Data-driven prediction of unsteady wake flow using neural networks

Abstract

The objective of the present study is to investigate capabilities and mechanisms of data-driven methods for predicting unsteady flow fields using neural networks. Deep learning algorithms based on convolutional neural networks have been developed for predicting two- and three-dimensional unsteady flow fields over a circular cylinder.

To investigate capabilities of deep learning algorithms for predicting two-dimensional unsteady flow fields, data of two-dimensional slices of unsteady flow over a circular cylinder are trained and predicted using four different convolutional neural network systems: generative adversarial networks with and without consideration of conservation laws and multi-resolution convolutional neural networks with and without consideration of conservation laws. Flow fields at future occasions are predicted based on information of flow fields at previous occasions, where the predictions have been conducted on flow fields at Reynolds numbers that were not informed during training. Physical loss functions are proposed to explicitly impose information of conservation of mass and momentum to convolutional neural network systems, and an adversarial training is applied to extract features of fluid dynamics in an unsupervised manner. Effects of the proposed physical loss functions and adversarial training on predicted flow fields, and the captured and missed flow physics from two-dimensional unsteady predictions of flow fields are investigated. The two-dimensional large-scale vortex dynamics predicted by the convolutional neural network systems is in favorable agreement with those computed by numerical simulations.

Capabilities and mechanisms of a deep learning algorithm for predicting three-dimensional unsteady flow have been investigated by developing a convolutional neural network system that predicts future three-dimensional unsteady wake flow using flow fields in the past occasions. Mechanisms of the developed convolutional neural network system for prediction of three-dimensional wake flow behind a circular cylinder are investigated in two flow regimes: the three-dimensional wake transition regime and the shear-layer transition regime. Feature maps in the convolutional neural network system are visualized to compare flow structures which are extracted by the convolutional neural network 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 convolutional neural network system for predicting wake flow in flow regimes with different wavenumber characteristics. It is found that convolution layers in the convolutional neural network system integrate and transport wavenumber information from flow to predict the dynamics. Characteristics of the convolutional neural network 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 convolutional neural network system. Structural similarities among feature maps in the convolutional neural network 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 found to be able to reduce the number of weights to learn in the convolutional neural network system without affecting the prediction performance.