Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow

Abstract

We investigate the applicability of machine learning based reduced order model (ML-ROM) to threedimensional complex flows. As an example, we consider a turbulent channel flow at the friction Reynolds number of Re τ = 110 in a minimum domain which can maintain coherent structures of turbulence. Training data set are prepared by direct numerical simulation (DNS). The present ML-ROM is constructed by combining a three-dimensional convolutional neural network autoencoder (CNN-AE) and a long short-term memory (LSTM). The CNN-AE works to map high-dimensional flow fields into a low-dimensional latent space. The LSTM is then utilized to predict a temporal evolution of the latent vectors obtained by the CNN-AE. The combination of CNN-AE and LSTM can represent the spatio-temporal high-dimensional dynamics of flow fields by only integrating the temporal evolution of the low-dimensional latent dynamics. The reproduced turbulent flow fields by the present ML-ROM show statistical agreement with the reference DNS data in time-ensemble sense, which can also be found through an orbit-based analysis. The influences on vortical structures over the domain and a time interval for temporal prediction for the ML-ROM performance are also investigated. The potential and limitation of the present ML-ROM for turbulence analysis are discussed at the end of our presentation.

Convolutional neural networks for fluid flow analysis: toward effective metamodeling and low-dimensionalization

“…where G = H/2 (where • represents the operation of rounding down the value to the nearest decimal), H is width and height of the filter, M is the number of input channel, n is the number of output channel, b is a bias, and ϕ is an activation function, respectively. Note that we showed the two-dimensional operation above since twodimensional flows are only handled through the present study, although its extension to three-dimensional flows are rather straightforward 27,46 albeit computationally more expensive. The nonlinear activation function ϕ enables a machine learning model to account for nonlinearlities into its estimation.…”

“…For instance, the work on superresolution analysis introduced above 10 reported the importance of the utilization of multi-size filters inside CNNs so as to account for a wide range of scales included in turbulence. The similar idea can also be found in the construction of NN-based reduced order modeling 27,28 and surrogate models for high-fidelity simulations 29 . Otherwise, several reports utilize additional scalar inputs which highly relates to fluid flow phenomena, e.g., angle of attack, Reynolds number, and bluff body shapes, to improve the estimation or low-dimensionalization abilities of CNNs [30][31][32][33][34][35][36][37][38] .…”

“…An AE 50 is used to map high-dimensional data into low-dimensional feature space referred to as latent vector. In particular, CNN-AE, an AE with convolutional layers, is known as a good candidate to extract key features of two-dimensional images 18,27,31,32,56 . An encoder part -the first half of CNN-AE -contains the pooling layers and the convolutional layers to extract key features of input data while reducing the dimension of data.…”

Model order reduction with neural networks: Application to laminar and turbulent flows

“…Hasegawa et al [37,38] proposed a CNN-LSTM based ROM to predict the temporal evolution of unsteady flows around a bluff body by following only the time series of low-dimensional latent space. The method is also extended to the examination for Reynolds number dependence [39] and turbulent flows [40]. With regard to the perspective on understanding latent modes obtained by AE, Murata et al [41] suggested a customized AE referred to as mode-decomposing CNN-AE.…”