Nonlinear model order reduction with low rank tensor approximation

In this article, two methods of model order reduction based on the low rank approximation of tensor are introduced for the large scale nonlinear problem. We first introduce some definitions and results on tensor extended from matrix theory. Then we show how the general nonlinear system can be converted into the low rank form we treated in this research. We put the model order reduction of it in two frameworks, that is, polynomial framework and moment-matching framework. In these two frameworks we construct the algorithms correspondingly, and analyze properties of these algorithms, including the preservation of stability, and moment-matching properties. Next the priorities of these algorithms are presented. Finally we setup several numerical experiments to validate the effectiveness of the algorithms.