Search

Summary: In this paper, we discuss a novel model reduction framework for linear structured dynamical systems. The transfer functions of these systems are assumed to have a special structure, for example, coming from second‐order linear systems or time‐delay systems, and they may also have parameter dependencies. Firstly, we investigate the connection between classic interpolation‐based model reduction methods with the reachability and observability subspaces of linear structured parametric systems. We show that if enough interpolation points are taken, the projection matrices of interpolation‐based model reduction encode these subspaces. Consequently, we are able to identify the dominant reachable and observable subspaces of the underlying system. Based on this, we propose a new model reduction algorithm combining these features and leading to reduced‐order systems. Furthermore, we discuss computational aspects of the approach and its applicability to a large‐scale setting. We illustrate the efficiency of the proposed approach with several numerical large‐scale benchmark examples. [ABSTRACT FROM AUTHOR]

Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection‐dominated problems. Nonlinear approaches have shown to outperform linear methods in terms of dimension reduction versus accuracy but, typically, come with a large computational overhead. In this work, we consider a quadratic reduction scheme which induces nonlinear structures that are well accessible to tensorized linear algebra routines. We discuss that nonintrusive approaches can be used to simultaneously reduce the complexity in the equations and propose an operator inference formulation that respects dynamics on nonlinear manifolds. [ABSTRACT FROM AUTHOR]