A Machine Learning Model for Unsteady Wake Dynamics

This work introduces a novel physical model for laminar wake-body interaction systems by learning low-dimensional approximation. Of particular interest is to predict a long time series of unsteady flow dynamics using a learned low-dimensional model. We use convolutional neural networks (CNN) to learn wake-body interaction dynamics, which assemble layers of linear convolutions with nonlinear activations to extract low-dimensional features. We first project the high-fidelity time series data from the finite element Navier-Stokes solver to a low-dimensional subspace using proper orthogonal decomposition (POD). The time-dependent coefficients of the POD subspace are mapped to the flow field via a CNN with nonlinear rectification, and the CNN is trained using stochastic gradient descent method to predict the POD time coefficients when a new flow field is fed to it. The mean flow field, POD basis vectors and the trained CNN are used to predict the long time series of the flow fields and results are compared with the full-order simulation results. POD-CNN predictions maintain a remarkable accuracy throughout the long time series for the entire fluid domain including a highly nonlinear near wake region.