  Reduced Order Models (ROMs) have gained a great attention by the scientific
community in the last years thanks to their capabilities of significantly
reducing the computational cost of the numerical simulations, which is a
crucial objective in applications like real time control and shape
optimization. This contribution aims to provide a brief overview about such a
topic. We discuss both an intrusive framework based on a Galerkin projection
technique and non-intrusive approaches, including Physics Informed Neural
Networks (PINN), purely Data-Driven Neural Networks (DDNN), Radial Basis
Functions (RBF), Dynamic Mode Decomposition (DMD) and Gaussian Process
Regression (GPR). We also briefly mention geometrical parametrization and
dimensionality reduction methods like Active Subspaces (AS). Then we present
some results related to academic test cases as well as a preliminary
investigation related to an industrial application.
