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In this paper, we introduce a modular deep neural network (DNN) framework fordata-driven reduced order modeling of dynamical systems relevant to fluidflows. We propose various deep neural network architectures which numericallypredict evolution of dynamical systems by learning from either using discretestate or slope information of the system. Our approach has been demonstratedusing both residual formula and backward difference scheme formulas. However,it can be easily generalized into many different numerical schemes as well. Wegive a demonstration of our framework for three examples: (i) Kraichnan-Orszagsystem, an illustrative coupled nonlinear ordinary differential equations, (ii)Lorenz system exhibiting chaotic behavior, and (iii) a non-intrusive modelorder reduction framework for the two-dimensional Boussinesq equations with adifferentially heated cavity flow setup at various Rayleigh numbers. Using onlysnapshots of state variables at discrete time instances, our data-drivenapproach can be considered truly non-intrusive, since any prior informationabout the underlying governing equations is not required for generating thereduced order model. Our \textit{a posteriori} analysis shows that the proposeddata-driven approach is remarkably accurate, and can be used as a robustpredictive tool for non-intrusive model order reduction of complex fluid flows.

A deep learning enabler for non-intrusive reduced order modeling of fluid flows