Model Reduction for Large Scale Systems

TL;DR

This paper explores adaptive Petrov-Galerkin model reduction techniques within a Trust Region framework to efficiently handle large-scale, multi-scale PDE-constrained parameter optimization problems, overcoming offline computational limitations.

Contribution

It introduces a novel adaptive basis enrichment method for Petrov-Galerkin model reduction applicable to large and multi-scale systems, bypassing traditional offline/online splitting.

Findings

Enhanced efficiency in large-scale PDE problems

Reduced offline computational time

Improved flexibility in model reduction applications

Abstract

Projection based model order reduction has become a mature technique for simulation of large classes of parameterized systems. However, several challenges remain for problems where the solution manifold of the parameterized system cannot be well approximated by linear subspaces. While the online efficiency of these model reduction methods is very convincing for problems with a rapid decay of the Kolmogorov n-width, there are still major drawbacks and limitations. Most importantly, the construction of the reduced system in the offline phase is extremely CPU-time and memory consuming for large scale and multi scale systems. For practical applications, it is thus necessary to derive model reduction techniques that do not rely on a classical offline/online splitting but allow for more flexibility in the usage of computational resources. A promising approach with this respect is model reduction with adaptive enrichment. In this contribution we investigate Petrov-Galerkin based model reduction with adaptive basis enrichment within a Trust Region approach for the solution of multi scale and large scale PDE constrained parameter optimization.