Convolutional-network models to predict wall-bounded turbulence from wall quantities

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 $R{e}_{\tau }=180$ 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 $R{e}_{\tau }=180$ to initialize those of the $R{e}_{\tau }=550$ 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.

31 pages, 17 figures

References in corpus (11)

• Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
• The role of artificial intelligence in achieving the Sustainable Development Goals
• Turbulence Modeling in the Age of Data
• A guide to convolution arithmetic for deep learning
• Super-resolution reconstruction of turbulent flows with machine learning
• Discovering physical concepts with neural networks
• Nonlinear mode decomposition with convolutional neural networks for fluid dynamics
• Deep Neural Networks for Data-Driven Turbulence Models
• Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors
• Logarithmic-layer turbulence: a view from the wall
• On the use of recurrent neural networks for predictions of turbulent flows

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