Cross-Gramian-Based Model Reduction: A Comparison

By Himpe Christian and Ohlberger Mario
Working Paper (2016)

Cross-Gramian-Based Dominant Subspaces

Working Paper (2018)

Benner Peter and Himpe Christian

On Reduced Input-Output Dynamic Mode Decomposition

Working Paper (2017)

Himpe Christian, Benner Peter, and Mitchell Tim

Fast Low-Rank Empirical Cross Gramians

Working Paper (2017)

Himpe Christian, Leibner Tobias, Rave Stephan, and Saak Jens

emgr - The Empirical Gramian Framework

Working Paper (2018)

Himpe Christian

Parareal in Time Intermediate Targets Methods for Optimal Control Problems

International Series of Numerical Mathematics (2013)

Mohamed Kamel Riahi, Maday Yvon, and Julien salomon

The Empirical Cross Gramian for Parametrized Nonlinear Systems

Working Paper (2015)

Himpe Christian and Ohlberger Mario

A Note on the Cross Gramian for Non-Symmetric Systems

Working Paper (2015)

Himpe Christian and Ohlberger Mario

Data-Driven Combined State and Parameter Reduction for Inverse Problems

Working Paper (2014)

Himpe Christian and Ohlberger Mario

Model Reduction for Complex Hyperbolic Networks

arXiv (2013)

Himpe Christian and Ohlberger Mario

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.

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Please cite the paper as follows:

Himpe C. and Ohlberger M. (2016) Cross-Gramian-Based Model Reduction: A Comparison. Working Paper.

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