For linear dynamical systems, model reduction has achieved great success. In the case of linear dynamics, we know how to construct, at a modest cost, (locally) optimal, input-independent reduced models; that is, reduced models that are uniformly good over all inputs having bounded energy. In addition, in some cases we can achieve this goal using only input/output data without a priori knowledge of internal dynamics. Even though model reduction has been successfully and effectively applied to nonlinear dynamical systems as well, in this setting, bot the reduction process and the reduced models are input dependent and the high fidelity of the resulting approximation is generically restricted to the training input/data. In this talk, we will offer remedies to this situation.
- Computational Mathematics and Applications Seminar