  We propose a projection-based model order reduction method for the solution
of parameter-dependent dynamical systems. The proposed method relies on the
construction of time-dependent reduced spaces generated from evaluations of the
solution of the full-order model at some selected parameters values. The
approximation obtained by Galerkin projection is the solution of a reduced
dynamical system with a modified flux which takes into account the time
dependency of the reduced spaces. An a posteriori error estimate is derived and
a greedy algorithm using this error estimate is proposed for the adaptive
selection of parameters values. The resulting method can be interpreted as a
dynamical low-rank approximation method with a subspace point of view and a
uniform control of the error over the parameter set.
