Data-driven model order reduction for wave propagation in materials with damage and nonlinearities

TL;DR

This paper explores data-driven and projection-based model order reduction techniques to efficiently simulate wave propagation in nonlinear and damaged materials, comparing their performance across multiple numerical examples.

Contribution

It provides a comprehensive comparison of intrusive and non-intrusive model reduction methods applied to complex wave propagation problems with nonlinearities and damage.

Findings

Projection-based POD effectively reduces model complexity.

Data-driven DMD and OpInf methods offer flexible alternatives.

All methods achieve significant acceleration with acceptable accuracy.

Abstract

In this work, we consider wave propagation in materials characterized by nonlinear properties or damage. To accelerate the simulations of the resulting high-dimensional problems, we apply model order reduction methods. Depending on the knowledge of the underlying equations and the availability of their discrete operators, intrusive methods (here projection-based approaches based on proper orthogonal decomposition (POD)) or non-instrusive methods (here data-driven approaches including dynamic mode decomposition (DMD) and operator inference (OpInf)) can be used. We recall the theoretical foundations of the methods and apply them to the problem of wave propagation. In three different numerical examples, we evaluate the performance of the reduction techniques.