Mechanisms of a Convolutional Neural Network for Learning Three-dimensional Unsteady Wake Flow

Abstract

In the present study, a convolutional neural network (CNN) system which consists of multiple multi-resolution CNNs to predict future three-dimensional unsteady wake flow using flow fields in the past occasions is developed. Mechanisms of the developed CNN system for prediction of wake flow behind a circular cylinder are investigated in two flow regimes: the three-dimensional wake transition regime and the shear-layer transition regime. Understanding of mechanisms of CNNs for learning fluid dynamics is highly necessary to design the network system or to reduce trial-and-errors during the network optimization. Feature maps in the CNN system are visualized to compare flow structures which are extracted by the CNN system from flow in the two flow regimes. In both flow regimes, feature maps are found to extract similar sets of flow structures such as braid shear-layers and shedding vortices. A Fourier analysis is conducted to investigate mechanisms of the CNN system for predicting wake flow in flow regimes with different wavenumber characteristics. It is found that a convolution layer in the CNN system integrates and transports wavenumber information from flow to predict the dynamics.Characteristics of the CNN system for transporting input information including time histories of flow variables are analyzed by assessing contributions of each flow variable and time history to feature maps in the CNN system. Structural similarities among feature maps in the CNN system are calculated to reveal the number of feature maps that contain similar flow structures.By reducing feature maps which contain similar flow structures, it is also able to successfully reduce the number of weights to learn in the CNN system without affecting prediction performance.

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