1.2SYDec 22, 2017
On Reduced Input-Output Dynamic Mode DecompositionPeter 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 data set, but generally approximate the input-output behavior of the data source. In this work, we consider the input-output dynamic mode decomposition method for system identification. We compare excitation approaches for the data-driven identification process and describe an optimization-based stabilization strategy for the identified systems.
2.4OCAug 22, 2019
Cross-Gramian-Based Dominant SubspacesPeter 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 system. The related dominant subspace projection model reduction method similarly utilizes these system properties, yet instead of balancing, the associated subspaces are directly conjoined. In this work we extend the dominant subspace approach by computation via the cross Gramian for linear systems, and describe an a-priori error indicator for this method. Furthermore, efficient computation is discussed alongside numerical examples illustrating these findings.
DatAasee -- A Metadata-Lake as Metadata Catalog for a Virtual Data-LakeChristian Himpe
Metadata management for distributed data sources is a long-standing but ever-growing problem. To counter this challenge in a research-data and library-oriented setting, this work constructs a data architecture, derived from the data-lake: the metadata-lake. A proof-of-concept implementation of this proposed metadata aggregator is presented and briefly evaluated.
2.9OCJun 13, 2016
Cross-Gramian-Based Model Reduction: A ComparisonChristian 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 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.
5.9MSJul 5, 2016
Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction SoftwareJörg Fehr, Jan Heiland, Christian Himpe et al.
Over the recent years the importance of numerical experiments has gradually been more recognized. Nonetheless, sufficient documentation of how computational results have been obtained is often not available. Especially in the scientific computing and applied mathematics domain this is crucial, since numerical experiments are usually employed to verify the proposed hypothesis in a publication. This work aims to propose standards and best practices for the setup and publication of numerical experiments. Naturally, this amounts to a guideline for development, maintenance, and publication of numerical research software. Such a primer will enable the replicability and reproducibility of computer-based experiments and published results and also promote the reusability of the associated software.