  Reduced order modeling (ROM) provides an efficient framework to compute
solutions of parametric problems. Basically, it exploits a set of precomputed
high-fidelity solutions --- computed for properly chosen parameters, using a
full-order model --- in order to find the low dimensional space that contains
the solution manifold. Using this space, an approximation of the numerical
solution for new parameters can be computed in real-time response scenario,
thanks to the reduced dimensionality of the problem. In a ROM framework, the
most expensive part from the computational viewpoint is the calculation of the
numerical solutions using the full-order model. Of course, the number of
collected solutions is strictly related to the accuracy of the reduced order
model. In this work, we aim at increasing the precision of the model also for
few input solutions by coupling the proper orthogonal decomposition with
interpolation (PODI) --- a data-driven reduced order method --- with the active
subspace (AS) property, an emerging tool for reduction in parameter space. The
enhanced ROM results in a reduced number of input solutions to reach the
desired accuracy. In this contribution, we present the numerical results
obtained by applying this method to a structural problem and in a fluid
dynamics one.
