An Adaptive Pole-Matching Method for Interpolating Reduced-Order Models

TL;DR

This paper introduces an adaptive pole-matching method for interpolating reduced-order models, enabling efficient and accurate parametric modeling with a novel pole-matching process and adaptive framework.

Contribution

It presents a new adaptive pole-matching approach with an optimization-based matching process and a framework for building repository ROMs at selected parameter values.

Findings

Effective pole-matching via branch and bound algorithm.

Adaptive framework allows larger parameter steps with maintained accuracy.

Compatibility with various model reduction methods.

Abstract

An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two reduced-order models correspond to the same parametric pole. First, the pole-matching in the scenario of parameter perturbation is discussed. It is formulated as a combinatorial optimization problem and solved by a branch and bound algorithm. Then, an adaptive framework is proposed to build repository ROMs at adaptively chosen parameter values, which well represent the parameter domain of interest. To achieve this, we propose techniques including a predictor-corrector strategy and an adaptive refinement strategy, which enable us to use larger steps to explore the parameter domain of interest with good accuracy. The framework also consists of regression as an optional post-processing phase to further reduce the data storage. The advantages over other parametric reduced-order modeling approaches are, e.g., compatibility with any model order reduction method, constant size of the parametric reduced-order model with respect to the number of parameters, and capability to deal with complicated parameter dependency.