), particularly in capturing instantaneous flow structures and local fluctuations.
• The FCN-POD model provides better predictions at larger wall-normal distances (e.g., y⁺ = 100), demonstrating improved representation of large-scale flow features.
• Both models outperform the linear EPOD method in predicting turbulence statistics and power-spectral densities, confirming their ability to model nonlinear interactions.
• Transfer learning enables the FCN model trained at Reτ = 550 to achieve performance comparable to the reference model when using only 50% and 25% of the original training data.
• The models are computationally efficient after pruning, making them suitable for real-time deployment on low-power hardware.
• The results demonstrate that deep learning models trained on DNS data can serve as accurate, non-intrusive sensors for closed-loop control of wall-bounded turbulence.