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