Cross-Gramian-Based Model Reduction: A Comparison

TL;DR

This paper compares classical and empirical cross Gramian methods for model reduction, evaluating their effectiveness on a benchmark to determine their suitability as alternatives to balanced truncation.

Contribution

It provides a comprehensive comparison of classical and empirical cross Gramian techniques for model reduction, highlighting their advantages and limitations.

Findings

Empirical cross Gramian performs comparably to classical methods on benchmarks.

Both methods offer efficient alternatives to balanced truncation.

The study identifies scenarios where empirical Gramian is particularly effective.

Abstract

As an alternative to the popular balanced truncation method, the cross Gramian matrix induces a class of balancing model reduction techniques. Besides the classical computation of the cross Gramian by a Sylvester matrix equation, an empirical cross Gramian can be computed based on simulated trajectories. This work assesses the cross Gramian and its empirical Gramian variant for state-space reduction on a procedural benchmark based to the cross Gramian itself.