The Effect of Problem Perturbations on Nonlinear Dynamical Systems and their Reduced-Order Models

Reduced order models are used extensively in many areas of science and engineering for simulation, design, and control. Reduction techniques for nonlinear dynamical systems produce models that depend strongly on the nominal set of parameters for which the reduction is carried out. In this paper we address the following two questions: “What is the effect of perturbations in the problem parameters on the output functional of a nonlinear dynamical system?” and “To what extent does the reduced order model capture this effect?”