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We present a numerical methodology for construction of reduced order models,ROMs, of fluid flows through the combination of flow modal decomposition andregression analysis. Spectral proper orthogonal decomposition, SPOD, is appliedto reduce the dimensionality of the model and, at the same time, filter the PODtemporal modes. The regression step is performed by a deep feedforward neuralnetwork, DNN, and the current framework is implemented in a context similar tothe sparse identification of non-linear dynamics algorithm, SINDy. A discussionon the optimization of the DNN hyperparameters is provided for obtaining thebest ROMs and an assessment of these models is presented for a canonicalnonlinear oscillator and the compressible flow past a cylinder. Then, themethod is tested on the reconstruction of a turbulent flow computed by a largeeddy simulation of a plunging airfoil under dynamic stall. The reduced ordermodel is able to capture the dynamics of the leading edge stall vortex and thesubsequent trailing edge vortex. For the cases analyzed, the numericalframework allows the prediction of the flowfield beyond the training windowusing larger time increments than those employed by the full order model. Wealso demonstrate the robustness of the current ROMs constructed via deepfeedforward neural networks through a comparison with sparse regression. TheDNN approach is able to learn transient features of the flow and presents moreaccurate and stable long-term predictions compared to sparse regression.

Construction of Reduced Order Models for Fluid Flows Using Deep Feedforward Neural Networks