Adaptive Sampling for Structure Preserving Model Order Reduction of Port-Hamiltonian Systems

TL;DR

This paper introduces an adaptive sampling strategy for structure-preserving model order reduction of port-Hamiltonian systems, reducing computational costs and improving accuracy over existing methods.

Contribution

It develops a new adaptive sampling approach that lowers computational demand and lessens the need for prior knowledge while maintaining high accuracy in structure-preserving MOR.

Findings

Effective reduction in computational demand.

High accuracy retained compared to other MOR algorithms.

Demonstrated success on a port-Hamiltonian benchmark system.

Abstract

We present an adaptive sampling strategy for the optimization-based structure preserving model order reduction (MOR) algorithm developed in [Schwerdtner, P. and Voigt, M. (2020). Structure preserving model order reduction by parameter optimization, Preprint arXiv:2011.07567]. This strategy reduces the computational demand and the required a priori knowledge about the given full order model, while at the same time retaining a high accuracy compared to other structure preserving but also unstructured MOR algorithms. A numerical study with a port-Hamiltonian benchmark system demonstrates the effectiveness of our method combined with its new adaptive sampling strategy. We also investigate the distribution of the sample points.