A Regression Algorithm for Model Reduction of Large-Scale Multi-Dimensional Problems

Abstract

Model reduction is an approach for fast and cost‐efficient modelling of large‐scale systems governed by Ordinary Differential Equations (ODEs). Multi‐dimensional model reduction has been suggested for reduction of the linear systems simultaneously with respect to frequency and any other parameter of interest. Multi‐dimensional model reduction is also used to reduce the weakly nonlinear systems based on Volterra theory. Multiple dimensions degrade the efficiency of reduction by increasing the size of the projection matrix. In this paper a new methodology is proposed to efficiently build the reduced model based on regression analysis. A numerical example confirms the validity of the proposed regression algorithm for model reduction.