Methods of model reduction

The subject of model reduction addresses the need for low order approximations of large systems of time dependent differential equations. This need is especially important in control theory, where efficiency is key. A dynamical-systems-based approach to model reduction will be presented. The ideas originate from the nonlinear Galerkin methods from fluid dynamics. These methods have a natural extension to a general model reduction setting. A new method will be derived, with analytic and numerical results. Among the analytic results are order of accuracy bounds and model cases. The numerical results include model problems, as well as applications to fluid dynamics and materials science.