Maximum entropy snapshot sampling for reduced basis modelling

Abstract

Purpose

The maximum entropy snapshot sampling (MESS) method aims to reduce the computational cost required for obtaining the reduced basis for the purpose of model reduction. Hence, it can significantly reduce the original system dimension whilst maintaining an adequate level of accuracy. The purpose of this paper is to show how these beneficial results are obtained.

Design/methodology/approach

The so-called MESS method is used for reducing two nonlinear circuit models. The MESS directly reduces the number of snapshots by recursively identifying and selecting the snapshots that strictly increase an estimate of the correlation entropy of the considered systems. Reduced bases are then obtained with the orthogonal-triangular decomposition.

Findings

Two case studies have been used for validating the reduction performance of the MESS. These numerical experiments verify the performance of the advocated approach, in terms of computational costs and accuracy, relative to gappy proper orthogonal decomposition.

Originality/value

The novel MESS has been successfully used for reducing two nonlinear circuits: in particular, a diode chain model and a thermal-electric coupled system. In both cases, the MESS removed unnecessary data, and hence, it reduced the snapshot matrix, before calling the QR basis generation routine. As a result, the QR-decomposition has been called on a reduced snapshot matrix, and the offline stage has been significantly scaled down, in terms of central processing unit time.

Citation

Bannenberg, M.W.F.M., Kasolis, F., Günther, M. and Clemens, M. (2022), "Maximum entropy snapshot sampling for reduced basis modelling", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 41 No. 3, pp. 954-966. https://doi.org/10.1108/COMPEL-02-2021-0050