  Simulating fluid flows in different virtual scenarios is of key importance in
engineering applications. However, high-fidelity, full-order models relying,
e.g., on the finite element method, are unaffordable whenever fluid flows must
be simulated in almost real-time. Reduced order models (ROMs) relying, e.g., on
proper orthogonal decomposition (POD) provide reliable approximations to
parameter-dependent fluid dynamics problems in rapid times. However, they might
require expensive hyper-reduction strategies for handling parameterized
nonlinear terms, and enriched reduced spaces (or Petrov-Galerkin projections)
if a mixed velocity-pressure formulation is considered, possibly hampering the
evaluation of reliable solutions in real-time. Dealing with fluid-structure
interactions entails even higher difficulties. The proposed deep learning
(DL)-based ROMs overcome all these limitations by learning in a non-intrusive
way both the nonlinear trial manifold and the reduced dynamics. To do so, they
rely on deep neural networks, after performing a former dimensionality
reduction through POD enhancing their training times substantially. The
resulting POD-DL-ROMs are shown to provide accurate results in almost real-time
for the flow around a cylinder benchmark, the fluid-structure interaction
between an elastic beam attached to a fixed, rigid block and a laminar
incompressible flow, and the blood flow in a cerebral aneurysm.
