  The basis generation in reduced order modeling usually requires multiple
high-fidelity large-scale simulations that could take a huge computational
cost. In order to accelerate these numerical simulations, we introduce a
FOM/ROM hybrid approach in this paper. It is developed based on an a posteriori
error estimation for the output approximation of the dynamical system. By
controlling the estimated error, the method dynamically switches between the
full-order model and the reduced-oder model generated on the fly. Therefore, it
reduces the computational cost of a high-fidelity simulation while achieving a
prescribed accuracy level. Numerical tests on the non-parametric and parametric
PDEs illustrate the efficacy of the proposed approach.
