Software

Software Packages

• MORLAB (Model Order Reduction LABoratory)
   Latest Version: 6.0
  This toolbox is a collection of MATLAB and Octave routines for model order reduction of dynamical systems. The implementation is based on spectral projection methods, like the matrix sign function and the matrix disk function, and on iterative low-rank solvers for large-scale sparse systems. For details and references see the official project website, the MORwiki entry and the latest Zenodo upload.
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• SOMDDPA (Second-Order Modally-Damped Dominant Pole Algorithm)
   Latest Version: 2.0
  For model order reduction via modal truncation, dominant poles have been proven to be an efficient and accurate approach. In case of modally-damped second-order systems, it is possible to extend the idea of dominant poles in a structure-preserving fashion to the mechanical system case. This package contains a structure-preserving implementation in MATLAB and Octave of the dominant pole algorithm for modally-damped second-order systems. Find the latest upload on Zenodo and checkout my dissertation for the theoretical background.
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• SOLBT (Limited Balanced Truncation for Large-Scale Sparse Second-Order Systems)
   Latest Version: 3.0
  In practical applications, only local approximations of system’s behavior in frequency or time domain are needed. This package extends the idea of frequency- and time-limited balanced truncation to large-scale sparse mechanical systems of second-order type with an implementation in MATLAB and Octave. Find the latest upload on Zenodo. Check out the corresponding paper for the theoretical background.
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Contributions to other Projects

• M-M.E.S.S. (Matrix Equation Sparse Solvers Library):
  From version 1.0.1 up to version 3.0, I made continuously updates in the MATLAB version of the M.E.S.S. library involving among other an implementation of the Riccati iteration, the RADI method and several bug fixes. For more details on my contributions see the contributors file and checkout the latest version on Zenodo.

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Supplementary code packages and data

1. J. Saak and S. W. R. Werner. Code, data and results for numerical experiments in “Using \(LDL^{T}\) factorizations in Newton’s method for solving general large-scale algebraic Riccati equations” (version 1.1), June 2024. doi:10.5281/zenodo.11390499
   BibTeX Paper

2. S. W. R. Werner. Code, data and results for numerical experiments in “Structure-preserving interpolation of quadratic-bilinear systems via regular multivariate transfer functions” (version 1.0), May 2024. doi:10.5281/zenodo.10946483
   BibTeX Paper

3. S. W. R. Werner. Code, data and results for numerical experiments in “System stabilization with policy optimization on unstable latent manifolds” (version 1.0), April 2024. doi:10.5281/zenodo.7897240
   BibTeX Paper

4. Q. Aumann and S. W. R. Werner. Code, data and results for numerical experiments in “Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction” (version 1.2), April 2024. doi:10.5281/zenodo.10945494
   BibTeX Paper

5. J. Heiland, Y. Kim, and S. W. R. Werner. Code, data and results for numerical experiments in “Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback design” (version 1.0), March 2024. doi:10.5281/zenodo.10783695
   BibTeX Paper

6. S. Reiter and S. W. R. Werner. Code and results for numerical experiments in “Interpolatory model order reduction of large-scale dynamical systems with root mean squared error measures” (version 1.0), March 2024. doi:10.5281/zenodo.10729524
   BibTeX Paper

7. J. Saak and S. W. R. Werner. Code, data and results for numerical experiments in “Using \(LDL^{T}\) factorizations in Newton’s method for solving general large-scale algebraic Riccati equations” (version 1.0), February 2024. doi:10.5281/zenodo.10619037
   BibTeX Paper

8. Q. Aumann and S. W. R. Werner. Code, data and results for numerical experiments in “Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction” (version 1.1), December 2023. doi:10.5281/zenodo.10435758
   BibTeX Paper

9. S. W. R. Werner. Code, data and results for numerical experiments in “Structured interpolation for multivariate transfer functions of quadratic-bilinear systems” (version 2.0), November 2023. doi:10.5281/zenodo.10116600
   BibTeX Paper

10. J. Heiland and S. W. R. Werner. Code, data and results for numerical experiments in “Low-complexity linear parameter-varying approximations of incompressible Navier-Stokes equations for truncated state-dependent Riccati feedback” (version 2.0), May 2023. doi:10.5281/zenodo.7977616
    BibTeX Paper

11. Q. Aumann and S. W. R. Werner. Code, data and results for numerical experiments in “Adaptive choice of near-optimal expansion points for interpolation-based structure-preserving model reduction” (version 1.0), April 2023. doi:10.5281/zenodo.7845175
    BibTeX Paper

12. S. W. R. Werner. Code, data and results for numerical experiments in “Structured interpolation for multivariate transfer functions of quadratic-bilinear systems” (version 1.0), April 2023. doi:10.5281/zenodo.7397069
    BibTeX Paper

13. S. W. R. Werner. Code, data and results for numerical experiments in “Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems” (version 1.0), March 2023. doi:10.5281/zenodo.7358813
    BibTeX Paper

14. J. Heiland and S. W. R. Werner. Code, data and results for numerical experiments in “Low-complexity linear parameter-varying approximations of incompressible Navier-Stokes equations for truncated state-dependent Riccati feedback” (version 1.0), March 2023. doi:10.5281/zenodo.7742469
    BibTeX Paper

15. S. W. R. Werner. Code, data and results for numerical experiments in “Context-aware controller inference for stabilizing dynamical systems from scarce data” (version 1.1), January 2023. doi:10.5281/zenodo.7530566
    BibTeX Paper

16. Q. Aumann and S. W. R. Werner. Code, data and results for numerical experiments in “Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods” (version 1.1), August 2022. doi:10.5281/zenodo.6806016
    BibTeX Paper

17. S. W. R. Werner. Code, data and results for numerical experiments in “Context-aware controller inference for stabilizing dynamical systems from scarce data” (version 1.0), July 2022. doi:10.5281/zenodo.6567552
    BibTeX Paper

18. S. W. R. Werner. Code, data and results for numerical experiments in “A unifying framework for tangential interpolation of structured bilinear control systems” (version 1.0), June 2022. doi:10.5281/zenodo.5793356
    BibTeX Paper

19. S. W. R. Werner. Code, data and results for numerical experiments in “Multifidelity robust controller design with gradient sampling” (version 1.0), May 2022. doi:10.5281/zenodo.6403121
    BibTeX Paper

20. S. W. R. Werner. Code, data and results for numerical experiments in “A low-rank solution method for Riccati equations with indefinite quadratic terms” (version 2.0), March 2022. doi:10.5281/zenodo.6308400
    BibTeX Paper

21. S. W. R. Werner. Code, data and results for numerical experiments in “On the sample complexity of stabilizing linear dynamical systems from data” (version 1.0), February 2022. doi:10.5281/zenodo.5902997
    BibTeX Paper

22. Q. Aumann and S. W. R. Werner. Code, data and results for numerical experiments in “Structured model order reduction for vibro-acoustic problems using interpolation and balancing methods” (version 1.0), January 2022. doi:10.5281/zenodo.5836047
    BibTeX Paper

23. S. W. R. Werner. Code, data and results for numerical experiments in “A low-rank solution method for riccati equations with indefinite quadratic terms” (version 1.0), November 2021. doi:10.5281/zenodo.5155993
    BibTeX Paper

24. S. W. R. Werner. Code, data and results for numerical experiments in “Structured vector fitting framework for mechanical systems” (version 1.0), October 2021. doi:10.5281/zenodo.5539944
    BibTeX Paper

25. J. Heiland and S. W. R. Werner. Code, data and results for numerical experiments in “Robust output-feedback stabilization for incompressible flows using low-dimensional \(\mathcal{H}_{\infty}\)-controllers” (version 2.0), October 2021. doi:10.5281/zenodo.5532539
    BibTeX Paper

26. R. Jendersie and S. W. R. Werner. Results of numerical experiments in “A comparison of numerical methods for model reduction of dense discrete-time systems” (version 1.0), May 2021. doi:10.5281/zenodo.4745518
    BibTeX Paper

27. S. W. R. Werner. Results of numerical experiments in “Structure-Preserving Model Reduction for Mechanical Systems” (version 1.0), April 2021. doi:10.5281/zenodo.4650422
    BibTeX Paper

28. S. W. R. Werner. Code and data for numerical experiments in “Structure-Preserving Model Reduction for Mechanical Systems” (version 1.0), April 2021. doi:10.5281/zenodo.4650402
    BibTeX Paper

29. J. Heiland and S. W. R. Werner. Code, data and results for numerical experiments in “Robust output-feedback stabilization for incompressible flows using low-dimensional \(\mathcal{H}_{\infty}\)-controllers” (version 1.0), March 2021. doi:10.5281/zenodo.4507759
    BibTeX Paper

30. J. Saak and S. W. R. Werner. Parametric and two-step model reduction using M-M.E.S.S. and MORLAB (version 1.1), June 2020. doi:10.5281/zenodo.3865495
    BibTeX Paper

31. J. Saak and S. W. R. Werner. Parametric and two-step model reduction using M-M.E.S.S. and MORLAB (version 1.0), February 2020. doi:10.5281/zenodo.3678213
    BibTeX Paper

32. J. Saak, D. Siebelts, and S. W. R. Werner. Reduction results for an artificial fish tail (version 19-02-14), February 2019. doi:10.5281/zenodo.2564050
    BibTeX Paper

33. J. Saak, D. Siebelts, and S. W. R. Werner. Second order reduction comparison for the fishtail model (version 1.0), February 2019. doi:10.5281/zenodo.2563874
    BibTeX Paper