An efficient trajectory-based algorithm for model order reduction of nonlinear systems via localized projection and global interpolation

Abstract

Trajectory-based methods offer an effective methodology for generating the reduced-order models (ROMs) for nonlinear systems. These methods first sample on the state trajectories driven by the training inputs, then linearize and reduce the linearized systems around the sample points. However, these methods depend on an single global reduction subspace generated by combining all the projection subspaces of the sample points on the trajectories. In order to address this problem, a localized reduction technique has been proposed. This method weaves together a larger set of smaller localized ROMs for the trajectory samples. However, since these localized ROMs do not share the same coordinates, these localized ROMs cannot be interpolated to derive new ROMs. As a result, a large number of localized ROMs are needed to cover the necessary state space and guarantee adequate reduction accuracy. In this paper, we propose a new, efficient trajectory-based model order reduction algorithm for nonlinear systems via localized projection and global interpolation. We employ an efficient procedure to transform the smaller localized ROMs into a set of equivalent ROMs with nearly consistent global coordinate. The ROMs for the nonlinear systems are then obtained by globally interpolating the localized ROMs. Because we can perform interpolation between these localized ROMs, the required number of localized ROMs can be greatly reduced.