Nonlinear reduced-order modeling for three-dimensional turbulent flow by large-scale machine learning

Abstract

A large-scale machine learning-based nonlinear reduced-order modeling method was developed for a three-dimensional turbulent flow field (Re=1000) using a neural-network with unsupervised learning. First, a mode decomposition method was applied to three-dimensional flow field data using a convolutional-autoencoder-like neural network. Then, a reduced-order model (ROM) was constructed using long short-term memory neural networks (LSTMs). Consequently, it was demonstrated that the time evolution of the turbulent three-dimensional flow field can be simulated at a significantly lower cost (approximately three orders of magnitude) without a major loss in accuracy. However, neural-network-based mode decomposition for the three-dimensional flow field requires a huge computational cost in terms of calculation and memory usage. Therefore, a distributed machine-learning method was implemented using a hybrid parallelism scheme tailored to the network structure. Thus, it was possible to decompose 1.7 million cells of the three-dimensional flow field data into 64 modes and reproduce those with sufficient accuracy. In this study, a uniform flow around a circular cylinder model was used as a test case. To validate the method, the reduction performance of the proposed mode decomposition method was compared with the proper orthogonal decomposition (POD) method. Furthermore, the target flow field was reproduced using ROM, and the reconstruction accuracy was evaluated in terms of various criteria compared with the accuracy based on POD in conjunction with Galerkin projection method.