Interpolation among reduced‐order matrices to obtain parameterized models for design, optimization and probabilistic analysis

TLDR

Model reduction offers significant potential for design, optimization, and probabilistic analysis, yet incorporating parameter dependence into reduced‑order models remains challenging. This work proposes interpolating reduced‑order matrices to generate parameterized reduced‑order models. The authors build fast, full‑order‑independent ROMs by spline‑interpolating reduced‑order system matrices in both the original and Riemannian tangent spaces, compare this with Kriging of predicted outputs, and introduce a heuristic criterion for selecting the optimal interpolation space. The approach is validated on a steady‑state thermal design problem and on probabilistic Monte Carlo analysis of an unsteady contaminant transport problem. © 2009 John Wiley & Sons, Ltd.

Abstract

Abstract Model reduction has significant potential in design, optimization and probabilistic analysis applications, but including the parameter dependence in the reduced‐order model (ROM) remains challenging. In this work, interpolation among reduced‐order matrices is proposed as a means to obtain parameterized ROMs. These ROMs are fast to evaluate and solve, and can be constructed without reference to the original full‐order model. Spline interpolation of the reduced‐order system matrices in the original space and in the space tangent to the Riemannian manifold is compared with Kriging interpolation of the predicted outputs. A heuristic criterion to select the most appropriate interpolation space is proposed. The interpolation approach is applied to a steady‐state thermal design problem and probabilistic analysis via Monte Carlo simulation of an unsteady contaminant transport problem. Copyright © 2009 John Wiley & Sons, Ltd.