Trajectory based methods for nonlinear MOR: Review and perspectives

Trajectory based methods constitute an important class amongst the techniques for Model Order Reduction (MOR) of nonlinear dynamical systems. This is an attempt to trace their development, right from the original formulation to the current state of the art. Outstanding issues that pose challenges and possible directions in which solutions can be found are discussed. Relevant insights from the authors experience in using these methods for nonlinear MOR are given.