Deep Neural Networks for Reduced Order Models for Fluid Flows

We present two numerical methodologies for construction of reduced order models, ROMs, of fluid flows through deep neural networks, DNNs. Here, the neural networks are used for regression and the frameworks are implemented in two contexts: one employs deep feedforward neural networks using a procedure similar to the sparse identification of non-linear dynamics algorithm, SINDy, and another is implemented using convolutional neural networks directly to the flow snapshots. The methods are tested on the reconstruction of a turbulent flow computed by a large eddy simulation of a plunging airfoil under dynamic stall. The reduced order models are able to capture the most energetic dynamics of dynamic stall including the leading edge stall vortex and the subsequent trailing edge vortex. The numerical framework allows the prediction of the flowfield beyond the training window and we demonstrate the robustness of the current ROMs constructed via deep neural networks through a comparison with sparse regression. The DNN approaches are able to learn transient features of the flow and present more accurate and stable long-term predictions compared to sparse regression.