MOR software. (English) Zbl 07359325

Benner, Peter (ed.) et al., Model order reduction. Volume 3: Applications. Berlin: De Gruyter. 431-460 (2021).
Summary: This chapter is devoted to an important requirement of successful model order reduction (MOR) application, namely, the software aspect. The most common situation is the existence of a so-called full model, i.e., a high-fidelity, high-dimensional simulation model, that needs to be accelerated by MOR techniques, optimally without reimplementing the partially complex reduction techniques, as presented in the first volume of this handbook.
Initially, as neither full simulation models nor MOR algorithms are to be reprogrammed, but ideally are reused from existing implementations, we concentrate on the aspect of the interplay of such packages. We will discriminate, discuss, and exemplify different levels of solver “intrusiveness” that allow corresponding reduction techniques to be applied. On the one hand, most effective MOR techniques require deep access into the full model’s simulation code. On the other hand, application-specific full model simulators may only offer very restricted access to internals, especially in case of commercial packages. This gap in requirements and practical accessibility motivates the discrimination into “white-box,” “gray-box,” and “black-box” simulation scenarios. In particular, we exemplify the ideal case of MOR for white-box situations on two examples, namely, parametric linear elliptic PDE and parametric nonlinear ODE systems. Depending on those access classes, different corresponding reduction techniques can be applied.
The second part of the current chapter then discusses existing MOR software. Several program packages exist which provide MOR techniques. They differ in availability, licensing, programming language, system types, physical application domains, external simulator bindings, etc. We give an overview of the most relevant of those MOR packages, such that applicants can identify potential suitable software library candidates.
For the entire collection see [Zbl 1455.93002].


65D15 Algorithms for approximation of functions
65-04 Software, source code, etc. for problems pertaining to numerical analysis
93C15 Control/observation systems governed by ordinary differential equations
68N30 Mathematical aspects of software engineering (specification, verification, metrics, requirements, etc.)
Full Text: DOI


[1] S. Alebrand, Efficient Schemes for Parametrized Multiscale Problems. PhD thesis, University of Stuttgart, 2015.
[2] A. C. Antoulas, Approximation of Large-Scale Dynamical Systems, SIAM Publications, Philadelphia, PA, 2005. · Zbl 1112.93002
[3] T. Bechtold, E. B. Rudnyi, and J. Korvink, Selected model reduction software, in Fast Simulation of Electro-Thermal MEMS: Efficient Dynamic Compact Models, Springer, 2007.
[4] P. Benner, M. Ohlberger, A. Cohen, and K. Willcox (eds.), Model Reduction and Approximation, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2017.
[5] P. Benner and S. W. R. Werner, MORLAB -Model Order Reduction LABoratory (version 4.0), December 2018. See also: http://www.mpi-magdeburg.mpg.de/projects/morlab.
[6] A. Castagnotto, M. Cruz Varona, L. Jeschek, and B. Lohmann, sss & sssMOR: analysis and reduction of large-scale dynamical systems in MATLAB, Automatisierungstechnik, 65 (2) (2017), 134-150.
[7] R. Chakir and Y. Maday, A two-grid finite-element/reduced basis scheme for the approximation of the solution of parameter dependent PDE, in 9e Colloque National en Calcul des Structures, 2009.
[8] S. Chaturantabut and D. Sorensen, Nonlinear model reduction via discrete empirical interpolation, SIAM J. Sci. Comput., 32 (5) (2010), 2737-2764. · Zbl 1217.65169
[9] M. Drohmann, B. Haasdonk, and M. Ohlberger, A software framework for reduced basis methods using DUNE-RB and RBMATLAB, in A. Dedner, B. Flemisch, and R. Klöfkorn (eds.), Advances in DUNE: Proceedings of the DUNE User Meeting, Held in October 6th-8th 2010 in Stuttgart, Springer, Germany, 2012.
[10] M. Drohmann, B. Haasdonk, and M. Ohlberger, Reduced basis approximation for nonlinear parametrized evolution equations based on empirical operator interpolation, SIAM J. Sci. Comput., 34 (2) (2012), A937-A969. · Zbl 1259.65133
[11] R. Everson and L. Sirovich, Karhunen-Loeve procedure for gappy data, J. Opt. Soc. Am. A, 12 (1995), 1657-1664.
[12] J. Fehr, D. Grunert, P. Holzwarth, B. Fröhlich, N. Walker, and P. Eberhard, MOREMBS -a model order reduction package for elastic multibody systems and beyond, in Reduced-Order Modeling (ROM) for Simulation and Optimization, pp. 141-166, Springer, 2018. · Zbl 1433.74004
[13] M. Geuss, A Black-Box Method for Parametric Model Order Reduction based on Matrix Interpolation with Application to Simulation and Control. PhD thesis, Technische Universität München, 2015.
[14] B. Haasdonk, Reduced basis methods for parametrized PDEs -a tutorial introduction for stationary and instationary problems, in P. Benner, A. Cohen, M. Ohlberger, and K. Willcox (eds.), Model Reduction and Approximation: Theory and Algorithms, pp. 65-136, SIAM, Philadelphia, 2017.
[15] B. Haasdonk and M. Ohlberger, Reduced basis method for explicit finite volume approximations of nonlinear conservation laws, in Hyperbolic Problems: Theory, Numerics and Applications. Proc. Sympos. Appl. Math., vol. 67, pp. 605-614, Amer. Math. Soc., Providence, RI, 2009. · Zbl 1407.76084
[16] B. Haasdonk, M. Ohlberger, and G. Rozza, A reduced basis method for evolution schemes with parameter-dependent explicit operators, Electron. Trans. Numer. Anal., 32 (2008), 145-161. · Zbl 1391.76413
[17] J. S. Hesthaven, G. Rozza, and B. Stamm, Certified Reduced Basis Methods for Parametrized Partial Differential Equations, SpringerBriefs in Mathematics, Springer International Publishing, 2015.
[18] C. Himpe, emgr -The empirical gramian framework, Algorithms, 11 (7) (2018), 91. · Zbl 1461.93059
[19] D. B. P. Huynh, D. J. Knezevic, and A. T. Patera, A static condensation reduced basis element method: complex problems, Comput. Methods Appl. Mech. Eng., 259 (2013), 197-216. · Zbl 1286.65160
[20] A. Ionita and A. Antoulas, Data-driven parametrized model reduction in the Loewner framework, SIAM J. Sci. Comput., 36 (3) (2014), A984-A1007. · Zbl 1297.65072
[21] R. Ionutiu, J. Rommes, and W. H. A. Schilders, SparseRC: sparsity preserving model reduction for RC circuits with many terminals, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., 30 (12) (2011), 1828-1841.
[22] L. Kazaz, Black box model order reduction of nonlinear systems with kernel and discrete empirical interpolation. Bachelor’s thesis, University of Stuttgart, 2014.
[23] D. J. Knezevic and J. W. Peterson, A high-performance parallel implementation of the certified reduced basis method, Comput. Methods Appl. Mech. Eng., 200 (13-16) (2011), 1455-1466. · Zbl 1228.76109
[24] P. Koutsovasilis and M. Beitelschmidt, MORPACK toolbox for coupling rigid and elastic multi-body dynamics, in Proc. of NAFEMS World Congress, 2009. · Zbl 1156.93324
[25] N. Kutz, S. L. Brunton, B. W. Brunton, and J. L. Proctor, Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems, SIAM, 2016. · Zbl 1365.65009
[26] C. Lein and M. Beitelschmidt, MORPACK-Schnittstelle zum Import von FE-Strukturen nach SIMPACK, Automatisierungstechnik, 60 (9) (2012), 547-559.
[27] R. Milk, S. Rave, and F. Schindler, pyMOR -generic algorithms and interfaces for model order reduction, SIAM J. Sci. Comput., 38 (5) (2016), S194-S216. · Zbl 1352.65453
[28] F. Negri, A. Manzoni, and D. Amsallem, Efficient model reduction of parametrized systems by matrix discrete empirical interpolation, J. Comput. Phys., 303 (2015), 431-454. · Zbl 1349.65154
[29] S. W. R. Werner and P. Benner, Model reduction of descriptor systems with the MORLAB toolbox, in Proc. 9th Vienna International Conference on Mathematical Modelling MATHMOD 2018, IFAC-PapersOnLine, vol. 51, pp. 547-552, 2018.
[30] A. T. Patera and G. Rozza, Reduced Basis Approximation and a Posteriori Error Estimation for Parametrized Partial Differential Equations, to appear in (tentative) MIT Pappalardo Graduate Monographs in Mechanical Engineering, MIT, 2007.
[31] B. Peherstorfer and K. Willcox, Data-driven operator inference for nonintrusive projection-based model reduction, Comput. Methods Appl. Mech. Eng., 306 (2016), 196-215. · Zbl 1436.93062
[32] C. Poussot-Vassal and P. Vuillemin, Introduction to MORE: a MOdel REduction toolbox, in Proc. IEEE International Conference on Control Applications, pp. 776-781, 2012.
[33] J. Rommes and N. Martins, Efficient computation of transfer function dominant poles using subspace acceleration, IEEE Trans. Power Syst., 21 (3) (2006), 1218-1226.
[34] J. Saak, M. Köhler, and P. Benner, M-M.E.S.S.-1.0.1 -the matrix equations sparse solvers library. DOI:10.5281/zenodo.50575, April 2016. See also: www.mpi-magdeburg.mpg.de/projects/mess.
[35] W. H. A. Schilders, H. A. Van der Vorst, and J. Rommes, Model Order Reduction: Theory, Research Aspects and Applications, vol. 13, Springer, 2008.
[36] G. Stabile, S. Hijazi, A. Mola, S. Lorenzi, and G. Rozza, POD-Galerkin reduced order methods for CFD using finite volume discretisation: vortex shedding around a circular cylinder, Commun. Appl. Ind. Math., 8 (1) (2017), 210-236. · Zbl 1383.35175
[37] G. Stabile and G. Rozza, Finite volume POD-Galerkin stabilised reduced order methods for the parametrised incompressible Navier-Stokes equations, Comput. Fluids, (2018). · Zbl 1410.76264
[38] Q. Wang, J. S. Hesthaven, and D. Ray, Non-intrusive reduced order modelling of unsteady flows using artificial neural networks with application to a combustion problem, J. Comput. Phys., 384 (2019), 289-307. · Zbl 1459.76117
[39] D. Wirtz, Model Reduction for Nonlinear Systems: Kernel Methods and Error Estimation. PhD Thesis, University of Stuttgart, October 2013.
[40] D. Wirtz, D. C. Sorensen, and B. Haasdonk, A posteriori error estimation for DEIM reduced nonlinear dynamical systems, SIAM J. Sci. Comput., 36 (2) (2014), A311-A338. · Zbl 1312.65127
[41] O. Zeeb, A numerical framework for semi-automated Reduced Basis Methods with blackbox solvers. PhD thesis, University of Ulm, 2015
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