In this work we will focus on recent advances in reduced order modelling for parametrized
problems in computational fluid dynamics, with a special attention to the case of
inverse problems, such as optimal flow control problems and data assimilation, and
multi-physics applications.Among the former, we will discuss applications arising in environmental marine sciences
and engineering, namely a pollutant control in the Gulf of Trieste, Italy and a solution
tracking governed by quasi-geostrophic equations describing North Atlantic Ocean dynamic.
Similar methodologies will also be employed in problems related to the modeling of
the cardiovascular system.Among the latter, we will present further recent developments on reduction of fluid-structure
interaction problems, based on our earlier work. Reduced order approaches for parametric
optimal flow control will also be applied in combination with domain decomposition
in view of further applications in multi-physics.This work is in collaboration with Y. Maday (UPMC Université Paris 06, France), L.
Jiménez-Juan (Sunnybrook Health Sciences Centre, Toronto, Canada), P. Triverio (University
of Toronto, Canada), R. Mosetti (National Institute of Oceanography and Applied Geophysics,