Difference between revisions of "Emgr"

Latest revision as of 23:34, 11 January 2024

Synopsis

emgr - Empirical Gramian Framework (Version 5.99). Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification. Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction. The emgr framework is a compact open source toolbox for gramian-based model reduction and compatible with OCTAVE and MATLAB.

Features

Application matrix for the empirical gramian framework

emgr encompasses seven types of gramians:

Empirical Controllability Gramian / Empirical Output Controllability Gramian
Empirical Observability Gramian / Empirical Average Observability Gramian
Empirical Cross Gramian / Empirical Non-Symmetric Cross Gramian
Empirical Linear Cross Gramian / Empirical Non-Symmetric Linear Cross Gramian
Empirical Sensitivity Gramian (parameter controllability)
Empirical Identifiability Gramian (parameter observability)
Empirical Joint Gramian (parameter observability)

emgr overview

Applications:

Model reduction
- Proper Orthogonal Decomposition (POD)
- Modified POD / Approximate Balancing
- Dominant Subspace Projection Model Reduction (DSPMR)
- Balanced Proper Orthogonal Decompsition (bPOD)
- Balanced Truncation
- Balanced Gains
- Dynamic Mode Decomposition-Galerkin
Parameter reduction
Combined state and parameter reduction
Decentralized control
State sensitivity
Parameter sensitivity
Parameter identification
Nonlinearity quantification
Uncertainty quantification
System indices
System norms
Tau function

Meta Information

Code Meta Data
name:	Empirical Gramian Framework (emgr)
version:	5.99 (2022-04-13)
id:	10.5281/zenodo.6457616 (doi)
author:	Christian Himpe (0000-0003-2194-6754)
topic:	Science, Mathematics, Model Reduction
type:	Toolbox
license:	BSD-2-Clause (open-source)
repository:	https://github.com/gramian/emgr (git)
language:	Matlab
dependencies:	Octave >=5.2, Matlab >=2017b
systems:	Linux, Windows
website:	https://gramian.de
keywords:	Controllability, Observability, Cross Gramian, Model Reduction, Model Order Reduction

Cite

Please cite emgr as:

C. Himpe (2021). emgr - EMpirical GRamian Framework (Version 5.99) [Software]. Available from https://gramian.de . doi:10.5281/zenodo.6457616

 @MISC{emgr599,
  author = {C.~Himpe},
  title = {{emgr - {EMpirical GRamian Framework} (Version~5.99)},
  howpublished = {\url{https://gramian.de}},
  year = {2022},
  doi = {10.5281/zenodo.6457616}
 }

References

C. Himpe. "emgr - EMpirical GRamian Framework 5.99". Transactions on Mathematical Software, 49(3): 31, 2023.

C. Himpe. "Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms". Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 141--164, 2021.

P. Benner, C. Himpe. "Cross-Gramian-Based Dominant Subspaces". Advances in Computational Mathematics 45(5): 91, 2533--2553, 2019.

S. Grundel, C. Himpe, J. Saak. "On Empirical System Gramians". Proceedings in Applied Mathematics and Mechanics, 19: e201900006, 2019.

C. Himpe. "emgr - The Empirical Gramian Framework". Algorithms 11(7): 91, 2018.

C. Himpe, T. Leibner, S. Rave, J. Saak. "Fast Low-Rank Empirical Cross Gramians". Proceedings in Applied Mathematics and Mechanics, 17: 841--842, 2017.

C. Himpe. "Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience". Westfälische Wilhelms Universität, Sierke Verlag Göttingen, 2017.

C. Himpe, M. Ohlberger. "A Note on the Cross Gramian for Non-Symmetric Systems". System Science and Control Engineering 4(1): 199--208, 2016.

C. Himpe, M. Ohlberger. "The Empirical Cross Gramian for Parametrized Nonlinear Systems". IFAC-PapersOnLine (8th Vienna International Conference on Mathematical Modelling), 48(1): 727--728, 2015.

C. Himpe, M. Ohlberger. "Model Reduction for Complex Hyperbolic Networks". Proceedings of the European Control Conference: 2739--2743, 2014.

C. Himpe, M. Ohlberger. "Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems". Mathematical Problems in Engineering, 2014: 843869, 2014.

C. Himpe, M. Ohlberger. "A Unified Software Framework for Empirical Gramians". Journal of Mathematics 2013: 365909, 2013.

Links

Official website: https://gramian.de

Github Repo: https://github.com/gramian/emgr

SWmath: Entry

Oberwolfach References on Mathematical Software: Entry

SIAM DSweb Dynamical Systems Software: Entry

Contact

Christian Himpe

@@ Line 1: / Line 1: @@
 [[Category:Software]]
-[[Category:Linear algebra]]
+[[Category:MATLAB]]
-[[Category:dense]]
+[[Category:Octave]]
-[[Category:nonlinear]]
+[[File:Emgr_box.png|200px|right|emgr box]]
-== ==
+== Synopsis ==
-[http://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework.
-Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction or system identification.
+[https://gramian.de emgr] - '''Em'''pirical '''Gr'''amian Framework (Version '''5.99''').
+Empirical gramians can be computed for linear and nonlinear control systems for purposes of model order reduction, uncertainty quantification and system identification.
 Model reduction using empirical gramians can be applied to the state space, to the parameter space or to both through combined reduction.
 The '''emgr''' framework is a compact open source toolbox for gramian-based model reduction and compatible with [http://www.gnu.org/software/octave/ OCTAVE] and [http://www.mathworks.de/products/matlab/ MATLAB].
 == Features ==
-[[File:Appmat.png|thumb|400px|right|Application matrix for the empirical gramian framework]]
+[[File:Appmat.PNG|thumb|400px|right|Application matrix for the empirical gramian framework]]
-'''emgr''' encompasses six types of gramians:
+'''emgr''' encompasses seven types of gramians:
-* Empirical Controllability Gramian
+* Empirical [[:Wikipedia:Controllability_Gramian|Controllability Gramian]] / Empirical Output Controllability Gramian
-* Empirical Observability Gramian
+* Empirical [[:Wikipedia:Observability_Gramian|Observability Gramian]] / Empirical Average Observability Gramian
-* Empirical Cross Gramian
+* Empirical [[:Wikipedia:Cross_Gramian|Cross Gramian]] / Empirical Non-Symmetric Cross Gramian
-* Empirical Sensitivity Gramian
+* Empirical Linear Cross Gramian / Empirical Non-Symmetric Linear Cross Gramian
-* Empirical Identifiability Gramian
+* Empirical Sensitivity Gramian (parameter controllability)
-* Empirical Joint Gramian
+* Empirical Identifiability Gramian (parameter observability)
+* Empirical Joint Gramian (parameter observability)
+[[File:emgr-flyer.pdf|thumb|right|emgr overview]]
-applicable to:
+=== Applications: ===
-* Linear + Nonlinear Systems
-* First + Second Order Systems
-* Parametric Systems
+* Model reduction
-and with sample implementations for:
+** Proper Orthogonal Decomposition (POD)
+** Modified POD / Approximate Balancing
+** Dominant Subspace Projection Model Reduction (DSPMR)
+** Balanced Proper Orthogonal Decompsition (bPOD)
+** Balanced Truncation
+** Balanced Gains
+** Dynamic Mode Decomposition-Galerkin
+* Parameter reduction
+* Combined state and parameter reduction
+* Decentralized control
+* State sensitivity
+* Parameter sensitivity
+* Parameter identification
+* Nonlinearity quantification
+* Uncertainty quantification
+* System indices
+* System norms
+* Tau function
+== Meta Information ==
-* Balanced Truncation + Direct Trunction
-* Parameter Identification + Sensitivity Analysis
+{| class="wikitable"
-* Parameter Reduction
+|+Code Meta Data
-* Combined State and Parameter Reduction
+|-
-* (Bayesian) Inverse Problem Reduction
+|style="text-align:right;" | '''name:'''
+|Empirical Gramian Framework (emgr)
+|-
+|style="text-align:right;" | '''version:'''
+|5.99 (2022-04-13)
+|-
+|style="text-align:right;" | '''id:'''
+|[https://doi.org/10.5281/zenodo.6457616 10.5281/zenodo.6457616] (doi)
+|-
+|style="text-align:right;" | '''author:'''
+|Christian Himpe ([http://orcid.org/0000-0003-2194-6754 0000-0003-2194-6754])
+|-
+|style="text-align:right;" | '''topic:'''
+|Science, Mathematics, Model Reduction
+|-
+|style="text-align:right;" | '''type:'''
+|Toolbox
+|-
+|style="text-align:right;" | '''license:'''
+|[[wikipedia:BSD_licenses#2-clause|BSD-2-Clause]] (open-source)
+|-
+|style="text-align:right;" | '''repository:'''
+|https://github.com/gramian/emgr (git)
+|-
+|style="text-align:right;" | '''language:'''
+|Matlab
+|-
+|style="text-align:right;" | '''dependencies:'''
+|[[wikipedia:GNU_Octave|Octave]] >=5.2, [[wikipedia:MATLAB|Matlab]] >=2017b
+|-
+|style="text-align:right;" | '''systems:'''
+|Linux, Windows
+|-
+|style="text-align:right;" | '''website:'''
+|https://gramian.de
+|-
+|style="text-align:right;" | '''keywords:'''
+|Controllability, Observability, Cross Gramian, Model Reduction, Model Order Reduction
+|}
+== Cite ==
+Please cite '''emgr''' as:
+C. Himpe (2021). emgr - EMpirical GRamian Framework (Version 5.99) [Software].
+Available from https://gramian.de . doi:10.5281/zenodo.6457616
+  @MISC{emgr599,
+   author = {C.~Himpe},
+   title = {{emgr - {EMpirical GRamian Framework} (Version~5.99)},
+   howpublished = {\url{https://gramian.de}},
+   year = {2022},
+   doi = {10.5281/zenodo.6457616}
+  }
 == References ==
-* C. Himpe, M. Ohlberger. "<span class="plainlinks">[http://arxiv.org/pdf/1301.6879v3 A Unified Software Framework for Empirical Gramians]</span>". arXiv E-print, arXiv:1301.6879 [math.OC], 2012.
+* [[User:Himpe|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1145/3609860 emgr - EMpirical GRamian Framework 5.99]</span>". Transactions on Mathematical Software, 49(3): 31, 2023.
+* [[User:Himpe|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1007/978-3-030-72983-7_7 Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms]</span>". Model Reduction of Complex Dynamical Systems, International Series of Numerical Mathematics 171: 141--164, 2021.
+* P. Benner, [[User:Himpe|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.1007/s10444-019-09724-7 Cross-Gramian-Based Dominant Subspaces]</span>". Advances in Computational Mathematics 45(5): 91, 2533--2553, 2019.
+* S. Grundel, [[User:Himpe|C. Himpe]], J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201900006 On Empirical System Gramians]</span>". Proceedings in Applied Mathematics and Mechanics, 19: e201900006, 2019.
+* [[User:Himpe|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.3390/a11070091 emgr - The Empirical Gramian Framework]</span>". Algorithms 11(7): 91, 2018.
+* [[User:Himpe|C. Himpe]], T. Leibner, S. Rave, J. Saak. "<span class="plainlinks">[https://doi.org/10.1002/pamm.201710388 Fast Low-Rank Empirical Cross Gramians]</span>". Proceedings in Applied Mathematics and Mechanics, 17: 841--842, 2017.
+* [[User:Himpe|C. Himpe]]. "<span class="plainlinks">[https://doi.org/10.14626/9783868448818 Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience]</span>". Westfälische Wilhelms Universität, Sierke Verlag Göttingen, 2017.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1080/21642583.2016.1215273 A Note on the Cross Gramian for Non-Symmetric Systems]</span>". System Science and Control Engineering 4(1): 199--208, 2016.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1016/j.ifacol.2015.05.163 The Empirical Cross Gramian for Parametrized Nonlinear Systems]</span>". IFAC-PapersOnLine (8th Vienna International Conference on Mathematical Modelling), 48(1): 727--728, 2015.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1109/ECC.2014.6862188 Model Reduction for Complex Hyperbolic Networks]</span>". Proceedings of the European Control Conference: 2739--2743, 2014.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2014/843869 Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems]</span>". Mathematical Problems in Engineering, 2014: 843869, 2014.
+* [[User:Himpe|C. Himpe]], M. Ohlberger. "<span class="plainlinks">[https://doi.org/10.1155/2013/365909 A Unified Software Framework for Empirical Gramians]</span>". Journal of Mathematics 2013: 365909, 2013.
 == Links ==
-* http://gramian.de
+* Official website: https://gramian.de
+* Github Repo: https://github.com/gramian/emgr
+* SWmath: [https://swmath.org/software/7554 Entry]
+* Oberwolfach References on Mathematical Software: [http://orms.mfo.de/project?id=345 Entry]
+* SIAM DSweb Dynamical Systems Software: [https://dsweb.siam.org/Software/emgr-empirical-gramian-framework Entry]
 == Contact ==