Non‐intrusive reduced order modeling: Geometrical framework, high‐order models, and a priori analysis of applicability

Abstract

We present an intuitive geometrical framework for non‐intrusive model reduction. Based on simple low‐dimensional geometry that is easy to visualize and interpret, the approach enables one to predict model features a priori and explain them a posteriori. Two simple a priori methods for analyzing the suitability of non‐intrusive model reduction are consequently presented and discussed. As a natural consequence of the interpretation proposed a method extension is proposed, namely, higher‐order temporal discretization. It is also demonstrated that some generic properties of the physical system modeled such as periodicity or convergence towards a steady state are easily represented in the framework proposed. The approaches are illustrated using a number of representative test problems including a three‐dimensional case of the Saffman–Taylor instability and an example exhibiting a propagating discontinuity. It is shown that this property makes the underlying non‐intrusive reduced order modeling nonsmooth meaning it will provide a poor representation of the system dynamics.