47 citations · 253 across the 14 of their papers we have counts for
16 papers
emgr -- EMpirical GRamian Framework Version 5.99
Christian Himpe
Version 5.99 of the empirical Gramian framework -- "emgr" -- completes a development cycle which focused on parametric model order reduction of gas network models while preserving…
Next-Gen Gas Network Simulation
Christian Himpe, Sara Grundel, Peter Benner
To overcome many-query optimization, control, or uncertainty quantification work loads in reliable gas and energy network operations, model order reduction is the mathematical tech…
Model Order Reduction for Gas and Energy Networks
Christian Himpe, Sara Grundel, Peter Benner
To counter the volatile nature of renewable energy sources, gas networks take a vital role. But, to ensure fulfillment of contracts under these circumstances, a vast number of poss…
Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms
Christian Himpe
In this work, the empirical-Gramian-based model reduction methods: Empirical poor man's truncated balanced realization, empirical approximate balancing, empirical dominant subspace…
Sustainable Research Software Hand-Over
Jörg Fehr, Christian Himpe, Stephan Rave +1
Scientific software projects evolve rapidly in their initial development phase, yet at the end of a funding period, the completion of a research project, thesis, or publication, fu…
Cross-Gramian-Based Dominant Subspaces
Peter Benner, Christian Himpe
A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying…
On Reduced Input-Output Dynamic Mode Decomposition
Peter Benner, Christian Himpe, Tim Mitchell
The identification of reduced-order models from high-dimensional data is a challenging task, and even more so if the identified system should not only be suitable for a certain dat…
emgr - The Empirical Gramian Framework
Christian Himpe
System Gramian matrices are a well-known encoding for properties of input-output systems such as controllability, observability or minimality. These so-called system Gramians were…
Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction Software
Jörg Fehr, Jan Heiland, Christian Himpe +1
Over the recent years the importance of numerical experiments has gradually been more recognized. Nonetheless, sufficient documentation of how computational results have been obtai…
Hierarchical Approximate Proper Orthogonal Decomposition
Christian Himpe, Tobias Leibner, Stephan Rave
Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale appl…
Cross-Gramian-Based Model Reduction: A Comparison
Christian Himpe, Mario Ohlberger
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…
A Note on the Cross Gramian for Non-Symmetric Systems
Christian Himpe, Mario Ohlberger
The cross gramian matrix is a tool for model reduction and system identification, but it is only computable for square control systems. For symmetric systems the cross gramian poss…
Data-Driven Combined State and Parameter Reduction for Extreme-Scale Inverse Problems
Christian Himpe, Mario Ohlberger
In this contribution we present an accelerated optimization-based approach for combined state and parameter reduction of a parametrized linear control system which is then used as…
Model Reduction for Complex Hyperbolic Networks
Christian Himpe, Mario Ohlberger
We recently introduced the joint gramian for combined state and parameter reduction [C. Himpe and M. Ohlberger. Cross-Gramian Based Combined State and Parameter Reduction for Large…
Cross-Gramian-Based Combined State and Parameter Reduction for Large-Scale Control Systems
Christian Himpe, Mario Ohlberger
This work introduces the empirical cross gramian for multiple-input-multiple-output systems. The cross gramian is a tool for reducing the state space of control systems, which conj…
A Unified Software Framework for Empirical Gramians
Christian Himpe, Mario Ohlberger
A common approach in model reduction is balanced truncation, which is based on gramian matrices classifiying certain attributes of states or parameters of a given dynamic system. I…