MODEL ORDER REDUCTION OF LARGE-SCALE DYNAMICAL SYSTEMS

The discretization of physical equations in complex three-dimensional domains typically leads to the solution of large-scale systems of equations. The goal of model reduction is to replace these sets of large-scale equations by an alternative set of equations of much smaller dimension that nevertheless retains the main characteristics of the original equations. Reducing the dimensionality and complexity of a given large-scale system then typically leads to a much faster solution time. Therefore, it enables routine analysis, model predictive control, data-driven systems, embedded and real-time computing, and faster design optimization, statistical studies, and uncertainty quantification. Many of the aforementioned applications involve variations in the physical parameters and operating conditions, and therefore variations in the reduced-order models. This typically leads to an expensive offline phase in which these are trained in order to be accurate in the online phase over the entire parametric domain of interest.