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

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.

Automated summary

This paper introduces an intuitive geometrical framework for non-intrusive model reduction, allowing for a priori prediction and post-hoc explanation of model features. The proposed framework also includes a higher-order temporal discretization extension, demonstrating the representation of generic properties of physical systems. The study illustrates that the nonsmooth nature of the underlying non-intrusive reduced order modeling may lead to a poor system dynamics representation.