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Freund}, title = {How to make theoretically passive reduced-order models passive in practice}, booktitle = {Proc. {IEEE} 1998 Custom Integrated Circuits Conference}, year = 1998, pages = {207--210}, publisher = {IEEE} } @InProceedings{morBaiMS05, author = {Bai, Z. and Meerbergen, K. and Su, Y.}, title = {{A}rnoldi Methods for Structure-Preserving Dimension Reduction of Second-Order Dynamical Systems}, booktitle = {Dimension Reduction of Large-Scale Systems}, year = 2005, editor = {Benner, P. and Mehrmann, V. and Sorensen, D.~C.}, volume = 45, series = LNCSE, pages = {173--189}, publisher = {Springer-Verlag, Berlin/Heidelberg, Germany}, doi = {10.1007/3-540-27909-1_7} } @Article{morBaiS05, author = {Z. Bai and Y.-F. Su}, title = {Dimension reduction of large-scale second-order dynamical systems via a second-order {A}rnoldi method}, journal = SIAMSciComp, year = 2005, volume = 26, number = 5, pages = {1692--1709} } @Article{morBaiS06, author = {Z. Bai and D. Skoogh}, title = {A projection method for model reduction of bilinear dynamical systems}, journal = LinAlgApp, year = 2006, volume = 415, number = {2--3}, pages = {406--425}, doi = {10.1016/j.laa.2005.04.032} } @Article{morBaiSSetal99, author = {Z. Bai and R.~D. Slone and W.~T. Smith and Q. Ye}, title = {Error Bound for Reduced System Model by {P}ad$\acute{e}$ Approximation via the {L}anczos Process}, journal = IEEETransCADCS, year = 1999, volume = 18, number = 2, pages = {133--141} } @Article{morBal20, author = {Balicki, L.}, title = {Low-Rank Alternating Direction Implicit Iteration in {pyMOR}}, journal = {GAMM Archive for Students}, year = 2020, volume = 2, number = 1, pages = {1-13}, month = Feb, doi = {10.14464/gammas.v2i1.420} } @Article{morBal96, author = {Balmes, E.}, title = {Optimal {R}itz vectors for component mode synthesis using the singular value decomposition}, journal = AIAA, year = 1996, volume = 34, number = 6, pages = {1256--1260} } @Article{morBalK16, author = {Ballani, J. and Kressner, D.}, title = {Reduced Basis Methods: From Low-Rank Matrices to Low-Rank Tensors}, journal = SIAMSciComp, year = 2016, volume = 38, number = 4, pages = {A2045--A2067}, doi = {10.1137/15M1042784} } @Article{morBalMRetal19, author = {Balicki, L. and Mlinari{\'c}, P. and Rave, S. and Saak, J.}, title = {System-theoretic model order reduction with py{MOR}}, journal = PAMM, year = 2019, volume = 19, number = 1, doi = {10.1002/pamm.201900459} } @Article{morBanAGetal21, title = {Index-Aware Model-Order Reduction for a Special Class of Nonlinear Differential-Algebraic Equations}, author = {Banagaaya, N. and Al{\`\i}, G. and Grundel, S. and Benner, P.}, journal = {Journal of Dynamics and Differential Equations}, pages = {1--25}, year = {2021}, doi = {10.1007/s10884-021-10063-9} } @InProceedings{morBanBF18, author = {Banagaaya, N. and Benner, P. and Feng, L.}, title = {Parametric Model Order Reduction for Electro-Thermal Coupled Problems with Many Inputs }, booktitle = {{Progress in Industrial Mathematics at ECMI 2016}}, series = {Mathematics in Industry}, volume = 26, pages = {263--270}, year = 2018, doi = {10.1007/978-3-319-63082-3_41} } @Article{morBanBFetal18, author = {Banagaaya, N. and Benner, P. and Feng, L. and Meuris, P. and Schoenmaker, W.}, title = {An index-aware parametric model order reduction method for parameterized quadratic differential-algebraic equations}, journal = {Applied Mathematics and Computation}, year = 2018, volume = 319, pages = {409--424}, doi = {10.1016/j.amc.2017.04.024} } @InProceedings{morBanBG19, author = {Banagaaya, N. and Benner, P. and Grundel, S.}, title = {Index-Preserving Model Order Reduction for Differential-Algebraic Systems Arising in Gas Transport Networks}, booktitle = {{Progress in Industrial Mathematics at ECMI 2018}}, year = 2019, volume = 30, series = {Mathematics in Industry}, pages = {291--297}, doi = {10.1007/978-3-030-27550-1_36} } @InCollection{morBanFB19, author = {Banagaaya, N. and Feng, L. and Benner, P.}, title = {Sparse {(P)MOR} for electro-thermal coupled problems with many inputs}, booktitle = {{Nanoelectronic Coupled Problems Solutions}}, publisher = {Springer}, year = 2019, volume = 29, series = {{Mathematics in Industry}}, pages = {311--328}, doi = {10.1007/978-3-030-30726-4_14} } @InProceedings{morBanFDetal24, author = {Bansal, V. and Feng, L. and de la Rubia, V. and Benner, P.}, title = {Parametric S-Parameter Prediction Using Deep Learning}, booktitle = {Proc. 33rd Conference on Electrical Performance of Electronic Packaging and Systems (EPEPS 2024)}, year = 2024, pages = {1--4}, publisher = {IEEE}, doi = {10.1109/EPEPS61853.2024.10754126} } @InProceedings{morBanFMetal15, author = {N. Banagaaya and L. Feng and P. Meuris, W. Schoenmaker and P. Benner}, title = {Model order reduction of an electro-thermal package model}, booktitle = {IFAC-PapersOnLine, 18th Vienna International Conference on Mathematical Modelling MATHMOD 2015}, year = 2015, volume = 48, pages = {934--935}, publisher = {Elsevier}, doi = {10.1016/j.ifacol.2015.05.212} } @InProceedings{morBanFSetal16, author = {Banagaaya, N. and Feng, L. and Schoenmaker, W. and Meuris, P. and Wieers, A. and Gillon, R. and Benner, P.}, title = {Model Order Reduction for Nanoelectronics Coupled Problems with Many Inputs}, booktitle = {Design, Automation, and Test in Europe (DATE)}, year = 2016, pages = {313--318}, url = {http://ieeexplore.ieee.org/document/7459329/} } @InProceedings{morBanFSetal18, author = {Banagaaya, N. and Feng, L. and Schoenmaker, W. and Meuris, P. and Gillon, R. and Benner, P.}, title = {Sparse Model Order Reduction for Electro-Thermal Problems with Many Inputs}, booktitle = {Scientific Computing in Electrical Engineering}, editor = {Langer, U. and Amrhein, W. and Zulehner, W.}, year = 2018, series = {Mathematics in Industry}, volume = {28}, address = {Cham}, publisher = {Springer}, doi = {10.1007/978-3-319-75538-0_18} } @InProceedings{morBanGB20, author = {Banagaaya, N. and Grundel, S. and Benner, P.}, title = {Index-aware {MOR} for Gas Transport Networks with Many Supply Inputs}, booktitle = {{IUTAM Symposium on Model Order Reduction of Coupled Systems}}, year = 2020, volume = 36, series = {IUTAM Bookseries}, pages = {191--207}, doi = {10.1007/978-3-030-21013-7_14} } @InProceedings{morBarBQ05, author = {S. Barrachina and P. Benner and E. Quintana-Ort{\'\i}}, title = {Parallel Algorithms for Balanced Truncation of Large-Scale Unstable Systems}, booktitle = {Proc. 44rd {IEEE} Conf. Decision Contr. and European Contr. Conf. ECC2005}, year = 2004, pages = {2248--2253}, publisher = {Omnipress, Madison, WI}, note = {CD Rom}, isbn = {0-7803-9568-9} } @InProceedings{morBarDN08, author = {Barbagallo, A. and De~Felice, V.~F. and Nagarajan, K.~K.}, title = {Reduced Order Modelling of a Couette Flow Using Balanced Proper Orthogonal Decomposition}, booktitle = {2nd Young ERCOFTAC Workshop}, year = 2008, url = {http://dokumente.unibw.de/pub/bscw.cgi/2700941} } @Article{morBarMNetal04, author = {Barrault, M. and Maday, Y. and Nguyen, N.~C. and Patera, A.~T.}, title = {An `empirical interpolation' method: application to efficient reduced-basis discretization of partial differential equations}, journal = {C.~R. Math. Acad. Sci. Paris}, year = 2004, volume = 339, number = 9, pages = {667--672}, fjournal = {Comptes Rendus Mathematique. Academie des Sciences. Paris}, issn = {1631-073X}, doi = {10.1016/j.crma.2004.08.006} } @TechReport{morBatR16, author = {Batlle, C. and Roqueiro, N.}, title = {Balanced model order reduction for systems depending on a parameter}, institution = {arXiv}, year = 2016, type = {e-prints}, number = {1604.08086}, note = {cs.SY}, url = {http://arxiv.org/abs/1604.08086} } @Article{morBatSSetal18, author = {Batten, B.~A. and Shoori, H. and Singler, J.~R. and Weerasinghe, M.~H.}, title = {Balanced Truncation Model Reduction of a Nonlinear Cable-Mass {PDE} System with Interior Damping}, journal = {Discrete \& Continuous Dynamical Systems - B}, year = 2018, volume = {Online First}, pages = {1--25}, doi = {10.3934/dcdsb.2018162} } @PhdThesis{morBau08, author = {U. Baur}, title = {Control-{O}riented {M}odel {R}eduction for {P}arabolic {S}ystems}, school = {Technische Universit{\"{a}}t Berlin}, year = 2008, type = {{Ph.D. Thesis}}, address = {Berlin}, note = {ISBN 978-3639074178 Vdm Verlag Dr. M{\"{u}}ller, available from \url{http://www.nbn-resolving.de/urn:nbn:de:kobv:83-opus-17608}} } @Article{morBauB08, author = {U. Baur and P. Benner}, title = {{G}ramian-Based Model Reduction for Data-Sparse Systems}, journal = SIAMSciComp, year = 2008, volume = 31, number = 1, pages = {776--798}, doi = {10.1137/070711578} } @InProceedings{morBauB08b, author = {Baur, U. and Benner, P.}, title = {Parametrische {M}odellreduktion mit d{\"{u}}nnen {G}ittern}, booktitle = {Tagungsband GMA-FA 1.30, 'Modellierung, Identifikation und Simulation in der Automatisierungstechnik', Workshop in Anif, 24.-26.9.2008}, year = 2008, editor = {B. Lohmann and A. Kugi}, pages = {262--271}, note = {ISBN: 978-3-9502451-1-0, available from \url{http://csc.mpi-magdeburg.mpg.de/mpcsc/benner/pub/BaurBenner-GMA-Proceedings2008.pdf}} } @Article{morBauB08c, author = {U. Baur and P. Benner}, title = {Cross-{G}ramian based model reduction for data-sparse systems}, journal = ETNA, year = 2008, volume = 31, pages = {256--270}, url = {http://eudml.org/doc/130548} } @Article{morBauB09, author = {U. Baur and P. Benner}, title = {Modellreduktion f{\"{u}}r parametrisierte {S}ysteme durch balanciertes {A}bschneiden und {I}nterpolation ({M}odel {R}eduction for {P}arametric {S}ystems {U}sing {B}alanced {T}runcation and {I}nterpolation)}, journal = atAutom, year = 2009, volume = 57, number = 8, pages = {411--420}, doi = {10.1524/auto.2009.0787} } @Article{morBauBB14, author = {U. Baur and C.~A. Beattie and P. Benner}, title = {Mapping parameters across system boundaries: parameterized model reduction with low-rank variability in dynamics}, journal = PAMM, year = 2014, volume = 14, number = 1, pages = {19--22}, month = dec, publisher = WileyVCH, organization = {GAMM}, doi = {10.1002/pamm.201410006} } @Article{morBauBBetal11, author = {Baur, U. and Beattie, C.~A. and Benner, P. and Gugercin, S.}, title = {Interpolatory Projection Methods for Parameterized Model Reduction}, journal = SIAMSciComp, year = 2011, volume = 33, number = 5, pages = {2489--2518}, doi = {10.1137/090776925} } @Article{morBauBF14, author = {Baur, U. and Benner, P. and Feng, L.}, title = {Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective}, journal = ArchCompEng, year = 2014, volume = 21, number = 4, pages = {331--358}, doi = {10.1007/s11831-014-9111-2} } @Article{morBauBGetal11, author = {U. Baur and P. Benner and A. Greiner and J.~G. Korvink and J. Lienemann and C. Moosmann}, title = {Parameter preserving model reduction for {MEMS} applications}, journal = MCMDS, year = 2011, volume = 17, number = 4, pages = {297--317} } @Article{morBauBH18, author = {Baumann, M. and Benner, P. and Heiland, J.}, title = {Space-time {G}alerkin {POD} with application in optimal control of semi-linear parabolic partial differential equations}, journal = SIAMSciComp, year = 2018, volume = 40, number = 3, pages = {A1611--A1641}, doi = {10.1137/17M1135281} } @InCollection{morBauBHetal17, author = {Baur, U. and Benner, P. and Haasdonk, B. and Himpe, C. and Martini, I. and Ohlberger, M.}, title = {Comparison of Methods for Parametric Model Order Reduction of Time-Dependent Problems}, booktitle = {Model Reduction and Approximation: Theory and Algorithms}, publisher = {SIAM}, year = 2017, editor = {Benner, P. and Cohen, A. and Ohlberger, M. and Willcox, K.}, pages = {377--407}, doi = {10.1137/1.9781611974829.ch9} } @InCollection{morBauHS15, author = {Baumann, M. and Heiland, J. and Schmidt, M.}, title = {Discrete Input/Output Maps and their Relation to {P}roper {O}rthogonal {D}ecomposition}, booktitle = {Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory}, publisher = {Springer, Cham}, year = 2015, editor = {Benner, P. and Bollh{\"{o}}fer, M. and Kressner, D. and Mehl, C. and Stykel, T.}, pages = {585--608}, doi = {10.1007/978-3-319-15260-8_21} } @TechReport{morBeaB14, author = {Beattie, C.~A. and Benner, P.}, title = {{$\mathcal{H}_2$}-Optimality Conditions for Structured Dynamical Systems}, institution = {Max Planck Institute Magdeburg}, year = 2014, type = {Preprint}, number = {MPIMD/14-18}, url = {https://csc.mpi-magdeburg.mpg.de/preprints/2014/18/} } @InProceedings{morBeaG05, author = {Beattie, C.~A. and Gugercin, S.}, title = {{K}rylov-based model reduction of second-order systems with proportional damping}, booktitle = {Proceedings of the 44th IEEE Conference on Decision and Control}, year = 2005, pages = {2278--2283}, month = dec, doi = {10.1109/CDC.2005.1582501} } @Article{morBeaG09, author = {Beattie, C.~A. and Gugercin, S.}, title = {Interpolatory Projection Methods for Structure-preserving Model Reduction}, journal = SCL, year = 2009, volume = 58, number = 3, pages = {225--232}, doi = {10.1016/j.sysconle.2008.10.016} } @InProceedings{morBeaG11, author = {Beattie, C.~A. and Gugercin, S.}, title = {Structure-preserving model reduction for nonlinear port-{H}amiltonian systems}, booktitle = {2011 50th IEEE Conference on Decision and Control and European Control Conference}, pages = {6564--6569}, year = {2011}, doi = {10.1109/CDC.2011.6161504} } @InProceedings{morBeaG12, author = {Beattie, C.~A. and Gugercin, S.}, title = {Realization-independent {$\mathcal{H}_2$}-approximation}, booktitle = {51st IEEE Conference on Decision and Control (CDC)}, year = 2012, pages = {4953--4958}, doi = {10.1109/CDC.2012.6426344} } @TechReport{morBeaG14, author = {Beattie, C.~A. and Gugercin, S.}, title = {Model Reduction by Rational Interpolation}, institution = {arXiv}, year = 2014, type = {e-prints}, number = {1409.2140v1}, note = {math.NA}, url = {http://arxiv.org/abs/1409.2140v1} } @Article{morBeaGM17, author = {Beattie, C. and Gugercin, S. and Mehrmann, V.}, title = {Model reduction for systems with inhomogeneous initial conditions}, journal = SCL, year = 2017, volume = 99, pages = {99--106}, doi = {10.1016/j.sysconle.2016.11.007} } @article{morBeaGT20, author = {Beattie, C. and Gugercin, S. and Tomljanovi{\'c}, Z.}, title = {Sampling-free model reduction of systems with low-rank parameterization}, journal = AdvComputMath, volume = 46, number = 6, pages = 83, year = 2020, doi = {10.1007/s10444-020-09825-8} } @Article{morBeaGW12, author = {C.~A. Beattie and S. Gugercin and S. Wyatt}, title = {Inexact solves in interpolatory model reduction}, journal = LinAlgApp, year = 2012, volume = 436, number = 8, pages = {2916--2943}, note = {Special Issue dedicated to Danny Sorensen's 65th birthday}, issn = {0024-3795}, doi = {10.1016/j.laa.2011.07.015} } @InProceedings{morBecHWetal95, author = {Bechtold, T. and Hildenbrand, J. and W{\"{o}}llenstein, J. and Korvink, J.~G.}, title = {Model Order Reduction of 3D Electro-Thermal Model for a Novel, Micromachined Hotplate Gas Sensor}, booktitle = {Proceedings of 5th International Conference on Thermal and Mechanical Simulation and Experiments in Microelectronics and Microsystems}, year = 1995, pages = {263--267}, doi = {10.1109/ESIME.2004.1304049} } @Article{morBedBDetal19, author = {Beddig, R.~S. and Benner, P. and Dorschky, I. and Reis, T. and Schwerdtner, P. and Voigt, M. and Werner, S.~W.~R.}, title = {Model Reduction for Second-Order Dynamical Systems Revisited}, journal = PAMM, year = 2019, volume = 19, number = 1, pages = {e201900224}, doi = {10.1002/pamm.201900224} } @InCollection{morBedBDetal24, author = {Beddig, R.~S. and Benner, P. and Dorschky, I. and Reis, T. and Schwerdtner, P. and Voigt, M. and Werner, S.~W.~R.}, title = {Structure-Preserving Model Reduction for Dissipative Mechanical Systems}, booktitle = {Calm, Smooth and Smart}, publisher = {Springer}, year = 2024, editor = {Eberhard, P.}, volume = 102, series = {Lect. Notes Appl. Comput. Mech.}, pages = {209--230}, address = {Cham}, doi = {10.1007/978-3-031-36143-2_11} } @InProceedings{morBelM14, author = {Belhocine, M. and Marinescu, B.}, title = {A mix balanced-modal truncations for power systems model reduction}, booktitle = {2014 European Control Conference (ECC)}, year = {2014}, pages = {14470358}, doi = {10.1109/ECC.2014.6862475} } @Article{morBen04, author = {P. Benner}, title = {Solving Large-Scale Control Problems}, journal = IEEEContSysMag, year = 2004, volume = 24, number = 1, pages = {44--59}, doi = {10.1109/MCS.2004.1272745} } @PhdThesis{morBen05, author = {Bennini, F.}, title = {Ordnungsreduktion von elektrostatisch-mechanischen {F}inite {E}lemente {M}odellen auf der {B}asis der modalen {Z}erlegung}, school = {Technische Universit{\"{a}}t Chemnitz}, year = 2005, type = {{Ph.D. Thesis}}, address = {Chemnitz} } @Article{morBen06, author = {P. Benner}, title = {Numerical Linear Algebra for Model Reduction in Control and Simulation}, journal = GAMMMit, year = 2006, volume = 29, number = 2, pages = {275--296}, doi = {10.1002/gamm.201490034} } @InProceedings{morBen06a, author = {Benner, P.}, title = {A {MATLAB} repository for model reduction based on spectral projection}, booktitle = {2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control}, year = 2006, pages = {19--24}, month = oct, doi = {10.1109/CACSD-CCA-ISIC.2006.4776618}, issn = {2165-3011} } @InProceedings{morBen09, author = {Benner, P.}, title = {System-Theoretic Methods for Model Reduction of Large-Scale Systems: Simulation, Control, and Inverse Problems}, booktitle = {ARGESIM Report (MATHMOD 2009 Proceedings)}, volume = {35}, pages = {126--145}, year = {2009}, doi = {10.11128/arep.35} } @InProceedings{morBen10, author = {P. Benner}, title = {Advances in balancing-related model reduction for circuit simulation}, booktitle = {Scientific Computing in Electrical Engineering SCEE 2008}, year = 2010, editor = {J. Roos and L.~R.~J. Costa}, volume = 14, series = {Mathematics in Industry}, pages = {469--482}, address = {Berlin/Heidelberg}, publisher = {Springer-Verlag} } @InProceedings{morBen13, author = {Benner, Peter}, title = {Balancing-related model reduction for parabolic control systems}, booktitle = {Proc. of the 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations - CPDE 2013}, year = 2013, volume = 1, pages = {257--262}, doi = {10.3182/20130925-3-FR-4043.00065}, edition = {PART 1} } @Book{morBen17, editor = {P. Benner}, title = {System Reduction for Nanoscale {IC} Design}, publisher = {Springer}, year = 2017, volume = 20, series = {Mathematics in Industry}, isbn = {978-3-319-07235-7}, doi = {10.1007/978-3-319-07236-4} } @Article{morBenB11, author = {Benner, P. and Breiten, T.}, title = {On {$H_2$}-model reduction of linear parameter-varying systems}, journal = PAMM, year = 2011, volume = 11, number = 1, pages = {805--806}, doi = {10.1002/pamm.201110391} } @InProceedings{morBenB12, author = {P. Benner and T. Breiten}, title = {{K}rylov-Subspace Based Model Reduction of Nonlinear Circuit Models Using Bilinear and Quadratic-Linear Approximations}, booktitle = {Progress in Industrial Mathematics at ECMI 2010}, year = 2012, editor = {M. G{\"{u}}nther and A. Bartel and M. Brunk and S. Sch{\"{o}}ps and M. Striebel}, volume = 17, series = {Mathematics in Industry}, pages = {153--159}, address = {Berlin}, publisher = Springer, doi = {10.1007/978-3-642-25100-9_18} } @Article{morBenB12b, author = {P. Benner and T. Breiten}, title = {Interpolation-based $\mathcal{H}_2$-model reduction of bilinear control systems}, journal = SIAMMatrix, year = 2012, volume = 33, number = 3, pages = {859--885}, doi = {10.1137/110836742} } @Article{morBenB15, author = {P. Benner and T. Breiten}, title = {Two-Sided Projection Methods for Nonlinear Model Order Reduction}, journal = SIAMSciComp, year = 2015, volume = 37, number = 2, pages = {B239--B260}, doi = {10.1137/14097255X} } @InCollection{morBenB17, author = {Benner, P. and Breiten, T.}, title = {Model Order Reduction Based on System Balancing}, booktitle = {Model Reduction and Approximation}, publisher = {SIAM}, year = 2017, editor = {Benner, P. and Cohen, A. and Ohlberger, M. and Willcox, K.}, series = {Computational Science \& Engineering}, pages = {261--295}, address = {Philadelphia, PA}, doi = {10.1137/1.9781611974829.ch6} } @Article{morBenBD10, author = {Benner, P. and Breiten, T. and Damm, T.}, title = {{K}rylov subspace methods for model order reduction of bilinear discrete-time control systems}, journal = PAMM, year = 2010, volume = 10, number = 1, pages = {601--602}, doi = {10.1002/pamm.201010293} } @Article{morBenBD11, author = {Benner, P. and Breiten, T. and Damm, T.}, title = {Generalized tangential interpolation for model reduction of discrete-time {MIMO} bilinear systems}, journal = IntControl, year = 2011, volume = 84, number = 8, pages = {1398--1407}, issn = {0020-7179}, doi = {10.1080/00207179.2011.601761}, publisher = {Taylor and Francis}, address = {London} } @InCollection{morBenBF15, author = {Benner, P. and Breiten, T. and Feng, L.}, title = {Matrix Equations and Model Reduction}, booktitle = {Matrix Functions and Matrix Equations}, publisher = {World Scientific}, year = 2015, volume = 19, series = {Series in Contemporary Applied Mathematics}, pages = {50--57}, editors = {Bai, Z. and Gao, W. and Su, Y.}, doi = {10.1142/9789814675772_0003} } @InProceedings{morBenBFetal09, author = {Benner, P. and Bonin, T. and Fa{\ss}bender, H. and Saak, J. and Soppa, A. and Zaeh, M.}, title = {Novel Model Reduction Techniques for Control of Machine Tools}, booktitle = {Proceedings of ANSYS Conference \& 27. CADFEM Users{\'{}} Meeting 2009, 18.-20. November 2009, Congress Center Leipzig}, year = 2009, address = {Grafing}, publisher = {CADFEM GmbH}, note = {ISBN/ISSN: 3-937523-06-5} } @InCollection{morBenBG18, author = {Benner, P. and Braukm{\"{u}}ller, M. and Grundel, S.}, title = {A Direct Index 1 {DAE} Model of Gas Networks}, booktitle = {Reduced-Order Modeling ({ROM}) for Simulation and Optimization}, publisher = {Springer, Cham}, year = 2018, editor = {Keiper, W. and Milde, A. and Volkwein, S.}, pages = {99--119}, doi = {10.1007/978-3-319-75319-5_5} } @Article{morBenBHetal20, author = {Benner, P. and Breiten, T. and Hartmann, C. and Schmidt, B.}, title = {Model reduction of controlled {F}okker-{P}lanck and {L}iouville-von {N}eumann equations}, journal = {Journal of Computational Dynamics}, year = 2020, volume = 7, number = 1, pages = {1--33}, doi = {10.3934/jcd.2020001} } @InProceedings{morBenCQetal04, author = {P. Benner and M. Castillo and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {Parallel Model Reduction of Large-Scale Unstable Systems}, booktitle = {Parallel Computing: Software Technology, Algorithms, Architectures \& Applications. Proc. Intl. Conf. ParCo2003, Dresden, Germany}, year = 2004, editor = {G.~R. Joubert and W.~E. Nagel and F.~J. Peters and W.~V. Walter}, volume = 13, series = {Advances in Parallel Computing}, pages = {251--258}, publisher = {Elsevier B.V. (North-Holland)}, isbn = {0-444-51689-1} } @ARTICLE{morBenCS19, author = {Benner, P. and Cao, X. and Schilders, W.}, title = {A bilinear $\mathcal{H}_{2}$ model order reduction approach to linear parameter-varying systems}, journal = AdvComputMath, volume = {45}, pages = {2241--2271}, year = {2019}, doi = {10.1007/s10444-019-09695-9} } @Article{morBenD11, author = {P. Benner and T. Damm}, title = {{L}yapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems}, journal = SIAMControlOpt, year = 2011, volume = 49, number = 2, pages = {686--711}, doi = {10.1137/09075041X} } @InCollection{morBenDEetal14, author = {Benner, P. and Dufrechou, E. and Ezzatti, P. and Igounet, P. and Quintana{-}Ort{{\'\i}}, E.~S. and Rem{\'{o}}n, A.}, title = {Accelerating Band Linear Algebra Operations on {GPU}s with Application in Model Reduction}, booktitle = {Computational Science and Its Applications - {ICCSA} 2014 - 14th International Conference, Guimar{\~{a}}es, Portugal, 2014, Proceedings, Part {VI}}, publisher = Springer, year = 2014, editor = {Beniamino Murgante and Sanjay Misra and Ana Maria A.~C. Rocha and Carmelo Maria Torre and Jorge Gustavo Rocha and Maria Irene Falc{\~{a}}o and David Taniar and Bernady O. Apduhan and Osvaldo Gervasi}, volume = 8584, series = LNCS, pages = {386--400}, isbn = {978-3-319-09152-5}, doi = {0.1007/978-3-319-09153-2_29} } @Article{morBenDEetal15, author = {Benner, P. and Dufrechou, E. and Ezzatti, P. and Quintana-Ort{\'i}, E.~S. and Rem{\'o}n, A.}, title = {Unleashing {GPU} acceleration for symmetric band linear algebra kernels and model reduction}, journal = {Cluster Computing}, year = 2015, volume = 18, number = 4, pages = {1351--1362}, issn = {1573-7543}, doi = {10.1007/s10586-015-0489-x} } @Article{morBenDRetal16, author = {Benner, P. and Damm, T. and Redmann, M. and Cruz Y.~R.~R.}, title = {Positive operators and stable truncation}, journal = LinAlgApp, year = 2016, volume = 498, pages = {74--87}, doi = {10.1016/j.laa.2014.12.005} } @Article{morBenDYetal20, author = {Benner, P. and Du, X. and Yang, G. and Ye, D.}, title = {Balanced truncation of linear time-invariant systems over finite-frequency ranges}, journal = AdvComputMath, volume = {46}, number = {}, pages = {82}, year = {2020}, doi = {10.1007/s10444-020-09823-w} } @TechReport{morBenEEetal18, author = {Benaceur, A. and Ehrlacher, V. and Ern, A. and Meunier, S.}, title = {A progressive reduced basis/empirical interpolation method for nonlinear parabolic problems}, institution = {Cornell University}, year = 2018, type = {arXiv e-prints}, number = {1710.00511v2}, note = {math.NA}, url = {https://arxiv.org/abs/1710.00511} } @InProceedings{morBenEKetal11, author = {Benner, P. and Eberhard, P. and Knoll, G. and K{\"{u}}rschner, P. and Nowakowski, Christine C.and Ochse, G.}, title = {Optimale {FE}-{R}eduktion, {M}oderne {M}odellreduktion elastischer {B}auteile f{\"{u}}r die {S}imulation flexibler {M}ehrk{\"{o}}rpersysteme}, booktitle = {Informationstagung Motoren: Fr{\"{u}}hjahrstagung 2011}, year = 2011, volume = {Heft R 553}, series = {Forschungsvereinigung Verbrennungskraftmaschinen}, pages = {175--197} } @InCollection{morBenEKetal12, author = {Benner, P. and Ezzatti, P. and Kressner, D. and Quintana-Ort{\'\i}, E.~S. and Rem{\'o}n, Alfredo}, title = {Accelerating Model Reduction of Large Linear Systems with Graphics Processors}, booktitle = {Applied Parallel and Scientific Computing}, publisher = Springer, year = 2012, editor = {J{\'o}nasson, Kristj{\'a}n}, volume = 7134, series = LNCS, pages = {88--97}, address = {Berlin/Heidelberg}, isbn = {978-3-642-28144-0}, doi = {10.1007/978-3-642-28145-7_9} } @InProceedings{morBenEQetal12, author = {Benner, P. and Ezzatti P. and Quintana{-}Ort{{\'\i}} E.~S. and Rem{\'{o}}n, A.}, title = {High Performance Implementations of the {BST} Method on Hybrid {CPU-GPU} Platforms}, booktitle = {10th {IEEE} International Symposium on Parallel and Distributed Processing with Applications, {ISPA} 2012, Leganes, Madrid, Spain, July 10-13, 2012}, year = 2012, pages = {662--668}, publisher = {IEEE}, isbn = {978-1-4673-1631-6}, doi = {10.1109/ISPA.2012.98} } @InCollection{morBenEQetal12a, author = {Benner, P. and Ezzatti P. and Quintana{-}Ort{{\'\i}} E.~S. and Rem{\'{o}}n, A.}, title = {Accelerating {BST} Methods for Model Reduction with Graphics Processors}, booktitle = {Parallel Processing and Applied Mathematics - 9th International Conference, {PPAM} 2011, Torun, Poland, September 11-14, 2011. Revised Selected Papers, Part {I}}, publisher = Springer, year = 2012, editor = {R. Wyrzykowski and J. Dongarra and K. Karczewski and J. Wasniewski}, volume = 7203, series = LNCS, pages = {549--558}, address = {Berlin/Heidelberg}, isbn = {978-3-642-31463-6}, doi = {10.1007/978-3-642-31464-3_56} } @Article{morBenF06, author = {P. Benner and H. Fa{\ss}bender}, title = {Numerische {M}ethoden zur passivit{\"{a}}tserhaltenden {M}odellreduktion}, journal = atAutom, year = 2006, volume = 54, number = 4, pages = {153--160} } @InProceedings{morBenF06a, author = {P. Benner and H. Fa{\ss}bender}, title = {Passivity Preserving Model Reduction via a Structured {L}anczos Method}, booktitle = {Proc. 2006 {IEEE} Conf. CACSD, Munich, Germany, Oct. 4-6}, year = 2006, pages = {8--13}, publisher = {IEEE} } @Article{morBenF15, author = {Benner, P. and Feng, L.}, title = {Model Order Reduction for Coupled Problems}, journal = {Applied and Computational Mathematics: An International journal}, year = 2015, volume = 14, number = 1, pages = {3--22}, url = {http://acmij.az/view.php?lang=az&menu=journal&id=372} } @InCollection{morBenF19, author = {Benner, P. and Fa{\ss}bender, H.}, title = {Model Order Reduction: Techniques and Tools}, booktitle = {Encyclopedia of Systems and Control}, editor = {Baillieul, J. and Samad, T.}, publisher = {Springer}, year = {2019}, doi = {10.1007/978-1-4471-5102-9_142-2} } @Book{morBenF24, author = {Benner, Peter and Fa{\ss}bender, Heike}, title = {{M}odellreduktion : {E}ine systemtheoretisch orientierte {E}inf{\"u}hrung}, publisher = {Springer Spektrum}, year = 2024, series = {{Springer Studium Mathematik (Master)}}, address = {Berlin, Heidelberg}, issn = {2509-9310; 2509-9329}, isbn = {978-3-662-67492-5; 978-3-662-67493-2}, doi = {10.1007/978-3-662-67493-2}, pages = {XIV, 259} } @InProceedings{morBenFLetal15, author = {Benner, P. and Feng, L. and Li, S. and Zhang, Y.}, title = {Reduced-Order Modeling and {ROM}-Based Optimization of Batch Chromatography}, booktitle = {Numerical Mathematics and Advanced Applications - ENUMATH 2013}, publisher = {Springer International Publishing}, pages = {427--435}, year = {2015}, doi = {10.1007/978-3-319-10705-9_42} } @Article{morBenFSM14, author = {Benner, P. and Feng, L. and Schoenmaker, W. and Meuris, P.}, title = {nano{COPS}: Parametric Modeling and Model Order Reduction of Coupled Problems}, journal = {ECMI Newsletter}, year = 2014, volume = 56, pages = {68--69}, url = {http://www.mafy.lut.fi/EcmiNL/issues.php?action=viewart&ID=352} } @Proceedings{morBenFSetal06, title = {{Special Issue} on "{O}rder {R}eduction of {L}arge-{S}cale {S}ystems"}, year = 2006, editor = {P. Benner and R.~W. Freund and D.~C. Sorensen and A. Varga}, volume = {415, issues 2--3}, series = {Linear Algebra and Its Applications}, month = jun } @Article{morBenFSetal06a, author = {P. Benner and R.~W. Freund and D.~C. Sorensen and A. Varga}, title = {{Preface Special Issue} on "{O}rder reduction of large-scale systems"}, journal = LinAlgApp, year = 2006, volume = 415, number = {2--3}, pages = {231--234} } @Article{morBenG15, author = {P. Benner and S. Grundel}, title = {Model order reduction for a family of linear systems with applications in parametric and uncertain systems}, journal = ApplMathLett, year = 2015, volume = 39, pages = {1--6}, doi = {10.1016/j.aml.2014.08.002} } @Article{morBenG16, author = {Benner, P. and Goyal, P.}, title = {Multipoint Interpolation of {V}olterra Series and $\mathcal{H}_2$-Model Reduction for a Family of Bilinear Descriptor Systems}, journal = SCL, year = 2016, volume = 97, pages = {1--11}, doi = {10.1016/j.sysconle.2016.08.008} } @InProceedings{morBenG16a, author = {Benner, P. and Goyal, P.}, title = {Algebraic {G}ramians for quadratic-bilinear systems and their application in model order reduction}, booktitle = {Proc. of the 22nd International Symposium on Mathematical Theory of Networks and Systems - MTNS 2016 , Minnesota, USA}, year = 2016, pages = {81--83}, url = {http://hdl.handle.net/11299/181518} } @TechReport{morBenG17, author = {Benner, P. and Goyal, P.}, title = {Balanced truncation model order reduction for quadratic-bilinear systems}, institution = {arXiv}, year = 2017, type = {e-prints}, number = {1705.00160}, note = {math.OC}, url = {https://arxiv.org/abs/1705.00160} } @InCollection{morBenG18, author = {Benner, P. and Goyal, P.}, title = {An iterative model reduction scheme for quadratic-bilinear descriptor systems with an application to {N}avier-{S}tokes equations}, booktitle = {Reduced-Order Modeling for Simulation and Optimization}, publisher = {Springer}, year = 2018, editor = {Keiper, W. and Milde, A. and Volkwein, S.}, pages = {1--19}, doi = {10.1007/978-3-319-75319-5_1} } @Article{morBenG21, author = {Benner, P. and Goyal, P.}, title = {Interpolation-Based Model Order Reduction for Polynomial Systems}, journal = SIAMSciComp, year = 2021, volume = 43, number = 1, pages = {A84--A108}, doi = {10.1137/19M1259171} } @Article{morBenGG18, author = {Benner, P. and Goyal, P. and Gugercin, S.}, title = {$\mathcal{H}_2$-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems}, journal = SIAMMatrix, year = 2018, volume = 39, number = 2, pages = {983--1032}, doi = {10.1137/16M1098280} } @Article{morBenGH15, author = {P. Benner and S. Grundel and N. Hornung}, title = {Parametric model order reduction with a small $\mathcal{H}_2$-error using radial basis functions}, journal = AdvComputMath, year = 2015, volume = 41, number = 5, pages = {1231--1253}, publisher = {Springer}, doi = {10.1007/s10444-015-9410-7} } @InProceedings{morBenGH18, author = {Benner, P. and Grundel, S. and Himpe, C.}, title = {Parametric Model Order Reduction for Gas Flow Models}, booktitle = {ScienceOpen Posters (MoRePaS 2018 - Model Reduction of Parametrized Systems IV)}, year = 2018, doi = {10.14293/P2199-8442.1.SOP-MATH.EJOCET.v1} } @Article{morBenGHetal22, author = {Benner, P. and Goyal, P. and Heiland, J. and Pontes Duff, I.}, title = {Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows}, journal = ETNA, year = 2022, volume = 56, pages = {28--51}, doi = {10.1553/etna_vol56s28} } @Article{morBenGHetal23, author = {Benner, P. and Goyal, P. and Heiland, J. and Pontes, I.}, title = {A quadratic decoder approach to nonintrusive reduced-order modeling of nonlinear dynamical systems}, journal = PAMM, year = 2023, volume = 23, number = 1, pages = {e202200049}, doi = {10.1002/pamm.202200049} } @Article{morBenGKetal20, author = {Benner, P. and Goyal, P. and Kramer, B. and Peherstorfer, B. and Willcox, K.}, title = {Operator Inference for Non-Intrusive Model Reduction of Systems with Non-Polynomial Nonlinear Terms}, journal = CompMethAppMechEng, year = 2020, volume = 372, pages = 113433, doi = {10.1016/j.cma.2020.113433} } @Article{morBenGM16, author = {Benner, P. and Grundel, S. and Mlinari{\'c}, P.}, title = {Stability preserving model reduction for linearly coupled linear time-invariant systems}, journal = PAMM, year = 2016, volume = 16, number = 1, pages = {817--818}, doi = {10.1002/pamm.201610397} } @InCollection{morBenGM20, author = {Benner, P. and Grundel, S. and Mlinari{\'c}, P.}, title = {Clustering-Based Model Order Reduction for Nonlinear Network Systems}, booktitle = {Model Reduction of Complex Dynamical Systems}, series = {International Series of Numerical Mathematics}, volume = {171}, editor = {Benner, P. and Breiten, T. and Fa{\ss}bender, H. and Hinze, M. and Stykel, T. and Zimmermann R.}, publisher = {Birkh{\"{a}}user, Cham}, pages = {75--96}, year = {2021}, doi = {10.1007/978-3-030-72983-7_4} } @InCollection{morBenGP22, author = {Benner, P. and Goyal, P. and Pontes Duff, I.}, title = {Data-driven identification of {R}ayleigh-damped second-order systems}, booktitle = {Realization and Model Reduction of Dynamical Systems - A Festschrift in Honor of the 70th Birthday of {T}hanos {A}ntoulas}, publisher = {Springer, Cham}, year = 2022, pages = {255-272}, editors = {Beattie, C. and Benner, P. and Embree, M. and Gugercin, S. and Lefteriu, S.}, doi = {10.1007/978-3-030-95157-3_14} } @Article{morBenGP22a, author = {Benner, P. and Goyal, P. and Pontes Duff, I.}, title = {{G}ramians, energy functionals and balanced truncation for linear dynamical systems with quadratic outputs}, journal = IEEETransAC, year = 2022, volume = 67, number = 2, pages = {886-893}, doi = {10.1109/TAC.2021.3086319} } @Article{morBenGP24, author = {Benner, P. and Goyal, P. and Pontes Duff, I.}, title = {Identification of Dominant Subspaces for Linear Structured Parametric Systems and Model Reduction}, journal = IntNumerEng, year = 2024, doi = {10.1002/nme.7496} } @Book{morBenGQetal21, editor = {Benner, P. and Grivet-Talocia, S. and Quarteroni, A. and Rozza, G. and Schilders, W.~H.~A. and Silveira, L.~M.}, title = {{Model Order Reduction. Volume 1: System- and Data-Driven Methods and Algorithms}}, publisher = {De~Gruyter}, year = 2021, address = {Berlin}, isbn = {978-3-11-050043-1}, doi = {10.1515/9783110498967} } @Book{morBenGQetal21a, editor = {Benner, P. and Grivet-Talocia, S. and Quarteroni, A. and Rozza, G. and Schilders, W.~H.~A. and Silveira, L.~M.}, title = {{Model Order Reduction. Volume 2: Snapshot-Based Methods and Algorithms}}, publisher = {De~Gruyter}, year = 2021, address = {Berlin}, isbn = {978-3-11-067140-7}, doi = {10.1515/9783110671490} } @Book{morBenGQetal21b, editor = {Benner, P. and Grivet-Talocia, S. and Quarteroni, A. and Rozza, G. and Schilders, W.~H.~A. and Silveira, L.~M.}, title = {{Model Order Reduction. Volume 3: Applications}}, publisher = {De~Gruyter}, year = 2021, address = {Berlin}, isbn = {978-3-11-050044-8}, doi = {10.1515/9783110499001} } @InCollection{morBenGR17, author = {Benner, P. and Goyal, P. and Redmann, M.}, title = {Truncated {G}ramians for bilinear systems and their advantages in model order reduction}, booktitle = {Model Reduction of Parametrized Systems}, publisher = {Springer}, year = 2017, editor = {Benner, P. and Ohlberger, M. and Patera, T. and Rozza, G. and Urban, K.}, volume = 17, series = {MS\&A - Modeling, Simulation and Applications}, pages = {285--300}, address = {Cham}, doi = {10.1007/978-3-319-58786-8_18} } @Article{morBenGV20, author = {Benner, P. and Goyal, P. and Van Dooren, P.}, title = {Identification of Port-{H}amiltonian Systems from Frequency Response Data}, journal = SCL, year = 2020, volume = 143, pages = {104741}, doi = {10.1016/j.sysconle.2020.104741} } @Article{morBenGW15, author = {Benner, P. and Gugercin, S. and Willcox, K.}, title = {A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems}, journal = SIAMReview, year = 2015, volume = 57, number = 4, pages = {483--531}, doi = {10.1137/130932715} } @Article{morBenGW21, author = {Benner, P. and Gugercin, S. and Werner, S.~W.~R.}, title = {Structure-Preserving Interpolation for Model Reduction of Parametric Bilinear Systems}, journal = Automatica, volume = {132}, pages = {109799}, year = {2021}, doi = {10.1016/j.automatica.2021.109799} } @ARTICLE{morBenGW21a, author = {Benner, P. and Gugercin, S. and Werner, S.~W.~R.}, title = {Structure-preserving interpolation of bilinear control systems}, journal = AdvComputMath, volume = {47}, number = {3}, pages = {43}, year = {2021}, doi = {10.1007/s10444-021-09863-w} } @Article{morBenGW24, author = {Benner, P. and Gugercin, S. and Werner, S.~W.~R.}, title = {Structured interpolation for multivariate transfer functions of quadratic-bilinear systems}, journal = AdvComputMath, year = 2024, volume = 50, number = 2, pages = {Paper No. 18}, doi = {10.1007/s10444-024-10109-8} } @article{morBenGW24a, author = {Benner, Peter and Gugercin, Serkan and Werner, Steffen W.~R.}, title = {Structure-preserving interpolation of quadratic-bilinear systems via regular multivariate transfer functions}, journal = PAMM, year = 2024, volume = 24, number = 3, pages = {e202400048}, doi = {10.1002/pamm.202400048} } @Article{morBenH12, author = {P. Benner and M.~W. Hess}, title = {The Reduced Basis Method for Time-Harmonic {M}axwell's Equations}, journal = PAMM, year = 2012, volume = 12, number = 1, pages = {661--662}, month = dec, organization = {GAMM}, doi = {10.1002/pamm.201210319} } @InCollection{morBenH15, author = {P. Benner and J. Heiland}, title = {{LQG}-Balanced Truncation Low-Order Controller for Stabilization of Laminar Flows}, booktitle = {Active Flow and Combustion Control 2014}, publisher = {Springer International Publishing}, year = 2015, editor = {R. King}, volume = 127, series = {Notes on Numerical Fluid Mechanics and Multidisciplinary Design}, pages = {365--379}, isbn = {978-3-319-11966-3}, doi = {10.1007/978-3-319-11967-0_22} } @InProceedings{morBenH16, author = {P. Benner and M.~W. Hess}, title = {Reduced Basis Modeling for Uncertainty Quantification of Electromagnetic Problems in Stochastically Varying Domains}, booktitle = {Scientific Computing in Electrical Engineering SCEE 2014}, year = 2016, editor = {A. Bartel and M. Clemens and M. G{\"{u}}nther and E.~J.~W. {ter Maten}}, volume = 23, series = {Mathematics in Industry}, pages = {215--222}, publisher = {Springer International Publishing}, doi = {10.1007/978-3-319-30399-4} } @Article{morBenH19, author = {Benner, P. and Himpe, C.}, title = {Cross-{G}ramian-Based Dominant Subspaces}, journal = AdvComputMath, year = 2019, volume = 45, number = 5, pages = {2533--2553}, doi = {10.1007/s10444-019-09724-7} } @Article{morBenH23, author = {Benner, P. and Heiland, J.}, title = {Space and Chaos-Expansion {G}alerkin {POD} Low-order Discretization of {PDE}s for Uncertainty Quantification}, journal = IntNumerEng, year = 2023, volume = 124, number = 12, pages = {2801--2817}, doi = {10.1002/nme.7229} } @InProceedings{morBenHK11, author = {Benner, P. and Hochstenbach, M.~E. and K{\"{u}}rschner, P.}, title = {Model order reduction of large-scale dynamical systems with {J}acobi-{D}avidson style eigensolvers}, booktitle = {International Conference on Communications, Computing and Control Applications (CCCA) 2011}, year = 2011, pages = {1--6}, month = mar, publisher = {IEEE}, doi = {10.1109/CCCA.2011.6031208} } @InProceedings{morBenHLetal18, author = {Benner, P. and Herzog, R. and Lang, N. and Riedel, I. and Saak, J.}, title = {Optimal sensor placement based on model order reduction}, booktitle = {Proceedings of the CIRP sponsored Conference on Thermal Issues in Machine Tools}, pages = {355--365}, year = 2018 } @Article{morBenHLetal19, author = {Benner, P. and Herzog, R. and Lang, N. and Riedel, I. and Saak, J.}, title = {Comparison of Model Order Reduction Methods for Optimal Sensor Placement for Thermo-Elastic Models}, journal = {Eng. Optim.}, year = {2019}, doi = {10.1080/0305215X.2018.1469133}, volume = 51, number = 3, pages = {465--483} } @Book{morBenHM11, editor = {Benner, P. and Hinze, M. and {ter Maten}, E.~J.~W.}, title = {Model Reduction for Circuit Simulation}, publisher = {Springer}, year = 2011, volume = 74, series = LNEE, address = {Dodrecht}, issn = {1876-1100}, isbn = {978-94-007-0088-8}, doi = {10.1007/978-94-007-0089-5}, pages = 315 } @Article{morBenHM18, author = {Benner, P. and Himpe, C. and Mitchell, T.}, title = {On Reduced Input-Output Dynamic Mode Decomposition}, journal = AdvComputMath, year = 2018, volume = 44, number = 6, pages = {1751--1768}, doi = {10.1007/s10444-018-9592-x} } @Article{morBenHS14, author = {Benner, P. and Hossain, M.-S. and Stykel, T.}, title = {Low-rank iterative methods for periodic projected {L}yapunov equations and their application in model reduction of periodic descriptor systems}, journal = NumerAlg, year = 2014, volume = 67, number = 3, pages = {669--690}, issn = {1017-1398}, doi = {10.1007/s11075-013-9816-6}, publisher = {J.C. Baltzer}, address = {Basel, Switzerland} } @Article{morBenHW22, author = {P. Benner and J. Heiland and S.~W.~R. Werner}, title = {Robust output-feedback stabilization for incompressible flows using low-dimensional {\(\mathcal{H}\)}\({}_{\mbox{{\(\infty\)} }}\)-controllers}, journal = {Comput. Optim. Appl.}, year = 2022, volume = 82, number = 1, pages = {225--249}, doi = {10.1007/s10589-022-00359-x} } @TechReport{morBenKS11, author = {P. Benner and M. K{\"{o}}hler and J. Saak}, title = {Sparse-Dense {S}ylvester Equations in {${H}_2$}-Model Order Reduction}, institution = {Max Planck Institute Magdeburg}, year = 2011, type = {Preprint}, number = {MPIMD/11-11}, url = {https://csc.mpi-magdeburg.mpg.de/preprints/2011/11/}, month = dec } @Article{morBenKS12, author = {Benner, P. and K{\"{u}}rschner, P. and Saak, J.}, title = {A Goal-Oriented Dual {LRCF-ADI} for Balanced Truncation}, journal = {IFAC Proceedings Volumes (7th Vienna International Conference on Mathematical Modelling)}, year = 2012, volume = 45, number = 2, pages = {752--757}, doi = {10.3182/20120215-3-AT-3016.00133} } @Article{morBenKS12a, author = {Benner, P. and K{\"{u}}rschner, P. and Saak, J.}, title = {Improved Second-Order Balanced Truncation for Symmetric Systems}, journal = {IFAC Proceedings Volumes (7th Vienna International Conference on Mathematical Modelling)}, year = 2012, volume = 45, number = 2, pages = {758--762}, doi = {10.3182/20120215-3-AT-3016.00134} } @Article{morBenKS13, author = {P. Benner and P. K{\"{u}}rschner and J. Saak}, title = {An Improved Numerical Method for Balanced Truncation for Symmetric Second Order Systems}, journal = MCMDS, year = 2013, volume = 19, number = 6, pages = {593--615}, doi = {10.1080/13873954.2013.794363} } @Article{morBenKS13a, author = {P. Benner and P. K{\"{u}}rschner and J. Saak}, title = {A Reformulated Low-Rank {ADI} Iteration with Explicit Residual Factors}, journal = PAMM, year = 2013, volume = 13, number = 1, pages = {585--586}, doi = {10.1002/pamm.201310273} } @Article{morBenKS16, author = {P. Benner and P. K{\"{u}}rschner and J. Saak}, title = {Frequency-Limited Balanced Truncation with Low-Rank Approximations}, journal = SIAMSciComp, year = 2016, volume = 38, number = 1, pages = {A471--A499}, month = Feb, doi = {10.1137/15M1030911} } @InCollection{morBenKS21, author = {Benner, P. and K{\"{o}}hler, M. and Saak, J.}, title = {Matrix Equations, Sparse Solvers: {M-M.E.S.S.}-2.0.1 -- Philosophy, Features and Application for (Parametric) Model Order Reduction}, booktitle = {Model Reduction of Complex Dynamical Systems}, series = {International Series of Numerical Mathematics}, volume = {171}, editor = {Benner, P. and Breiten, T. and Fa{\ss}bender, H. and Hinze, M. and Stykel, T. and Zimmermann, R.}, publisher = {Birkh{\"{a}}user, Cham}, pages = {369--392}, year = {2021}, doi = {10.1007/978-3-030-72983-7_18} } @Article{morBenKSetal12, author = {Benner, P. and Kranz, B. and Saak, J. and Uddin, M.~M.}, title = {Efficient Reduced Order State Space Model Computation for a Class of Second Order Index One Systems}, journal = PAMM, year = 2012, volume = 12, number = 1, pages = {699--700}, doi = {10.1002/pamm.201210338} } @Article{morBenKTetal16, author = {Benner, P. and K{\"{u}}rschner, P. and Tomljanovi{\'c}, Z. and Truhar, N.}, title = {Semi-active damping optimization of vibrational systems using the parametric dominant pole algorithm}, journal = ZAngewMathMech, year = 2016, volume = 96, number = 5, pages = {604--619}, doi = {10.1002/zamm.201400158}, publisher = WileyVCH } @Article{morBenL04, author = {J.~K. Bennighof and R.~B. Lehoucq}, title = {An automated multilevel substructuring method for eigenspace computation in linear elastodynamics}, journal = SIAMSciComp, year = 2004, volume = 25, number = 6, pages = {2084--2106} } @Article{morBenLS13, author = {Benner, P. and Lang, N. and Saak, J.}, title = {Modeling structural variability in reduced order models of machine tool assembly groups via parametric {MOR}}, journal = PAMM, year = 2013, volume = 13, pages = {481--482}, month = dec, publisher = WileyVCH, organization = {GAMM}, doi = {10.1002/pamm.201310233} } @InProceedings{morBenLS13a, author = {Benner, P. and Lang, N. and Saak, J.}, title = {Modellordnungsreduktion f{\"{u}}r geschaltete, gekoppelte thermo-elastische {S}ysteme}, booktitle = {Tagungsband des GMA-Fachausschusses 1.30 "Modellbildung, Identifikation und Simulation in der Automatisierungstechnik"}, year = 2013, editor = {Sawodny, O. and Adamy, J.}, pages = {215--227}, organization = {Institut f{\"{u}}r Automatisierungstechnik und Mechatronik}, publisher = {Technische Universit{\"{a}}t Darmstadt} } @Article{morBenLS23, author = {Benner, P. and Lund, K. and Saak, J.}, title = {Towards a benchmark framework for model order reduction in the {M}athematical {R}esearch {D}ata {I}nitiative ({MaRDI})}, journal = PAMM, year = 2023, volume = 23, number = 3, pages = {e202300147}, doi = {10.1002/pamm.202300147} } @InCollection{morBenMQetal02, author = {P. Benner and R. Mayo and E.~S. Quintana and G. Quintana-Ort{\'\i}}, title = {Enhanced services for remote model reduction of large-scale dense linear systems}, booktitle = {PARA'02 Conference on Applied Parallel Computing, Espoo (Finland), 2002}, publisher = Springer, year = 2002, editor = {J. Fagerholm and J. Haataja and J. J{\"{a}}rvinen and M. Lyly and P. Raback and V. Savolainen}, volume = 2367, pages = {329--338}, annote = {ISBN: 3-540-43786-X}, sweries = LNCS } @InCollection{morBenMQetal04, author = {P. Benner and R. Mayo and E.~S. Quintana and G. Quintana-Ort{\'\i}}, title = {A Model Reduction Web Environment for Very Large Linear Dynamical Systems}, booktitle = {Parallel and Distributed Scientific and Engineering Computing: Practice and Experience}, publisher = {NOVA Science Publishers, Hauppauge, NY}, year = 2004, editor = {V.~Y. Pan and L.~T. Yang}, volume = 15, series = {Advances in Computation: Theory and Practice}, pages = {23--33}, annote = {ISBN: 1-59033-956-8} } @Book{morBenMS05, author = {Benner, P. and Mehrmann, V. and Sorensen, D.~C.}, title = {Dimension Reduction of Large-Scale Systems}, publisher = Springer, year = 2005, volume = 45, series = LNCSE, address = {Berlin/Heidelberg, Germany}, doi = {10.1007/3-540-27909-1} } @Book{morBenOCetal17, editor = {Benner, P. and Ohlberger, M. and Cohen, A. and Willcox, K.}, title = {Model Reduction and Approximation: Theory and Algorithms}, publisher = {Society for Industrial and Applied Mathematics}, address = {Philadelphia, PA}, series = {Computational Science \& Engineering}, year = {2017}, doi = {10.1137/1.9781611974829}, isbn = {978-1-611974-81-2} } @Book{morBenOPetal17, editor = {Benner, P. and Ohlberger, M. and Patera, A.~T. and Rozza, G. and Urban, K.}, title = {Model Reduction of Parametrized Systems}, publisher = {Springer International Publishing}, year = 2017, doi = {10.1007/978-3-319-58786-8}, isbn = {978-3-319-58786-8} } @InProceedings{morBenQ05, author = {Benner, P. and Quintana-Ort{\'\i}, E.~S.}, title = {Model Reduction Based on Spectral Projection Methods}, booktitle = {Dimension Reduction of Large-Scale Systems}, year = 2005, editor = {Benner, P. and Mehrmann, V. and Sorensen, D.}, volume = 45, series = LNCSE, pages = {5--45}, address = {Berlin/Heidelberg, Germany}, publisher = {Springer}, doi = {10.1007/3-540-27909-1_1} } @Article{morBenQQ00, author = {Benner, P. and Quintana-Ort{\'\i}, E.~S. and Quintana-Ort{\'\i}, G.}, title = {Balanced Truncation Model Reduction of Large-Scale Dense Systems on Parallel Computers}, journal = MCMDS, year = 2000, volume = 6, number = 4, pages = {383--405}, annote = {Berichte aus der Techno\-mathe\-ma\-tik, Report 99--07, FB3~--~Mathematik und Informatik, Universit{\"{a}}t Bremen, 28334 Bremen (Germany), September 1999}, publisher = {Taylor \& Francis}, doi = {10.1076/mcmd.6.4.383.3658} } @InCollection{morBenQQ00a, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {Singular Perturbation Approximation of Large, Dense Linear Systems}, booktitle = {Proc. 2000 {IEEE} Intl. Symp. CACSD, Anchorage, Alaska, USA, September 25--27, 2000}, publisher = {IEEE Press, Piscataway, NJ}, year = 2000, pages = {255--260}, annote = {ISBN 0-7803-6488-0} } @InProceedings{morBenQQ00b, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {Efficient Numerical Model Reduction Methods for Discrete-Time Systems}, booktitle = {Proc. IMACS Symp. Math. Modelling, 3rd MATHMOD Vienna, \upshape{Vol. 1}}, year = 2000, editor = {I. Troch and F. Breitenecker}, number = 15, series = {ARGESIM Reports}, pages = {277--280}, month = feb, address = {Vienna (Austria)} } @Article{morBenQQ01, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {Efficient Numerical Algorithms for Balanced Stochastic Truncation}, journal = IntJAppCompSci, year = 2001, volume = 11, number = 5, pages = {1123--1150}, annote = {Berichte aus der Techno\-mathe\-ma\-tik, Report 01--03, FB3~--~Mathematik und Informatik, Universit{\"{a}}t Bremen, 28334 Bremen (Germany), March 2001} } @InProceedings{morBenQQ01b, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {{PSLICOT} Routines for Model Reduction of Stable Large-Scale Systems}, booktitle = {Proc. 3rd NICONET Workshop on Numerical Software in Control Engineering, Louvain-la-Neuve, Belgium, January 19, 2001}, year = 2001, pages = {39--44} } @TechReport{morBenQQ02, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {Experimental evaluation of the parallel model reduction routines in {PSLICOT}}, institution = {Niconet e.V.}, year = 2002, type = {SLICOT Working Note}, number = {2002--7}, month = aug, note = {Available from \url{www.slicot.org}} } @Article{morBenQQ03, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {State-Space Truncation Methods for Parallel Model Reduction of Large-Scale Systems}, journal = ParComputing, year = 2003, volume = 29, pages = {1701--1722} } @Article{morBenQQ03a, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {Parallel Algorithms for Model Reduction of Discrete-Time Systems}, journal = {Internat. J. Systems Sci.}, year = 2003, volume = 34, number = 5, pages = {319--333}, annote = {FB3~--~Mathematik und Informatik, Universit{\"{a}}t Bremen, Berichte aus der Techno\-mathe\-ma\-tik, Report 00--18, 28334 Bremen (Germany), December2000.} } @InProceedings{morBenQQ04, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {Computing Optimal {H}ankel Norm Approximations of Large-Scale Systems}, booktitle = {Proc. 43rd {IEEE} Conf. Decision Contr.}, year = 2004, pages = {3078--3083}, publisher = {Omnipress, Madison, WI}, annote = {CD Rom}, isbn = {0-7803-8683-3} } @InProceedings{morBenQQ04a, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {Computing Passive Reduced-Order Models for Circuit Simulation}, booktitle = {Proc. Intl. Conf. Parallel Comp. in Elec. Engrg. PARELEC 2004}, year = 2004, pages = {146--151}, publisher = {IEEE Computer Society, Los Alamitos, CA}, isbn = {0-7695-2080-4} } @InProceedings{morBenQQ05, author = {P. Benner and E.~S. Quintana-Ort{\'\i} and G. Quintana-Ort{\'\i}}, title = {Parallel Model Reduction of Large-Scale Linear Descriptor Systems via Balanced Truncation}, booktitle = {High Performance Computing for Computational Science - VECPAR 2004}, year = 2005, editor = {M. Dayd{\'e} and J.~J. Dongarra and V. Hern{\'a}ndez and J.~M.~L.~M. Palma}, volume = 3402, series = LNCS, pages = {340--353}, address = {Berlin/Heidelberg, Germany}, publisher = Springer, isbn = {3-540-25424-2}, doi = {10.1007/11403937_27} } @Article{morBenR15, author = {Benner, P. and Redmann, M.}, title = {Model reduction for Stochastic systems}, journal = {Stochastics Partial Differential Equations: Analysis and Computations}, year = 2015, volume = 3, number = 3, pages = {291--338}, doi = {10.1007/s40072-015-0050-1} } @Article{morBenR17a, author = {P. Benner and M. Redmann}, title = {An {$\mathcal H_2$}-Type Error Bound for Balancing- Related Model Order Reduction of Linear Systems with {L}{\'e}vy Noise}, journal = {Systems \& Control Letters}, year = 2017, volume = 105, pages = {1--5}, doi = {10.1016/j.sysconle.2017.04.004} } @Article{morBenR18, author = {Benner, P. and Redmann, M.}, title = {Singular Perturbation Approximation for Linear Systems with {L}{\'e}vy Noise}, journal = {Stochastics and Dynamics}, year = 2018, volume = {18}, number = {4}, pages = {1850033}, doi = {10.1142/S0219493718500338} } @InProceedings{morBenS05, author = {P. Benner and J. Saak}, title = {A Semi-Discretized Heat Transfer Model for Optimal Cooling of Steel Profiles}, booktitle = {Dimension Reduction of Large-Scale Systems}, year = 2005, editor = {P. Benner and V. Mehrmann and D. Sorensen}, volume = 45, series = LNCSE, pages = {353--356}, publisher = {Springer-Verlag, Berlin/Heidelberg, Germany}, doi = {10.1007/3-540-27909-1_19} } @InProceedings{morBenS09, author = {P. Benner and J. Saak}, title = {Efficient {B}alancing based {MOR} for {S}econd {O}rder {S}ystems {A}rising in {C}ontrol of {M}achine {T}ools}, booktitle = {Proceedings of the MathMod 2009}, year = 2009, editor = {I. Troch and F. Breitenecker}, number = 35, series = {ARGESIM-Reports}, pages = {1232--1243}, month = jan, address = {Vienna, Austria}, organization = {Vienna Univ. of Technology}, publisher = {ARGE Simulation News}, note = {ISBN/ISSN: 978-3-901608-35-3} } @InProceedings{morBenS10, author = {Benner, P. and Schneider, A.}, title = {{Balanced Truncation Model Order Reduction for {LTI} Systems with many Inputs or Outputs}}, booktitle = {Proc. of the 19th International Symposium on Mathematical Theory of Networks and Systems}, year = 2010, editor = {Edelmayer, Andr{\'a}s}, pages = {1971--1974}, address = {Budapest, Hungary}, isbn = {978-963-311-370-7} } @Article{morBenS11, author = {P. Benner and J. Saak}, title = {Efficient balancing-based {MOR} for large-scale second-order systems}, journal = MCMDS, year = 2011, volume = 17, number = 2, pages = {123--143}, doi = {10.1080/13873954.2010.540822} } @InProceedings{morBenS11a, author = {P. Benner and A. Schneider}, title = {Model Reduction for Linear Descriptor Systems with Many Ports}, booktitle = {Progress in Industrial Mathematics at ECMI 2010}, year = 2012, editor = {Michael G{\"{u}}nther and Andreas Bartel and Markus Brunk and Sebastian Sch{\"{o}}ps and Michael Striebel}, volume = 17, series = {Mathematics in Industry}, pages = {137--143}, address = {Berlin}, publisher = Springer, doi = {10.1007/978-3-642-25100-9_16} } @InCollection{morBenS11b, author = {Benner, P. and Schneider, A.}, title = {On Stability, Passivity and Reciprocity Preservation of {ESVDMOR}}, booktitle = {Model Reduction for Circuit Simulation}, publisher = Springer, year = 2011, editor = {Benner, Peter and Hinze, Michael and {ter Maten}, E.~J.~W.}, volume = 74, series = LNEE, pages = {277--288}, isbn = {978-94-007-0088-8}, doi = {10.1007/978-94-007-0089-5_16} } @InCollection{morBenS12, author = {Benner, P. and Schneider, A.}, title = {Some Remarks on A Priori Error Estimation for {ESVDMOR}}, booktitle = {Scientific Computing in Electrical Engineering SCEE 2010}, publisher = {Springer-Verlag}, year = 2012, editor = {Bastiaan, Michielsen and Poirier, Jean-Ren{\'e}}, volume = 16, series = {Mathematics in Industry / The European Consortium for Mathematics in Industry}, pages = {15--24}, address = {Berlin}, isbn = {978-3-642-22452-2}, doi = {10.1007/978-3-642-22453-9_2} } @TechReport{morBenS13, author = {Benner, P. and Schneider, J.}, title = {Uncertainty Quantification for {M}axwell's Equations Using Stochastic Collocation and Model Order Reduction}, institution = {Max Planck Institute Magdeburg}, year = 2013, type = {Preprint}, number = {MPIMD/13-19}, month = oct, note = {Submitted to International Journal for Uncertainty Quantification} } @Article{morBenS15, author = {Benner, P. and Schneider, J.}, title = {Uncertainty quantification for {M}axwell's equations using stochastic collocation and model order reduction}, journal = {International Journal for Uncertainty Quantification}, year = 2015, volume = 5, number = 3, pages = {195--208}, doi = {10.1615/Int.J.UncertaintyQuantification.2015010170} } @InCollection{morBenS17, author = {Benner, P. and Stykel, T.}, title = {Model Order Reduction for Differential-Algebraic Equations: A Survey}, booktitle = {Surveys in Differential-Algebraic Equations IV}, publisher = {Springer International Publishing}, year = 2017, editor = {Ilchmann, Achim and Reis, Timo}, series = {Differential-Algebraic Equations Forum}, pages = {107--160}, month = mar, address = {Cham}, isbn = {978-3-319-46618-7}, doi = {10.1007/978-3-319-46618-7_3} } @InCollection{morBenS17a, author = {Benner, P. and Schneider, A.}, title = {Reduced Representation of Power Grid Models}, booktitle = {System Reduction for Nanoscale {IC} Design}, publisher = {Springer}, year = 2017, editor = {Benner, P.}, volume = 20, series = {Mathematics in Industry}, pages = {87--134}, address = {Cham}, doi = {10.1007/978-3-319-07236-4_3} } @BOOK{morBenSGetal21, author = {Benner, P. and Schilders, W. and Grivet-Talocia, S. and Quarteroni, A. and Rozza, G. and Silveira, L.~M.}, title = {Model Order Reduction}, publisher = {De Gruyter}, address = {Berlin, Boston}, year = {2021}, url = {https://www.degruyter.com/view/title/523453} } @InProceedings{morBenSU12, author = {Benner, P. and Saak, J. and Uddin, M.~M.}, title = {Second Order to Second Order Balancing for Index-1 Vibrational Systems}, booktitle = {{7th International Conference on Electrical \& Computer Engineering (ICECE) 2012}}, year = 2012, pages = {933--936}, organization = {IEEE}, doi = {10.1109/ICECE.2012.6471704} } @Article{morBenSU16, author = {Benner, P. and Saak, J. and Uddin, M.~M.}, title = {Balancing based model reduction for structured index-2 unstable descriptor systems with application to flow control}, journal = {Numer. Algebra Control Optim.}, year = 2016, volume = 6, number = 1, pages = {1--20}, month = mar, issn = {2155-3289}, doi = {10.3934/naco.2016.6.1} } @Article{morBenSU16a, author = {Benner, P. and Saak, J. and Uddin, M.~M.}, title = {Structure preserving model order reduction of large sparse second-order index-1 systems and application to a mechatronics model}, journal = MCMDS, year = 2016, volume = 22, number = 6, pages = {509--523}, month = aug, doi = {10.1080/13873954.2016.1218347} } @InProceedings{morBenSU16b, author = {Benner, P. and Saak, J. and Uddin, M.~M.}, title = {Reduced-Order Modeling of Index-1 Vibrational Systems Using Interpolatory Projections}, booktitle = {Proceedings of the 19th International Conference On Computer and Information Technology}, year = 2016, pages = {134--138}, month = dec, address = {Dhaka, Bangladesh}, publisher = {IEEE Publications}, doi = {10.1109/ICCITECHN.2016.7860183} } @InCollection{morBenSV14, author = {Benner, P. and Sachs, E. and Volkwein, S.}, title = {Model Order Reduction for {PDE} Constrained Optimization}, booktitle = {Trends in PDE Constrained Optimization}, publisher = {Birkh{\"{a}}user}, year = 2014, editor = {Leugering, G. and P. Benner and S. Engell and A. Griewank and H. Harbrecht and M. Hinze and R. Rannacher and S. Ulbrich}, volume = 165, series = {International Series of Numerical Mathematics}, pages = {303--326}, address = {Basel}, doi = {10.1007/978-3-319-05083-6_19} } @InProceedings{morBenTT11, author = {Benner, P. and Tomljanovi{\'c}, Z. and Truhar, N.}, title = {Damping Optimization for Linear Vibrating Systems Using Dimension Reduction}, booktitle = {Vibration Problems ICOVP 2011}, year = 2011, editor = {N{\'a}prstek, J. and Hor{\'a}{\v c}ek, J. and Okrouhl{\'\i}k, M. and Marvalov{\'a}, B. and Verhulst, F. and Sawicki, J.~T.}, volume = {139, Part 5}, series = {Springer Proceedings in Physics}, pages = {297--305}, address = {Prag, Czech Republic}, publisher = Springer, isbn = {978-94-007-2068-8}, doi = {10.1007/978-94-007-2069-5_41} } @Article {morBenTT11a, author = {Benner, P. and Tomljanovi{\'c}, Z. and Truhar, N.}, title = {Dimension reduction for damping optimization in linear vibrating systems}, journal = ZAngewMathMech, year = 2011, volume = 91, number = 3, pages = {179--191}, publisher = WileyVCH, issn = {1521-4001}, doi = {10.1002/zamm.201000077} } @Article{morBenTT13, author = {Benner, P. and Tomljanovi{\'c}, Z. and Truhar, N.}, title = {Optimal damping of selected eigenfrequencies using dimension reduction}, journal = NumAlgAppl, year = 2013, volume = 20, number = 1, pages = {1--17}, issn = {1070-5325}, doi = {10.1002/nla.833}, publisher = WileySons, address = {Chichester, West Sussex, UK} } @Article{morBenW17, author = {Benner, P. and Werner, S.~W.~R.}, title = {On the transformation formulas of the {H}ankel-norm approximation}, journal = PAMM, year = 2017, volume = 17, number = 1, pages = {823--824}, publisher = WileyVCH, doi = {10.1002/pamm.201710379} } @Misc{morBenW17a, author = {Benner, P. and Werner, S.~W.~R.}, title = {{MORLAB}-3.0 -- Model Order Reduction Laboratory}, year = 2017, note = {see also: \url{http://www.mpi-magdeburg.mpg.de/projects/morlab}}, key = {MORLAB}, doi = {10.5281/zenodo.842659} } @InProceedings{morBenW17b, author = {Benner, P. and Werner, S.~W.~R.}, title = {{MORLAB} - {M}odellreduktion in {MATLAB}}, booktitle = {Tagungsband GMA-FA 1.30 'Modellierung, Identifikation und Simulation in der Automatisierungstechnik' und GMA-FA 1.40 'Theoretische Verfahren der Regelungstechnik', Workshop in Anif, Salzburg, 18.-22.09.2017}, year = 2017, editor = {Meurer, T. and Woittennek, F.}, pages = {508--517}, url = {http://www.control.tf.uni-kiel.de/files/gma/2017/Tagungsband2017.pdf} } @Article{morBenW18, author = {Benner, P. and Werner, S.~W.~R.}, title = {Model Reduction of Descriptor Systems with the {MORLAB} Toolbox}, journal = {{IFAC-PapersOnLine} 9th Vienna International Conference on Mathematical Modelling {MATHMOD} 2018, Vienna, Austria, 21--23 February 2018}, year = 2018, volume = 51, number = 2, pages = {547--552}, doi = {10.1016/j.ifacol.2018.03.092} } @Article{morBenW18a, author = {Benner, P. and Werner, S.~W.~R.}, title = {Balancing Related Model Reduction with the {MORLAB} Toolbox}, journal = PAMM, year = 2018, volume = 18, number = 1, pages = {e201800083}, doi = {10.1002/pamm.201800083} } @Misc{morBenW18b, key = {MORLAB}, author = {Benner, P. and Werner, S.~W.~R.}, title = {{MORLAB} -- {Model Order Reduction LABoratory} (Version 4.0)}, year = 2018, doi = {10.5281/zenodo.1574083}, note = {see also: \url{http://www.mpi-magdeburg.mpg.de/projects/morlab}} } @Misc{morBenW19, author = {Benner, P. and Werner, S.~W.~R.}, title = {{SOMDDPA} -- {S}econd-{O}rder {M}odally {D}amped {D}ominant {P}ole {A}lgorithm (Version 1.0)}, year = 2019, doi = {10.5281/zenodo.2553902} } @Misc{morBenW19a, author = {Benner, P. and Werner, S.~W.~R.}, title = {Limited Balanced Truncation for Large-Scale Sparse Second-Order Systems (Version 1.0)}, year = 2019, doi = {10.5281/zenodo.2553926} } @MISC{morBenW19b, key = {MORLAB}, author = {Benner, P. and Werner, S.~W.~R.}, title = {{MORLAB} -- {Model Order Reduction LABoratory} (Version 5.0)}, year = 2019, doi = {10.5281/zenodo.3332716}, note = {see also: \url{http://www.mpi-magdeburg.mpg.de/projects/morlab}} } @InProceedings{morBenW19c, author = {Benner, P. and Werner, S.~W.~R.}, title = {{MORLAB} -- {M}odel {O}rder {R}eduction {LAB}oratory}, booktitle = {Tagungsband GMA-FA 1.30 'Modellbildung, Identifikation und Simulation in der Automatisierungstechnik' und GMA-FA 1.40 'Systemtheorie und Regelungstechnik', Workshops in Anif, Salzburg, 23.-27.09.2019}, year = 2019, editor = {Meurer, T. and Woittennek, F.}, pages = {337--342}, url = {http://www.control.tf.uni-kiel.de/files/gma/2019/Tagungsband2019.pdf} } @InProceedings{morBenW19d, author = {Benner, P. and Werner, S.~W.~R.}, title = {Frequenz- und zeitbeschr{\"{a}}nktes balanciertes {A}bschneiden f{\"{u}}r {S}ysteme zweiter {O}rdnung}, booktitle = {Tagungsband GMA-FA 1.30 'Modellbildung, Identifikation und Simulation in der Automatisierungstechnik' und GMA-FA 1.40 'Systemtheorie und Regelungstechnik', Workshops in Anif, Salzburg, 23.-27.09.2019}, year = 2019, editor = {Meurer, T. and Woittennek, F.}, pages = {460--474}, url = {http://www.control.tf.uni-kiel.de/files/gma/2019/Tagungsband2019.pdf} } @Misc{morBenW20, author = {Benner, P. and Werner, S.~W.~R.}, title = {Limited Balanced Truncation for Large-Scale Sparse Second-Order Systems (Version 2.0)}, year = 2020, doi = {10.5281/zenodo.3331592} } @Misc{morBenW20a, author = {Benner, P. and Werner, S.~W.~R.}, title = {{SOMDDPA} -- {S}econd-{O}rder {M}odally-{D}amped {D}ominant {P}ole {A}lgorithm (Version 1.1)}, year = 2020, doi = {10.5281/zenodo.3332706} } @ARTICLE{morBenW20d, author = {Benner, P. and Werner, S.~W.~R.}, title = {{H}ankel-norm approximation of large-scale descriptor systems}, journal = AdvComputMath, volume = {46}, number = {3}, pages = {40}, year = {2020}, doi = {10.1007/s10444-020-09750-w} } @INCOLLECTION{morBenW20e, author = {Benner, P. and Werner, S.~W.~R.}, title = {{MORLAB} -- {A} Model Order Reduction Framework in {MATLAB} and {O}ctave}, booktitle = {Mathematical Software -- ICMS 2020}, series = LNCS, volume = {12097}, editor = {Bigatti, A.~M. and Carette, J. and Davenport, J.~H. and Joswig, M. and de~Wolff, T.}, publisher = {Springer International Publishing}, address = {Cham}, pages = {432--441}, year = {2020}, doi = {10.1007/978-3-030-52200-1_43} } @Misc{morBenW21, author = {Benner, P. and Werner, S.~W.~R.}, title = {{SOMDDPA} -- {S}econd-{O}rder {M}odally-{D}amped {D}ominant {P}ole {A}lgorithm (Version 2.0)}, month = apr, year = 2021, doi = {10.5281/zenodo.3997649} } @Misc{morBenW21a, author = {Benner, P. and Werner, S.~W.~R.}, title = {{SOLBT} -- {L}imited Balanced Truncation for Large-Scale Sparse Second-Order Systems (Version 3.0)}, month = apr, year = 2021, doi = {10.5281/zenodo.4600763} } @Article{morBenW21b, author = {Benner, P. and Werner, S.~W.~R.}, title = {Frequency- and time-limited balanced truncation for large-scale second-order systems}, journal = LinAlgApp, year = {2021}, volume = {623}, pages = {68--103}, note = {Special issue in honor of P.~Van~Dooren, Edited by F.~Dopico, D.~Kressner, N.~Mastronardi, V.~Mehrmann, and R.~Vandebril}, doi = {10.1016/j.laa.2020.06.024} } @InCollection{morBenW21c, author = {Benner, P. and Werner, S.~W.~R.}, title = {{MORLAB} -- The {M}odel {O}rder {R}eduction {LAB}oratory}, booktitle = {Model Reduction of Complex Dynamical Systems}, series = {International Series of Numerical Mathematics}, volume = {171}, editor = {Benner, P. and Breiten, T. and Fa{\ss}bender, H. and Hinze, M. and Stykel, T. and Zimmermann, R.}, publisher = {Birkh{\"{a}}user, Cham}, pages = {393--415}, year = 2021, doi = {10.1007/978-3-030-72983-7_19} } @Article{morBenZ22, author = {Bendokat, T. and Zimmermann, R.}, title = {Geometric Optimization for Structure-Preserving Model Reduction of {Hamiltonian} Systems}, journal = {IFAC-PapersOnLine: 10th Vienna International Conference on Mathematical Modelling MATHMOD 2022}, year = 2022, volume = 55, number = 20, pages = {457-462}, issn = {2405-8963}, doi = {10.1016/j.ifacol.2022.09.137} } 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Bl{\"{o}}meling}, title = {Multi-Level Substructuring Methods for Model Order Reduction}, school = {Technische Universit{\"{a}}t Hamburg-Harburg}, year = 2008, type = {{Ph.D. Thesis}}, address = {Hamburg} } @TechReport{morBoeNB10, author = {C. Boess and N.~K. Nichols and A. Bunse-Gerstner}, title = {Model order reduction for discrete unstable control systems using a balanced truncation approach}, institution = {University of Reading}, year = 2010, type = {Preprint}, number = {MPS\_2010\_06}, note = {Available from \url{https://www.reading.ac.uk/maths-and-stats/research/maths-preprints.aspx}} } @InCollection{morBolE17, author = {Bollh{\"{o}}fer, M. and Eppler, A.~K.}, title = {Low-Rank {C}holesky Factor {K}rylov Subspace Methods for Generalized Projected {L}yapunov Equations}, booktitle = {System Reduction for Nanoscale {IC} Design}, publisher = {Springer}, year = 2017, editor = {Benner, P.}, volume = 20, series = {Mathematics in Industry}, pages = {157--193}, address = {Cham}, doi = {10.1007/978-3-319-07236-4_5} } @InProceedings{morBonD05, author = {Bond, B. and Daniel, L.}, title = {Parameterized Model Order Reduction of Nonlinear Dynamical Systems}, booktitle = {Proc. IEEE/ACM Conference on Computer-Aided Design, ICCAD-2005}, year = 2005, pages = {487--494}, month = nov, doi = {10.1109/ICCAD.2005.1560117} } @InProceedings{morBonD08, author = {Bond, B.~N. and Daniel, L.}, title = {Guaranteed stable projection-based model reduction for indefinite and unstable linear systems}, booktitle = {2008 IEEE/ACM International Conference on Computer-Aided Design}, year = {2008}, doi = {10.1109/ICCAD.2008.4681657} } @Article{morBonD09, author = {B. Bond and L. Daniel}, title = {Stable reduced models for nonlinear descriptor systems through piecewise-linear approximation and projection}, journal = IEEETransCADCS, year = 2009, volume = 28, number = 10, pages = {1467--1480} } @Article{morBonFAetal15, author = {Bonin, T. and Fa{\ss}bender, H. and Soppa, A. and Zaeh, M.}, title = {A fully adaptive rational global {A}rnoldi method for the model-order reduction of second-order {MIMO} systems with proportional damping}, journal = {Math. Comput. 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Benner}, title = {Modale versus moderne {O}rdnungsreduktionsverfahren: {E}ffiziente {S}imulation von {W}erk\-zeug\-ma\-schi\-nen}, journal = {Mechatronik}, year = 2009, volume = 117, number = {11--12}, pages = {46--47}, month = nov, note = {ISBN/ISSN: 1867-2590} } @InProceedings{morBorGZ16, author = {Borggaard, J. and Gugercin, S. and Zietsman, L.}, title = {Feedback stabilization of fluids using reduced-order models for control and compensator design}, booktitle = {2016 IEEE 55th Conference on Decision and Control (CDC)}, year = 2016, pages = {7579--7585}, doi = {10.1109/CDC.2016.7799440} } @Article{morBouH17, author = {Bouvrie, J. and Hamzi, B.}, title = {Kernel Methods for the Approximation of Nonlinear Systems}, journal = {SIAM J. Control Optim.}, year = 2017, volume = 55, number = 4, pages = {2460--2492}, doi = {10.1137/14096815X} } @Article{morBoyBLetal10, author = {Boyaval, S. and Le Bris, C. and Leli{\`{e}}vre, T. and Maday, Y. and Nguyen, N.~C. and Patera, A.~T.}, title = {Reduced Basis Techniques for Stochastic Problems}, journal = ArchCompEng, year = 2010, volume = 17, number = 4, pages = {435--454}, issn = {1134-3060}, doi = {10.1007/s11831-010-9056-z}, publisher = {Springer Netherlands} } @Article{morBraGAetal25, author = {Bradde, T. and Grivet-Talocia, S. and Aumann, Q. and Gosea, I.~V.}, title = {A modified {AAA} algorithm for learning stable reduced-order models from data}, journal = JSciComput, year = 2025, volume = 103, number = 14, pages = {1--28}, publisher = {Springer}, doi = {10.1007/s10915-025-02825-0} } @InProceedings{morBraGG24, author = {Bradde, T. and Gosea, I.~V. and Grivet-Talocia, S.}, title = {Fast macromodeling of large-scale multiports with guaranteed stability}, booktitle = {2024 IEEE International Symposium on Electromagnetic Compatibility, Signal \& Power Integrity (EMC+SIPI)}, year = 2024, volume = {}, number = {}, pages = {472--477}, doi = {10.1109/EMCSIPI49824.2024.10705502} } @Article{morBre04, author = {C. Brezinski}, title = {Model reduction by state space projection}, journal = {Comm. Appl. Anal.}, year = 2004, volume = 8, number = 3, pages = {323--333} } @MastersThesis{morBre09, author = {T. Breiten}, title = {{K}rylov Subspace Methods for Model Order Reduction of Bilinear Control Systems}, school = {Fach\-be\-reich Mathematik, Technische Universit{\"{a}}t Kaiserslautern}, year = 2009, type = {Diploma Thesis}, address = {Kaiserslautern}, month = nov } @PhdThesis{morBre13, author = {Breiten, T.}, title = {Interpolatory Methods for Model Reduction of Large-Scale Dynamical Systems}, type = {{D}issertation}, school = OVGU, address = {Magdeburg, Germany}, year = 2013, doi = {10.25673/3917} } @Article{morBre16, author = {Breiten, T.}, title = {Structure-preserving model reduction for integro-differential equations}, journal = SIAMControlOpt, year = 2016, volume = 54, number = 6, pages = {2992--3015}, doi = {10.1137/15M1032296} } @InProceedings{morBreB10, author = {Breiten, T. and Benner, P.}, title = {Nonlinear Model Order Reduction via Quadratic Bilinear Differential Algebraic Equations}, booktitle = {Tagungsband GMA-FA 1.30, 'Modellbildung, Identifikation und Simulation in der Automatisierungstechnik'}, year = 2010, editor = {Lohmann, B. and Kugi, A.}, pages = {138--153}, address = {Salzburg, {\"{o}}sterreich}, isbn = {978-39502451-7-2} } @Article{morBreBG15, author = {Breiten, T. and Beattie, C. and Gugercin, S.}, title = {Near-optimal frequency-weighted interpolatory model reduction}, journal = SCL, year = 2015, volume = 78, pages = {8--18}, issn = {0167-6911}, doi = {10.1016/j.sysconle.2015.01.005} } @TechReport{morBreBG19, author = {T. Breiten and C.~A. Beattie and S. Gugercin}, title = {{$\mathcal{H}_2$}-gap model reduction for stabilizable and detectable systems}, institution = {arXiv}, year = 2019, type = {e-print}, number = {1909.13764}, note = {math.NA}, url = {https://arxiv.org/abs/1909.13764} } @InProceedings{morBreCI06, author = {Brennan, C. and Condon, M. and Ivanov, R.}, title = {Model Order Reduction of Nonlinear Dynamical Systems}, booktitle = {Progress in Industrial Mathematics at ECMI 2004}, year = 2006, volume = 8, pages = {114--118}, doi = {10.1007/3-540-28073-1_11} } @Article{morBreD10, author = {T. Breiten and T. Damm}, title = {{K}rylov subspace methods for model order reduction of bilinear control systems}, journal = SCL, year = 2010, volume = 59, number = 8, pages = {443--450}, doi = {10.1016/j.sysconle.2010.06.003} } @InProceedings{morBreGFetal16, author = {Bremer, J. and Goyal, P. and Feng, L. and Benner, P. and Sundmacher, K.}, title = {Nonlinear model order reduction for catalytic tubular reactors}, booktitle = {Proc. of the 26th European Symposium on Computer Aided Process Engineering}, year = 2016, pages = {2373--2378}, doi = {10.1016/B978-0-444-63428-3.50400-8} } @Article{morBreGFetal17, author = {Bremer, J. and Goyal, P. and Feng, L. and Benner, P. and Sundmacher, K.}, title = {{POD-DEIM} for Efficient Reduction of a Dynamic 2D Catalytic Reactor Model}, journal = {Computers \& Chemical Engineering}, year = 2017, volume = {106}, pages = {777--784}, doi = {10.1016/j.compchemeng.2017.02.032} } @InProceedings{morBreHBetal21, author = {Bremer, J. and Heiland, J. and Benner, P. and Sundmacher, K.}, title = {Non-intrusive Time {G}alerkin {POD} for Optimal Control of a Fixed-Bed Reactor for {CO2} Methanation}, booktitle = {11th International Symposium on Advanced Control of Chemical Processes (ADCHEM)}, series = {IFAC-PapersOnLine}, volume = {54}, pages = {122--127}, year = {2021}, doi = {10.1016/j.ifacol.2021.08.229} } @Article{morBreU22, author = {Breiten, T. and Unger, B.}, title = {Passivity preserving model reduction via spectral factorization}, journal = Automatica, year = 2022, volume = 142, pages = {Paper No. 110368, 12}, issn = {0005-1098}, doi = {10.1016/j.automatica.2022.110368} } @PhdThesis{morBru15, author = {Bruns, A.}, title = {Bilinear {$\mathcal{H}_2$}-optimal Model Order Reduction with Applications to Thermal Parametric Systems}, type = {{D}issertation}, school = OVGU, address = {Magdeburg, Germany}, year = 2015 } @Article{morBruB15, author = {Bruns, A. and Benner, P.}, title = {Parametric model order reduction of thermal models using the bilinear interpolatory rational {K}rylov algorithm}, journal = MCMDS, year = 2015, volume = 21, number = 2, pages = {103--129}, issn = {1387-3954}, doi = {10.1080/13873954.2014.924534} } @Article{morBruCT02, author = {Bru, R. and Coll, C. and Thome, N.}, title = {Symmetric Singular Linear Control Systems}, journal = {Applied Mathematics Letters}, year = 2002, volume = 15, number = 6, pages = {671--675}, doi = {10.1016/S0893-9659(02)00026-5} } @Article{morBruJOetal16, author = {Brunton, B.~W. and Johnson, L.~A. and Ojemann, J.~G. and Kutz, J.~N.}, title = {Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition}, journal = {Journal of Neuroscience Methods}, year = 2016, volume = 258, pages = {1--15}, doi = {10.1016/j.jneumeth.2015.10.010} } @Article{morBucBH19, author = {Buchfink, P. and Bhatt, A. and Haasdonk, B.}, title = {Symplectic Model Order Reduction with Non-Orthonormal Bases}, journal = {Math. Comput. Appl.}, year = 2019, volume = 24, number = 2, pages = 43, doi = {10.3390/mca24020043} } @InProceedings{morBuiW05, author = {Bui-Thanh, T. and Willcox, K.}, title = {Model Reduction for Large-Scale {CFD} Applications Using Balanced Proper Orthogonal Decomposition}, booktitle = {17th AIAA Computational Fluid Dynamics Conference}, year = 2005, pages = {1--15}, doi = {10.2514/6.2005-4617} } @Article{morBuiWG08, author = {Bui-Thanh, T. and Willcox, K. and Ghattas, O.}, title = {Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space}, journal = SIAMSciComp, year = 2008, volume = 30, pages = {3270--3288}, publisher = {SIAM} } @Article{morBuiWGetal07, author = {Bui-Thanh, T. and Willcox, K. and Ghattas, O. and van Bloemen Waanders, B.}, title = {Goal-oriented, model-constrained optimization for reduction of large-scale systems}, journal = JComputPhys, year = 2007, volume = 224, number = 2, pages = {880--896}, publisher = {Elsevier} } @Article{morBulB86, author = {Bultheel, A. and Van~Barel, M.}, title = {{P}ad{\'e} techniques for model reduction in linear system theory: a survey}, journal = CompApplMath, year = 1986, volume = 14, number = 3, pages = {401--438}, doi = {10.1016/0377-0427(86)90076-2} } @Article{morBunKVetal10, author = {A. 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Veliz}, title = {Reduced-Order Transfer Matrices From {RLC} Network Descriptor Models of Electric Power Grids}, journal = IEEETransPS, year = 2011, volume = 26, number = 4, pages = {1905--1916}, doi = {10.1109/TPWRS.2011.2136442} } @Article{morFrePR16, author = {Freitas, F.~D. and Pulch, R. and Rommes, J.}, title = {Fast and Accurate Model Reduction for Spectral Methods in Uncertainty Quantification}, journal = {Int. J. for Uncertainty Quantification}, year = 2016, volume = 6, number = 3, pages = {271--286}, doi = {10.1615/Int.J.UncertaintyQuantification.2016016646} } @Article{morFreRM08, author = {F. Freitas and J. Rommes and N. 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The Solution of Parametric and Stochastic Equations -- Proper Generalized Decomposition}, journal = SIAMSciComp, year = 2015, volume = 37, number = 1, pages = {A347--A368}, doi = {10.1137/140969063} } @Article{morGkiATetal25, author = {Gkimisis, L. and Aretz, N. and Tezzele, M. and Richter, T. and Benner, P. and Willcox, K.~E.}, title = {Non-intrusive reduced-order modeling for dynamical systems with spatially localized features}, journal = CMAME, year = 2025, volume = 444, pages = 118115, doi = {10.1016/j.cma.2025.118115} } @Article{morGkiPGetal26, author = {Gkimisis, L. and Pontes Duff, I. and Goyal, P. and Benner, P.}, title = {On the representation of energy-preserving quadratic operators with application to {Operator Inference}}, journal = ApplMathLett, year = 2026, volume = 173, pages = 109761, issn = {0893-9659}, doi = {10.1016/j.aml.2025.109761} } @Article{morGkiRB23, author = {Gkimisis, L. and Richter, T. and Benner, P.}, title = {Adjacency-based, non-intrusive reduced-order modeling for fluid-structure interactions}, journal = PAMM, year = 2023, volume = 23, number = 4, pages = {e202300047}, doi = {10.1002/pamm.202300047} } @Article{morGkiRB24, author = {Gkimisis, L. and Richter, T. and Benner, P.}, title = {Adjacency-based, non-intrusive model reduction for Vortex-Induced Vibrations}, journal = {Comp. \& Fluids}, year = 2024, volume = 275, number = 106248, fjournal = {Computers \& Fluids}, doi = {10.1016/j.compfluid.2024.106248} } @Article{morGkiYRetal26, author = {Gkimisis, L. and Y{\i}ld{\i}z, S. and Richter, T. and Benner, P.}, title = {A {CFL}-type condition and theoretical insights for discrete-time sparse full-order model inference}, journal = CompApplMath, year = 2026, volume = 482, pages = 117269, issn = {0377-0427}, doi = {10.1016/j.cam.2025.117269} } @InProceedings{morGlaMM98, author = {Glava{\v{s}}ki, S. and Marsden, J.~E. and Murray, R.~M.}, title = {Model Reduction, Centering, and the {K}arhunen-{L}oeve Expansion}, booktitle = {Decision and Control, 1998. Proceedings of the 37th IEEE Conference on}, year = 1998, volume = 2, pages = {2071--2076}, doi = {10.1109/CDC.1998.758639} } @Article{morGlo84, author = {Glover, K.}, title = {All optimal {H}ankel-norm approximations of linear multivariable systems and their {L}$^\infty$-error norms}, journal = IntControl, year = 1984, volume = 39, number = 6, pages = {1115--1193}, doi = {10.1080/00207178408933239} } @Article{morGlo87, author = {Glover, K.}, title = {Model Reduction: A Tutorial on {H}ankel-Norm Methods and Lower Bounds on {$L^2$}~Errors}, journal = {IFAC Proceedings Volume (10th Triennial IFAC Congress on Automatic Control)}, year = 1987, volume = 20, number = 5, pages = {293--298}, doi = {10.1016/S1474-6670(17)55515-9} } @Article{morGloK05, author = {Gl{\"{o}}smann, P. and Kreuzer, E.}, title = {Monitoring of Railway Vehicles-Detection of Critical Rolling States of Railway Wheelsets}, journal = {Machine Dynamics Problems}, year = 2005, volume = 29, number = 4, pages = {47--58} } @InCollection{morGloP87, author = {Glover, K. and Partington, J.~R.}, title = {Bounds on the Achievable Accuracy in Model Reduction}, booktitle = {Modelling, Robustness and Sensitivity Reduction in Control Systems}, publisher = {Springer}, year = 1987, editor = {Curtain, R.~F.}, volume = 30, series = {{NATO} {ASI} Series (Series F: Computer and Systems Sciences)}, pages = {95--118}, doi = {10.1007/978-3-642-87516-8_7} } @Article{morGos22, author = {Gosea, I.~V.}, title = {Exact and Inexact Lifting Transformations of Nonlinear Dynamical Systems: Transfer Functions, Equivalence, and Complexity Reduction}, journal = {Applied Sciences}, year = 2022, volume = 12, number = 5, pages = 2333, publisher = {Multidisciplinary Digital Publishing Institute}, doi = {10.3390/app12052333} } @InProceedings{morGosA15, author = {Gosea, I.~V. and Antoulas, A.~C.}, title = {Model reduction of linear and nonlinear systems in the {L}oewner framework: A summary,}, booktitle = {14th European Control Conference ({ECC}), July 15--17, Linz, Austria}, year = {2015}, pages = {345--349}, doi = {10.1109/ECC.2015.7330568} } @InProceedings{morGosA16, author = {Gosea, I.~V. and Antoulas, A.~C.}, title = {Stability preserving post-processing methods applied in the {L}oewner framework}, booktitle = {{IEEE} 20th Workshop on Signal and Power Integrity ({SPI}), Turin, Italy, May 8--11}, year = {2016}, pages = {1--4}, doi = {10.1109/SaPIW.2016.7496283} } @Article{morGosA18, author = {Gosea, I.~V. and Antoulas, A.~C.}, title = {Data-driven model order reduction of quadratic-bilinear systems}, journal = NumAlgAppl, year = 2018, volume = 25, number = 6, pages = {e2200}, doi = {10.1002/nla.2200} } @InProceedings{morGosA18a, author = {Gosea, I.~V. and Antoulas, A.~C.}, title = {On the $\mathcal{H}_2$ norm and iterative model order reduction of linear switched systems}, booktitle = {18th European Control Conference ({ECC}), June 12--15, Limassol, Cyprus}, year = {2018}, pages = {2983--2988}, doi = {10.23919/ECC.2018.8550591} } @InProceedings{morGosA19, author = {Gosea, I.~V. and Antoulas, A.~C.}, title = {A two-sided iterative framework for model reduction of linear systems with quadratic output}, booktitle = {58th {IEEE} Conference on Decision and Control ({CDC}), December 11--13, Nice, France}, year = {2019}, pages = {7812--7817}, doi = {10.1109/CDC40024.2019.9030025} } @InProceedings{morGosA19a, author = {Gosea, I.~V. and Antoulas, A.~C.}, title = {A note on modeling some classes of nonlinear systems from data}, booktitle = {15th International Conference on Computational Plasticity ({COMPLAS}), September 3--5, Barcelona, Spain}, year = {2019}, pages = {145--156}, url = {https://congress.cimne.com/complas2019/frontal/Doc/EbookCOMPLAS2019.pdf} } @InProceedings{morGosG20, author = {Gosea, I.~V. and Gugercin, S.}, title = {The {AAA} framework for modeling linear dynamical systems with quadratic output}, booktitle = {21st IFAC World Congress, Berlin, Germany, July 12--17}, year = {2020}, note = {extended abstract, accepted for publication} } @Article{morGosG21a, author = {Gosea, I.~V. and G{\"{u}}ttel, S.}, title = {Algorithms for the Rational Approximation of Matrix-Valued Functions}, journal = {SIAMSciComp}, year = 2021, volume = 43, number = 5, pages = {A3033--A3054}, doi = {10.1137/20M1324727} } @Article{morGosG22, author = {Gosea, I.~V. and Gugercin, S.}, title = {Data-driven modeling of linear dynamical systems with quadratic output in the {AAA} framework}, journal = {J. Sci. Comput.}, year = 2022, volume = 91, number = 1, pages = {1--28}, publisher = {Springer}, doi = {10.1007/s10915-022-01771-5} } @Article{morGosGB22, author = {Gosea, I.~V. and Gugercin, S. and Beattie, C.}, title = {Data-driven balancing of linear dynamical systems}, journal = SIAMSciComp, year = 2022, volume = 44, number = 1, pages = {A554--A582}, publisher = {SIAM}, doi = {10.1137/21M1411081} } @Article{morGosGB24, author = {Gosea, I.~V. and Gugercin, S. and Beattie, C.}, title = {A non-intrusive data-based reformulation of a hybrid projection-based model reduction method}, journal = {IFAC-PapersOnLine}, year = 2024, volume = 58, number = 17, pages = {226--231}, note = {26th IFAC Symposium on Mathematical Theory of Networks and Systems MTNS 2024}, doi = {10.1016/j.ifacol.2024.10.171}, issn = {2405-8963}, } @InProceedings{morGosGU21, author = {Gosea, I.~V. and Gugercin, S. and Unger, B.}, title = {Parametric model reduction via rational interpolation along parameters}, booktitle = {60th {IEEE} Conference on Decision and Control ({CDC}), December 14--17, Austin, TX, USA}, year = 2021, pages = {6895--6900}, doi = {10.1109/CDC45484.2021.9682841} } @Article{morGosGW24, author = {Gosea, I.~V. and Gugercin, S. and Werner, S.~W.~R.}, title = {Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems}, journal = AdvComputMath, year = 2024, volume = 50, number = 2, pages = {1--32}, doi = {10.1007/s10444-024-10118-7} } @InProceedings{morGosH24, author = {Gosea, I.~V. and Heiland, J.}, title = {Implicit and Explicit Matching of Non-Proper Transfer Functions in the {L}oewner Framework}, booktitle = {2024 European Control Conference (ECC)}, year = 2024, volume = {}, number = {}, pages = {3452--3457}, doi = {10.23919/ECC64448.2024.10590815} } @InProceedings{morGosKA20, author = {Gosea, I.~V. and Karachalios, D. and Antoulas, A.~C.}, title = {Modeling in the {L}oewner framework: from linear dynamics to quadratic nonlinearities}, booktitle = {21st IFAC World Congress, Berlin, Germany, July 12--17}, year = 2020, note = {accepted for publication} } @InProceedings{morGosKA21, author = {Gosea, I.~V. and Karachalios, D. and Antoulas, A.~C.}, title = {Reduced-order modeling of block-oriented nonlinear systems from data}, booktitle = {24th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Cambridge, UK, August 23--27}, year = {2021}, note = {extended abstract, accepted for publication} } @Article{morGosKA21a, author = {Gosea, I.~V. and Karachalios, D.~S. and Antoulas, A.~C.}, title = {On computing reduced-order bilinear models from time-domain data}, journal = PAMM, year = 2021, volume = 21, number = 1, pages = {e202100254}, doi = {10.1002/pamm.202100254}, note = {accepted September 2021} } @InProceedings{morGosKA21b, author = {Gosea, I.~V. and Karachalios, D.~S. and Antoulas, A.~C.}, title = {Learning reduced-order models of quadratic control systems from input-output data}, booktitle = {Proc. European Control Conf. 2021, Delft, Netherlands}, year = 2021, pages = {1426--1431}, publisher = {IEEE}, doi = {10.23919/ECC54610.2021.9654993} } @InCollection{morGosP21, author = {Gosea, I.~V. and Pontes Duff, I.}, title = {Toward fitting structured nonlinear systems by means of dynamic mode decomposition}, booktitle = {Model Reduction of Complex Dynamical Systems}, series = {International Series of Numerical Mathematics}, volume = {171}, editors = {Benner, P. and Breiten, T. and Fa{\ss}bender, H. and Hinze, M. and Stykel, T. and Zimmermann, R.}, publisher = {Birkh{\"{a}}user, Cham}, pages = {53--74}, year = {2021}, doi = {10.1007/978-3-030-72983-7_3} } @InProceedings{morGosP22, author = {Gosea, I.~V. and Pontes Duff, I.}, title = {An iterative realization-free approach for model reduction of bilinear systems via {H}ermitian interpolation}, booktitle = {20th European Control Conference (ECC)}, year = 2022, pages = {584--589}, doi = {10.23919/ECC55457.2022.9838095} } @Article{morGosPA18, author = {Gosea, I.~V. and Petreczky, M. and Antoulas, A.~C.}, title = {Data-Driven Model Order Reduction of Linear Switched Systems in the {L}oewner Framework}, journal = SIAMSciComp, year = 2018, volume = 40, number = 2, pages = {B572--B610}, doi = {10.1137/17M1120233} } @InProceedings{morGosPA21, author = {Gosea, I.~V. and Petreczky, M. and Antoulas, A.~C.}, title = {Reduced-order modeling of {LPV} systems in the {L}oewner framework}, booktitle = {60th {IEEE} Conference on Decision and Control ({CDC}), December 14--17, Austin, TX, USA}, year = 2021, pages = {3299--3305}, doi = {10.1109/CDC45484.2021.9683742} } @InProceedings{morGosPA21a, author = {Gosea, I.~V. and Poussot-Vassal, C. and Antoulas, A.~C.}, title = {On enforcing stability for data-driven reduced-order models}, booktitle = {29th Mediterranean Conference on Control and Automation (MED), Virtual}, year = {2021}, pages = {487--493}, doi = {10.1109/MED51440.2021.9480216} } @InCollection{morGosPA22, author = {Gosea, I.~V. and Poussot-Vassal, C. and Antoulas, A.~C.}, title = {Data-driven modeling and control of large-scale dynamical systems in the {L}oewner framework: methodology and applications}, booktitle = {Numerical Control: Part A}, publisher = {Elsevier}, year = 2022, editor = {Zuazua, E. and Trelat, E.}, volume = 23, series = {Handbook on Numerical Analysis}, chapter = 15, pages = {499--530}, doi = {10.1016/bs.hna.2021.12.015} } @Article{morGosPAetal18, author = {Gosea, I.~V. and Petreczky, M. and Antoulas, A.~C. and Fiter, C.}, title = {Balanced truncation for linear switched systems}, journal = AdvComputMath, year = 2018, volume = 44, number = 6, pages = {1845--1886}, publisher = {Springer}, doi = {10.1007/s10444-018-9610-z} } @InProceedings{morGosPBetal19, author = {Gosea, I.~V. and Pontes Duff, I. and Benner, P. and Antoulas, A.~C.}, title = {Model order reduction of bilinear time-delay systems}, booktitle = {18th European Control Conference (ECC)}, year = 2019, pages = {2289--2294}, doi = {10.23919/ECC.2019.8796085} } @InCollection{morGosPBetal20, author = {Gosea, I.~V. and Pontes Duff, I. and Benner, P. and Antoulas, A.~C.}, title = {Model Order Reduction of Switched Linear Systems with Constrained Switching}, booktitle = {IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22--25, 2018}, publisher = {Springer}, year = {2020}, volume = {36}, series = {IUTAM Bookseries}, pages = {41--53}, address = {Cham, Switzerland}, doi = {10.1007/978-3-030-21013-7_3} } @InProceedings{morGosPFetal20, author = {Gosea, I.~V. and Petreczky, M. and Fiter, C. and Antoulas, A.~C.}, title = {Balanced Truncation for Linear Switched Systems}, booktitle = {Book of Abstracts of XXI Householder Symposium on Numerical Linear Algebra, Selva di Fasano, Italy, June 14--19}, year = {2020}, url = {https://users.ba.cnr.it//iac/irmanm21/HHXXI/book_of_abstracts_HHXXI0.pdf} } @InCollection{morGosPGetal25, author = {Gosea, I.~V. and Peterson, L. and Goyal, P. and Bremer, J. and Sundmacher, K. and Benner, P.}, title = {Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2023}, publisher = {Springer, Cham}, year = 2025, editor = {Sequeira, A. and Silvestre, A. and Valtchev, S. and Janela, J.}, volume = 153, series = LNCSE, pages = {365--376}, doi = {10.1007/978-3-031-86173-4_37} } @InProceedings{morGosPLetal20a, author = {Gosea, I.~V. and Petreczky, M. and Leth, J. and Wisniewski, R. and Antoulas, A.~C.}, title = {Model reduction of linear hybrid systems}, booktitle = {59th {IEEE} Conference on Decision and Control ({CDC}), December 14--18, Jeju Island, Republic of Korea}, year = 2020, pages = {110--117}, doi = {10.1109/CDC42340.2020.9303918} } @Article{morGosZA20, author = {Gosea, I.~V. and Zhang, Q. and Antoulas, A.~C.}, title = {Preserving the {DAE} Structure in the {L}oewner Model Reduction and Identification Framework}, journal = AdvComputMath, year = 2020, volume = 46, number = 3, publisher = {Springer}, doi = {10.1007/s10444-020-09752-8} } @InProceedings{morGosZA21, author = {Gosea, I.~V. and Zhang, Q. and Antoulas, A.~C.}, title = {Data-driven modeling from noisy measurements}, booktitle = {Special Issue: 7th GAMM Juniors' Summer School on Applied Mathematics and Mechanics (SAMM)}, year = {2021}, doi = {10.1002/pamm.202000358} } @InProceedings{morGosZKetal23, author = {Gosea, I.~V. and Zivkovic, L.~A. and Karachalios, D.~S. and Vidakovic-Koch T. and Antoulas, A.~C.}, title = {A data-driven nonlinear frequency response approach based on the {L}oewner framework: preliminary analysis}, booktitle = {IFAC-PapersOnLine, 12th Symposium on Nonlinear Control Systems NOLCOS 2022 Canberra, Australia, January 4-6, 2023}, year = 2023, volume = 56, pages = {234--239}, publisher = {Elsevier}, doi = {10.1016/j.ifacol.2023.02.040} } @PhdThesis{morGoy18, author = {Goyal, P.~K.}, title = {System-theoretic model order reduction for bilinear and quadratic-bilinear systems}, school = OVGU, year = 2018, type = {{D}issertation}, address = {Magdeburg, Germany}, doi = {10.25673/5319} } @InProceedings{morGoyAP15, author = {Goyal, P. and Ahmad, M.~I. and Benner, P.}, title = {Model reduction of quadratic-bilinear descriptor systems via {C}arleman bilinearization}, booktitle = {Proc. European Control Conf. 2015, Linz}, year = 2015, pages = {1177--1182}, publisher = {IEEE}, doi = {10.1109/ECC.2015.7330699} } @InProceedings{morGoyB16, author = {Goyal, P. and Benner, P.}, title = {An iterative model order reduction scheme for a special class of bilinear descriptor systems appearing in constraint circuit simulation}, booktitle = {ECCOMAS Congress 2016, VII European Congress on Computational Methods in Applied Sciences and Engineering}, year = 2016, volume = 2, pages = {4196--4212}, url = {https://drive.google.com/open?id=0B04URlVl3wyuVHhMeFVBSldGX2c} } @TechReport{morGoyB21, author = {Goyal, P. and Benner, P.}, title = {{LQResNet}: A Deep Neural Network Architecture for Learning Dynamic Processes}, institution = {arXiv}, year = 2021, type = {e-print}, number = {2103.02249}, url = {https://arxiv.org/abs/2103.02249}, note = {cs.LG} } @TechReport{morGoyB21b, author = {Goyal, P. and Benner, P.}, title = {Learning Dynamics from Noisy Measurements using Deep Learning with a {R}unge-{K}utta Constraint}, institution = {arXiv}, year = 2021, type = {e-prints}, number = {2109.11446}, note = {math.LG}, url = {https://arxiv.org/abs/2109.11446} } @InProceedings{morGoyB21c, author = {Goyal, P. and Benner, P.}, title = {Learning Dynamics from Noisy Measurements using Deep Learning with a {R}unge-{K}utta Constraint}, booktitle = {Proc. The Symbiosis of Deep Learning and Differential Equations - NeurIPS}, year = {2021}, url = {https://openreview.net/forum?id=G5i2aj7v7i} } @TechReport{morGoyB21d, author = {Goyal, P. and Benner, P.}, title = {Learning low-dimensional quadratic-embeddings of high-fidelity nonlinear dynamics using deep learning}, institution = {arXiv}, year = 2021, type = {e-print}, number = {2111.12995}, note = {cs.LG}, url = {http://arxiv.org/abs/2111.12995} } @Article{morGoyB22a, author = {Goyal, P. and Benner, P.}, title = {Discovery of nonlinear dynamical systems using a {R}unge-{K}utta inspired dictionary-based sparse regression approach}, journal = {Philos. Trans. Roy. Soc. A}, year = 2022, volume = 478, number = 2262, pages = 20210883, doi = {10.1098/rspa.2021.0883} } @Article{morGoyB23, author = {Goyal, P. and Benner, P.}, title = {Neural ordinary differential equations with irregular and noisy data}, journal = {Roy. Soc. Open Sci.}, year = 2023, volume = 10, number = 7, pages = 221475, doi = {10.1098/rsos.221475} } @Article{morGoyB24, author = {Pawan Goyal and Peter Benner}, title = {Generalized quadratic embeddings for nonlinear dynamics using deep learning}, journal = {Physica D: Nonlinear Phenomena}, year = 2024, volume = 463, pages = 134158, doi = {10.1016/j.physd.2024.134158} } @TechReport{morGoyPB23a, author = {Goyal, P. and Pontes Duff, I. and Benner, P.}, title = {Inference of Continuous Linear Systems from Data with Guaranteed Stability}, institution = {arXiv}, year = 2023, type = {e-print}, number = {2301.10060}, note = {cs.LG}, doi = {10.48550/arXiv.2301.10060} } @TechReport{morGoyPB23b, author = {Goyal, P. and Pontes Duff, I. and Benner, P.}, title = {Guaranteed Stable Quadratic Models and their applications in {SINDy} and Operator Inference}, institution = {arXiv}, year = 2023, type = {e-print}, number = {2308.13819}, note = {Submited to Nonlinear Dynamics}, doi = {10.48550/arXiv.2308.13819} } @Article{morGoyPB24, author = {Goyal, P. and Peherstorfer, B. and Benner, P.}, title = {Rank-Minimizing and Structured Model Inference}, journal = SIAMSciComp, year = 2024, volume = 46, number = 3, pages = {A1879--A1902}, doi = {10.1137/23M1554308} } @Article{morGoyPB24a, author = {Goyal, P. and Pontes Duff, I. and Benner, P.}, title = {Dominant Subspaces of High-Fidelity Polynomial Structured Parametric Dynamical Systems and Model Reduction}, journal = AdvComputMath, year = 2024, volume = 50, pages = 42, doi = {10.1007/s10444-024-10133-8} } @Article{morGoyR19, author = {Goyal, P. and Redmann, M.}, title = {Time-limited $\mathcal{H}_2$-optimal model order reduction}, journal = ApplMathComp, volume = {355}, pages = {184--197}, year = {2019}, doi = {10.1016/j.amc.2019.02.065} } @Article{morGra74, author = {Gragg, W.~B.}, title = {Matrix interpretations and applications of the continued fraction algorithm}, journal = {Rocky Mountain J. 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Grimme}, title = {{K}rylov projection methods for model reduction}, school = {Univ. of Illinois at Urbana-Champaign, USA}, year = 1997, type = {{Ph.D. Thesis}}, url = {https://perso.uclouvain.be/paul.vandooren/ThesisGrimme.pdf} } @Article{morGriABetal07, author = {S. Grivet-Talocia and S. Acquadro and M. Bandinu and F.~G. Canavero and I. Kelander and M. Rouvala}, title = {A parameterization scheme for lossy transmission line macromodels with application to high speed interconnects in mobile devices}, journal = IEEETransEMC, year = 2007, volume = 49, number = 1, pages = {18--24} } @Book{morGriG15, editor = {Grivet-Talocia, S. and Gustavsen, B.}, title = {Passive Macromodeling: Theory and Applications}, publisher = {John Wiley and Sons}, year = 2016, doi = {10.1002/9781119140931}, isbn = {978-1-119-14093-1} } @Article{morGriG16, author = {Grivet-Talocia, S. and Gustavsen, B.}, title = {Black-box macromodeling and its {EMC} applications}, journal = {{IEEE} Electroman. Comp. M.}, year = 2016, volume = 5, number = 3, pages = {71--78}, doi = {10.1109/MEMC.0.7764255} } @Article{morGriSOetal15, author = {Grivet-Talocia, S. and Signorini, G. and Olivadese, S.~B. and Siviero, C. and Brenner, P.}, title = {Thermal Noise Compliant Synthesis of Linear Lumped Macromodels}, journal = IEEETransCPMT, year = 2015, volume = 5, number = 1, pages = {75--85}, doi = {10.1109/TCPMT.2014.2370096} } @Article{morGriSV96, author = {E.~J. Grimme and D.~C. 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Grundel and L. Jansen}, title = {Efficient simulation of transient gas networks using {IMEX} integration schemes and {MOR} methods}, booktitle = {54th IEEE Conference on Decision and Control (CDC)}, year = 2015, pages = {4579--4584}, doi = {10.1109/CDC.2015.7402934} } @Article{morGruJ15a, author = {S. Grundel and L. Jansen}, title = {A joint {IMEX-MOR} approach for Water Networks}, journal = {IFAC-PapersOnLine}, year = 2015, volume = 48, number = 1, pages = {260--261}, doi = {10.1016/j.ifacol.2015.05.201} } @InCollection{morGruJHetal14, author = {S. Grundel and L. Jansen and N. Hornung and T. Clees and C. Tischendorf and P. 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G{\"{u}}nzel}, title = {Balanced truncation for descriptor systems arising in interconnect modeling}, school = {Fakult{\"{a}}t f{\"{u}}r Mathematik, TU Chemnitz}, year = 2008, type = {Diploma Thesis}, address = {Chemnitz}, month = aug } @PhdThesis{morGug08, author = {Gugel, D.}, title = {Ordnungsreduktion in der Mikrosystemtechnik}, school = {Technische Universit{\"{a}}t Chemnitz}, year = 2008, type = {{Ph.D. Thesis}}, address = {Chemnitz} } @InProceedings{morGugA00, author = {S. Gugercin and A.~C. Antoulas}, title = {A comparative study of 7 algorithms for model reduction}, booktitle = {Proc. 39th {IEEE} Conference on Decision and Control, {S}ydney, {A}ustralia}, year = 2000, volume = 3, pages = {2367--2372}, doi = {10.1109/CDC.2000.914153} } @InProceedings{morGugA03, author = {S. Gugercin and A.~C. Antoulas}, title = {A survey of balancing methods for model reduction}, booktitle = {Proc. European Control Conf. ECC~2003, Cambridge, UK}, year = 2003, note = {CD Rom} } @Article{morGugA04, author = {Gugercin, S. and Antoulas, A.~C.}, title = {A survey of model reduction by balanced truncation and some new results}, journal = IntControl, year = 2004, volume = 77, number = 8, pages = {748--766}, doi = {10.1080/00207170410001713448} } @Article{morGugA06, author = {S. Gugercin and A.~C. Antoulas}, title = {Model reduction of large-scale systems by least squares}, journal = LinAlgApp, year = 2006, volume = 415, number = {2--3}, pages = {290--321} } @Article{morGugAB08, author = {Gugercin, S. and Antoulas, A.~C. and Beattie, C.}, title = {{$\mathcal{H}_2$} Model Reduction for Large-Scale Linear Dynamical Systems}, journal = SIAMMatrix, year = 2008, volume = 30, number = 2, pages = {609--638}, doi = {10.1137/060666123} } @InProceedings{morGugL05, author = {S. Gugercin and J.-R. Li}, title = {Smith-type methods for balanced truncation of large systems}, booktitle = {Dimension Reduction of Large-Scale Systems}, year = 2005, editor = {P. Benner and V. Mehrmann and D. Sorensen}, volume = 45, series = LNCSE, pages = {49--82}, publisher = {Springer-Verlag, Berlin/Heidelberg, Germany} } @Article{morGugPBetal12, author = {Gugercin, S. and Polyuga, R.~V. and Beattie, C. and van~der Schaft, A.}, title = {Structure-preserving tangential interpolation for model reduction of port-{H}amiltonian systems}, journal = Automatica, year = 2012, volume = 48, number = 9, pages = {1963--1974}, doi = {10.1016/j.automatica.2012.05.052} } @Article{morGugSW13, author = {Gugercin, S. and Stykel, T. and Wyatt, S.}, title = {Model Reduction of Descriptor Systems by Interpolatory Projection Methods}, journal = SIAMSciComp, year = 2013, volume = 35, number = 5, pages = {B1010--B1033}, doi = {10.1137/130906635} } @Article{morGuiO13, author = {Guiver, C. and Opmeer, M.~R.}, title = {Error bounds in the gap metric for dissipative balanced approximations}, journal = LinAlgApp, year = 2013, volume = 439, number = 12, pages = {3659--3698}, doi = {10.1016/j.laa.2013.09.032} } @Article{morGunKN02, author = {P.K. Gunupudi and R. Khazaka and M.S. Nakhla}, title = {Analysis of Transmission Line Circuits Using Multidimensional Model Reduction Techniques}, journal = IEEETransAP, year = 2002, volume = 25, number = 2, pages = {174--180} } @Article{morGunKetal03, author = {Gunupudi, P.~K. and Khazaka, R. and Nakhla, M.~S. and Smy, T. and Celo, D.}, title = {Passive parameterized time-domain macromodels for high-speed transmission-line networks}, journal = IEEETransMTT, year = 2003, volume = 51, number = 12, pages = {2347--2354}, month = dec, doi = {10.1109/TMTT.2003.820169}, issn = {0018-9480} } @Article{morGusS99, author = {Gustavsen, B. and Semlyen, A.}, title = {Rational approximation of frequency domain responses by vector fitting}, journal = IEEETransPD, year = 1999, volume = 14, number = 3, pages = {1052--1061}, doi = {10.1109/61.772353}} @Article{morGuy65, author = {Guyan, R.~J.}, title = {Reduction of stiffness and mass matrices}, journal = AIAA, year = 1965, volume = 2, pages = 380, doi = {10.2514/3.2874} } @Article{morHaa13, author = {B. 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Control}, year = 2019, volume = 41, number = 8, pages = {2310--2318}, doi = {10.1177/0142331218798893} } @InCollection{morHarHW18, author = {Hartmann, D. and Herz, M. and Wever, U.}, title = {Model Order Reduction a Key Technology for Digital Twins}, booktitle = {Reduced-Order Modeling ({ROM}) for Simulation and Optimization}, publisher = {Springer, Cham}, year = 2018, editor = {Keiper, W. and Milde, A. and Volkwein, S.}, pages = {167--179}, doi = {10.1007/978-3-319-75319-5_8} } @Article{morHarVS10, author = {Hartmann, C. and Vulcanov, V.-M. and Sch{\"{u}}tte, C.}, title = {Balanced truncation of linear second-order systems: a {H}amiltonian approach}, journal = {Multiscale Model. Simul.}, year = 2010, volume = 8, number = 4, pages = {1348--1367}, issn = {1540-3459}, doi = {10.1137/080732717} } @Article{morHecAV05, author = {Heckmann, A. and Arnold, M. and Vacul{\'I}n, O.}, title = {A Modal Multifield Approach for an Extended Flexible Body Description in Multibody Dynamics}, journal = {Multibody System Dynamics}, year = 2005, volume = 13, number = 3, pages = {299--322}, publisher = Springer } @Article{morHeiBB22, author = {Heiland, J and Benner, P. and Bahmani, R}, title = {Convolutional Neural Networks for Very Low-Dimensional {LPV} Approximations of Incompressible {N}avier-{S}tokes Equations}, journal = {Frontiers Appl. Math. Stat.}, year = 2022, volume = 8, pages = 879140, doi = {10.3389/fams.2022.879140} } @InProceedings{morHeiGRetal25, author = {Heiland, J. and Gosea, I.~V. and R{\"{o}}mer, U. and Pradovera, D. and Sreekumar, H. and Langer, S.}, title = {Adaptive Rational Interpolation and Higher-order {SVD} for Low-rank Tensor Approximation in Structural Dynamics Simulations}, booktitle = {23rd European Control Conference ({ECC}), June 24--27, Thessaloniki, Greece}, year = 2025, pages = {3213--3218}, doi = {10.23919/ECC65951.2025.11186909} } @Article{morHeiK22, author = {Heiland, J. and Kim, Y.}, title = {Convolutional Autoencoders and Clustering for Low-dimensional Parametrization of Incompressible Flows}, journal = {IFAC-PapersOnLine}, year = 2022, volume = 55, number = 30, pages = {430--435}, note = {25th IFAC Symposium on Mathematical Theory of Networks and Systems MTNS 2022}, doi = {10.1016/j.ifacol.2022.11.091}, issn = {2405-8963}, url = {https://www.sciencedirect.com/science/article/pii/S2405896322027240} } @Article{morHeiK24, author = {Heiland, J. and Kim, Y.}, title = {Convolutional autoencoders, clustering, and {POD} for low-dimensional parametrization of flow equations}, journal = CAMWA, year = 2024, volume = 175, pages = {49--61}, issn = {0898-1221}, doi = {10.1016/j.camwa.2024.08.032} } @TechReport{morHeiK24a, author = {Heiland, J. and Kim, Y.}, title = {Polytopic Autoencoders with Smooth Clustering for Reduced-order Modelling of Flows}, institution = {arXiv}, year = 2024, type = {e-print}, number = {2401.10620}, note = {cs.LG} } @Article{morHeiK25, author = {Heiland, J. and Kim, Y.}, fauthor = {Heiland, Jan and Kim, Yongho}, title = {Polytopic Autoencoders with Smooth Clustering for Reduced-order Modeling of Flows}, journal = {J. Comput. Phys.}, year = 2025, volume = 521, pages = 113526, doi = {10.1016/j.jcp.2024.113526} } @Article{morHeiK25a, author = {Heiland, J. and Kim, Y.}, fauthor = {Heiland, Jan and Kim, Yongho}, title = {Polytopic Autoencoders for Very Low-Dimensional Parametrizations of Fluid Flow Models}, journal = PAMM, year = 2025, volume = 25, number = 2, pages = {e70008}, note = {94th GAMM Annual Meeting}, doi = {10.1002/pamm.70008} } @TechReport{morHeiKW24, author = {Heiland, J. and Kim, Y. and Werner, S.~W.~R.}, title = {Deep Polytopic Autoencoders for Low-dimensional Linear Parameter-varying Approximations and Nonlinear Feedback Design}, institution = {arXiv}, year = 2024, type = {e-print}, number = {2403.18044}, note = {submitted to IEEE-LCSS}, doi = {10.48550/arXiv.2403.18044} } @Article{morHeiKW25, author = {Heiland, J. and Kim, Y. and Werner, S.~W.~R.}, title = {Deep Polytopic Autoencoders for Low-dimensional Linear Parameter-varying Approximations and Nonlinear Feedback Controller Design}, journal = AdvComputMath, year = 2025, volume = 51, number = 6, pages = {Paper No. 55}, doi = {10.1007/s10444-025-10269-1} } @Article{morHeiRA11, author = {Heinkenschloss, M. and Reis, T. and Antoulas, A.~C.}, title = {Balanced truncation model reduction for systems with inhomogeneous initial conditions}, journal = Automatica, year = 2011, volume = 47, number = 3, pages = {559--564}, doi = {10.1016/j.automatica.2010.12.002} } @Article{morHeiSS08, author = {M. Heinkenschloss and D.~C. Sorensen and K. Sun}, title = {Balanced truncation model reduction for a class of descriptor systems with application to the {O}seen equations}, journal = SIAMSciComp, year = 2008, volume = 30, number = 2, pages = {1038--1063}, doi = {10.1137/070681910} } @TechReport{morHeiU21, author = {Heiland, J. and Unger, B.}, title = {Identification of linear time-invariant systems with {D}ynamic {M}ode {D}ecomposition}, institution = {arXiv}, year = 2021, type = {e-print}, number = {2109.06765}, note = {math.NA}, url = {http://arxiv.org/abs/2109.06765} } @Article{morHeiW23, author = {Heiland, J. and Werner, S.~W.~R.}, title = {Low-Complexity Linear Parameter-Varying Approximations of Incompressible {N}avier-{S}tokes Equations for Truncated State-Dependent {R}iccati Feedback}, journal = IEEEContSysLett, year = 2023, volume = 7, pages = {3012--3017}, doi = {10.1109/LCSYS.2023.3291231} } @PhdThesis{morHes16, author = {Hess, M.}, title = {Reduced Basis Approximations for Electromagnetic Applications}, school = OVGU, year = 2016, type = {{D}issertation}, address = {Magdeburg, Germany}, url = {https://d-nb.info/1113687223/34} } @Article{morHesB13, author = {M.~W. Hess and P. Benner}, title = {Fast Evaluation of Time-Harmonic {M}axwell's Equations Using the Reduced Basis Method}, journal = IEEETransMTT, year = 2013, volume = 61, number = 6, pages = {2265--2274}, doi = {10.1109/TMTT.2013.2258167} } @InProceedings{morHesB13a, author = {M.~W. Hess and P. Benner}, title = {Reduced Basis Generation for {M}axwell's Equations by Rigorous Error Estimation}, booktitle = {Proceedings of 19th International Conference on the Computation of Electromagnetic Fields (COMPUMAG 2013), Paper PD2-10 (2 pp.)}, year = 2013, url = {http://www.mht.bme.hu/~bilicz/compumag2013/files/pd2-10.pdf} } @Article{morHesB14, author = {M.~W. Hess and P. Benner}, title = {A Reduced Basis Method for Microwave Semiconductor Devices with Geometric Variations}, journal = {COMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering}, year = 2014, volume = 33, number = 4, pages = {1071--1081}, doi = {10.1108/COMPEL-12-2012-0377} } @Article{morHesGB15, author = {M.~W. Hess and S. Grundel and P. Benner}, title = {Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic {M}axwell's Equations}, journal = IEEETransMTT, year = 2015, volume = 63, number = 11, pages = {3549--3557}, publisher = {IEEE} } @Book{morHesRS16, author = {Hesthaven, J.~S. and Rozza, G. and Stamm, B.}, title = {Certified {R}educed {B}asis {M}ethods for {P}arametrized {P}artial {D}ifferential {E}quations}, publisher = {Springer}, year = 2016, series = {SpringerBriefs in Mathematics}, address = {Cham}, isbn = {978-3-319-22469-5}, doi = {10.1007/978-3-319-22470-1} } @Article{morHesSZ14, author = {Hesthaven, J.~S. and Stamm, B. and Zhang, S.}, title = {Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods}, journal = {ESAIM: Math. Model. Numer. Anal.}, year = 2014, volume = 48, number = 1, pages = {259--283}, doi = {10.1051/m2an/2013100} } @InProceedings{morHicSHetal25, author = {Hickisch, P. and Saak, J. and Hohlfeld, D. and Bechtold, T.}, title = {Two-step Model Order Reduction for a Thermal Finite Element Model of a Power Electronics Module}, booktitle = {11th Vienna International Conference on Mathematical Modelling MATHMOD 2025}, year = 2025, volume = 59, pages = {379--384}, address = {Vienna, Austria}, note = {11th Vienna International Conference on Mathematical Modelling MATHMOD 2025}, fauthor = {Hickisch, Philipp and Saak, Jens and Hohlfeld, Dennis and Bechtold, Tamara}, doi = {10.1016/j.ifacol.2025.03.065}, journal = {{IFAC PapersOnline}}, } @Misc{morHim16a, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.0)}, howpublished = {\url{http://gramian.de}}, year = 2016, key = {emgr50}, doi = {10.5281/zenodo.162135} } @PhdThesis{morHim17, author = {Himpe, C.}, title = {Combined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience}, school = {Westf{\"{a}}lische Wilhelms-Universit{\"{a}}t M{\"{u}}nster}, year = 2017, note = {Sierke Verlag G{\"{o}}ttingen, ISBN 9783868448818}, doi = {10.14626/9783868448818} } @Misc{morHim17a, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.1)}, howpublished = {\url{http://gramian.de}}, year = 2017, key = {emgr51}, doi = {10.5281/zenodo.580804} } @Misc{morHim17b, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.2)}, howpublished = {\url{http://gramian.de}}, year = 2017, key = {emgr52}, doi = {10.5281/zenodo.837237} } @Misc{morHim18, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.3)}, howpublished = {\url{http://gramian.de}}, year = 2018, key = {emgr53}, doi = {10.5281/zenodo.1134429} } @Misc{morHim18a, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.4)}, howpublished = {\url{http://gramian.de}}, year = 2018, key = {emgr54}, doi = {10.5281/zenodo.1241532} } @Article{morHim18b, author = {Himpe, C.}, title = {emgr -- The {E}mpirical {G}ramian {F}ramework}, journal = {Algorithms}, year = 2018, volume = 11, number = 7, pages = 91, doi = {10.3390/a11070091} } @Misc{morHim18c, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.5)}, howpublished = {\url{https://gramian.de}}, year = 2018, key = {emgr55}, doi = {10.5281/zenodo.1401500} } @Misc{morHim19, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.6)}, howpublished = {\url{https://gramian.de}}, year = 2019, key = {emgr56}, doi = {10.5281/zenodo.2530021} } @Misc{morHim19a, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.7)}, howpublished = {\url{https://gramian.de}}, year = 2019, key = {emgr57}, doi = {10.5281/zenodo.2577980} } @Misc{morHim20a, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.8)}, howpublished = {\url{https://gramian.de}}, year = 2020, key = {emgr58}, doi = {10.5281/zenodo.3779889} } @InCollection{morHim21, author = {Himpe, C.}, title = {Comparing (Empirical-{G}ramian-Based) Model Order Reduction Algorithms}, booktitle = {Model Reduction of Complex Dynamical Systems}, publisher = {Birkh{\"{a}}user, Cham}, editor = {Benner, P. and Breiten, T. and Fa{\ss}bender, H. and Hinze, M. and Stykel, T. and Zimmermann, R.}, series = {International Series of Numerical Mathematics}, volume = {171}, year = 2021, pages = {141--164}, doi = {10.1007/978-3-030-72983-7_7} } @Misc{morHim21a, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.9)}, howpublished = {\url{https://gramian.de}}, year = 2021, key = {emgr59}, doi = {10.5281/zenodo.4454679} } @Misc{morHim22, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework (Version~5.99)}, howpublished = {\url{https://gramian.de}}, year = 2022, key = {emgr599}, doi = {10.5281/zenodo.6457616} } @TechReport{morHim22a, author = {Himpe, C.}, title = {{emgr -- EMpirical GRamian} Framework Version~5.99}, institution = {arXiv}, year = 2022, type = {e-print}, number = {2209.03833}, url = {https://arxiv.org/abs/2209.03833} } @Article{morHimGB21a, author = {Himpe, C. and Grundel, S. and Benner, P.}, title = {Model Order Reduction for Gas and Energy Networks}, journal = {Journal of Mathematics in Industry}, volume = {11}, pages = {13}, year = {2021}, doi = {10.1186/s13362-021-00109-4} } @InProceedings{morHimGB21b, author = {Himpe, C. and Grundel, S. and Benner, P.}, title = {Next-Gen Gas Network Simulation}, booktitle = {Progress in Industrial Mathematics at ECMI 2021}, editor = {}, pages = {(Accepted)}, year = 2021, doi = {} } @InCollection{morHimGB22, author = {Himpe, C. and Grundel, S. and Benner, P.}, title = {Efficient Gas Network Simulations}, booktitle = {German Success Stories in Industrial Mathematics}, editor = {Bock, H.~G. and K{\"{u}}fer, K.~H. and Maa{\ss}, P. and Milde, A. and Schulz, V.}, series = {Mathematics in Industry}, volume = {35}, publisher = {Springer, Cham}, pages = {17--22}, year = {2022}, doi = {10.1007/978-3-030-81455-7_4} } @InProceedings{morHimLR17, author = {Himpe, C. and Leibner, T. and Rave, S.}, title = {Comprehensive Memory-Bound Simulations on Single Board Computers}, booktitle = {Book of Abstracts of 2nd Workshop on Power-Aware Computing}, year = 2017, address = {Ringberg Castle}, url = {http://hdl.handle.net/21.11116/0000-0000-781E-9} } @InProceedings{morHimLR18, author = {Himpe, C. and Leibner, T. and Rave, S.}, title = {{HAPOD} - Fast, Simple and Reliable Distributed {POD} Computation}, booktitle = {ARGESIM Report (MATHMOD 2018 Extended Abstract Volume)}, year = 2018, volume = 55, pages = {119--120}, doi = {10.11128/arep.55.a55283} } @Article{morHimLR18a, author = {Himpe, C. and Leibner, T. and Rave, S.}, title = {Hierarchical Approximate Proper Orthogonal Decomposition}, journal = SIAMSciComp, year = 2018, volume = 40, number = 5, pages = {A3267--A3292}, doi = {10.1137/16M1085413} } @Article{morHimLRetal17, author = {Himpe, C. and Leibner, T. and Rave, S. and Saak, J.}, title = {Fast Low-Rank Empirical Cross {G}ramians}, journal = PAMM, year = 2017, volume = 17, number = 1, pages = {841--842}, doi = {10.1002/pamm.201710388} } @Article{morHimO13, author = {Himpe, C. and Ohlberger, M.}, title = {A Unified Software Framework for Empirical {G}ramians}, journal = {J. Math.}, year = 2013, volume = 2013, pages = {1--6}, doi = {10.1155/2013/365909} } @Article{morHimO14, author = {Himpe, C. and Ohlberger, M.}, title = {Cross-{G}ramian Based Combined State and Parameter Reduction for Large-Scale Control Systems}, journal = {Mathematical Problems in Engineering}, year = 2014, volume = 2014, pages = 843869, doi = {10.1155/2014/843869} } @InProceedings{morHimO14a, author = {Himpe, C. and Ohlberger, M.}, title = {Model Reduction for Complex Hyperbolic Networks}, booktitle = {Proc. Eur. Control Conf.}, year = 2014, pages = {2739--2743}, doi = {10.1109/ECC.2014.6862188} } @Article{morHimO14b, author = {C. Himpe and M. Ohlberger}, title = {Combined State and Parameter Reduction}, journal = PAMM, year = 2014, volume = 14, number = 1, pages = {825--826}, doi = {10.1002/pamm.201410393} } @InProceedings{morHimO15, author = {Himpe, C. and Ohlberger, M.}, title = {The Versatile Cross {G}ramian}, booktitle = {ScienceOpen Posters}, year = 2015, volume = {MoRePas 3}, doi = {10.14293/P2199-8442.1.SOP-MATH.PSAHPZ.v1} } @Article{morHimO15a, author = {Himpe, C. and Ohlberger, M.}, title = {The Empirical Cross {G}ramian for Parametrized Nonlinear Systems}, journal = {IFAC-PapersOnLine (Proceedings of the 8th Vienna International Conference on Mathematical Modelling)}, year = 2015, volume = 48, number = 1, pages = {727--728}, doi = {10.1016/j.ifacol.2015.05.163} } @TechReport{morHimO15b, author = {Himpe, C. and Ohlberger, M.}, title = {Accelerating the Computation of Empirical {G}ramians and Related Methods}, institution = {Extended Abstract 5th IWMRRF}, year = 2015, doi = {10.5281/zenodo.46643} } @Article{morHimO15c, author = {Himpe, C. and Ohlberger, M.}, title = {Data-driven combined state and parameter reduction for inverse problems}, journal = AdvComputMath, year = 2015, volume = 41, number = 5, pages = {1343--1364}, doi = {10.1007/s10444-015-9420-5} } @Article{morHimO16, author = {Himpe, C. and Ohlberger, M.}, title = {A note on the cross {G}ramian for non-symmetric systems}, journal = {Systems Science and Control Engineering}, year = 2016, volume = 4, number = 1, pages = {199--208}, doi = {10.1080/21642583.2016.1215273} } @InCollection{morHimO17, author = {Himpe, C. and Ohlberger, M.}, title = {Cross-{G}ramian-Based Model Reduction: A Comparison}, booktitle = {Model Reduction of Parametrized Systems}, publisher = {Springer}, year = 2017, editor = {Benner, P. and Ohlberger, M. and Patera, A. and Rozza, G. and Urban, K.}, volume = 17, series = {Modeling, Simulation and Applications}, pages = {271--283}, address = {Cham}, doi = {10.1007/978-3-319-58786-8_17} } @Misc{morHimR19, author = {Himpe, C. and Rave, S.}, title = {{hapod} -- {H}ierarchical {A}pproximate {P}roper {O}rthogonal {D}ecomposition (Version~2.0)}, howpublished = {\url{https://git.io/hapod}}, year = 2019, key = {hapod20} } @Misc{morHimR20, author = {Himpe, C. and Rave, S.}, title = {{hapod} -- {H}ierarchical {A}pproximate {P}roper {O}rthogonal {D}ecomposition (Version~3.0)}, howpublished = {\url{https://git.io/hapod}}, year = 2020, key = {hapod30} } @Misc{morHimR20a, author = {Himpe, C. and Rave, S.}, title = {{hapod} -- {H}ierarchical {A}pproximate {P}roper {O}rthogonal {D}ecomposition (Version~3.1)}, howpublished = {\url{https://git.io/hapod}}, year = 2020, key = {hapod31} } @Misc{morHimR21, author = {Himpe, C. and Rave, S.}, title = {{hapod} -- {H}ierarchical {A}pproximate {P}roper {O}rthogonal {D}ecomposition (Version~3.2)}, howpublished = {\url{https://git.io/hapod}}, year = 2021, key = {hapod32} } @InCollection{morHinKMetal17, author = {Hinze, M. and Kunkel, M. and Matthes, U. and Vierling, M.}, title = {Model Order Reduction of Integrated Circuits in Electrical Networks}, booktitle = {System Reduction for Nanoscale {IC} Design}, publisher = {Springer}, year = 2017, editor = {Benner, P.}, volume = 20, series = {Mathematics in Industry}, pages = {1--37}, address = {Cham}, doi = {978-3-319-07236-4_1} } @InProceedings{morHinV05, author = {M. Hinze and S. Volkwein}, title = {Proper Orthogonal Decomposition Surrogate Models for Nonlinear Dynamical Systems: Error Estimates and Suboptimal Control}, booktitle = {Dimension Reduction of Large-Scale Systems}, year = 2005, editor = {P. Benner and V. Mehrmann and D.C. Sorensen}, volume = 45, series = LNCSE, pages = {261--306}, publisher = {Springer-Verlag, Berlin/Heidelberg, Germany} } @Article{morHinV08, author = {Hinze, M. and Volkwein, S.}, title = {Error estimates for abstract linear-quadratic optimal control problems using proper orthogonal decomposition}, journal = {Comput. Optim. Appl.}, year = 2008, volume = 39, number = 3, pages = {319--345}, fjournal = {Computational Optimization and Applications. An International Journal}, issn = {0926-6003} } @InProceedings{morHipAS05, author = {Hippmann, G. and Arnold, M. and Schittenhelm, M.}, title = {Efficient simulation of bush and roller chain drives}, booktitle = {Proceedings of Multibody Dynamics 2005 (ECCOMAS Thematic Conference), Madrid, Spain, 21-24 June}, year = 2005, editor = {Cuadrado, J. and Orden, J.~C.~G. and Goicolea, J.~M.} } @Article{morHirHKetal20, author = {Hirsch, S.~M. and Harris, K.~D. and Kutz, J.~N. and Brunton, B.~W.}, title = {Centering Data Improves the Dynamic Mode Decomposition}, journal = SIAMAppDynSys, volume = {19}, number = {3}, pages = {1920--1955}, year = {2020}, doi = {10.1137/19M1289881} } @PhdThesis{morHoc00, author = {Hockenberry, J.~R.}, title = {Evaluation of uncertainty in dynamic reduced-order power system models}, school = {Massachusetts Institute of Technology}, year = {2000}, url = {http://hdl.handle.net/1721.1/46685} } @Article{morHocL04, author = {Hockenberry, J.~R. and Lesieutre, B.~C.}, title = {Evaluation of uncertainty in dynamic simulations of power system models: The probabilistic collocation method}, journal = {IEEE Transactions on Power Systems}, year = {2004}, volume = {19}, number = {3}, pages = {1483--1491}, doi = {10.1109/TPWRS.2004.831689} } @InCollection{morHocVRetal13, author = {A. Hochman and D.~M. Vasilyev and M.~J. Rewie{\'n}ski and J.~K. White}, title = {Projection-based nonlinear model order reduction}, booktitle = {System-Level Modeling of {MEMS}}, publisher = WileyVCH, year = 2013, editor = {T. Bechtold and G. Schrag and L. Feng}, series = {Advanced Micro {\&} Nanosystems}, vol = 10, isbn = {978-3-527-31903-9} } @InProceedings{morHof02, author = {Hofer, A.}, title = {Controller Reduction in l1-optimal Control}, booktitle = {Proceedings of the 20th American Control Conference, Anchorage}, year = 2002, pages = {1162--1167} } @InProceedings{morHof06, author = {Hofer, A.}, title = {A Special Method for Controller Reduction}, booktitle = {Proceedings of the 5th MATHMOD Vienna Symposium on Mathematical Modelling}, year = 2006 } @Article{morHof08, author = {Hofer, A.}, title = {Two controller reduction methods based on convex programming}, journal = MCMDS, year = 2008, volume = 14, number = 5, pages = {451--468}, annote = {Taylor and Francis} } @Article{morHohZ04, author = {Hohlfeld, D. and Zappe, H.}, title = {An all-dielectric tunable optical filter based on the thermo-optic effect}, journal = {Journal of Optics A: Pure and Applied Optics}, year = 2004, volume = 6, number = 6, pages = {504--511}, doi = {10.1088/1464-4258/6/6/002} } @Book{morHolLB96, author = {Holmes, P. and Lumley, J.~L. and Berkooz, G.}, title = {Turbulence, coherent structures, dynamical systems and symmetry}, publisher = {Cambridge University Press}, year = 1996, series = {Cambridge Monographs on Mechanics}, address = {Cambridge}, pages = {xviii+420}, isbn = 0521551420 } @Book{morHolLBetal12, author = {Holmes, P. and Lumley, J.~L. and Berkooz, G. and Rowley, C.~W.}, title = {Turbulence, coherent structures, dynamical systems and symmetry}, publisher = {Cambridge University Press}, year = 2012, series = {Cambridge Monographs on Mechanics}, address = {Cambridge}, pages = 402, doi = {10.1017/CBO9780511919701}, isbn = 9781107008250 } @Article{morHomPS05, author = {C. Homescu and L.~R. Petzold and R. Serban}, title = {Error estimation for reduced order models of dynamical systems}, journal = SIAMNumAnal, year = 2005, volume = 43, number = 4, pages = {1693--1714}, doi = {10.1137/040603541} } @Article{morHorDFetal06, author = {Horenko, I. and Dittmer, E. and Fischer, A. and Sch{\"{u}}tte, C.}, title = {Automated model reduction for complex systems exhibiting metastability}, journal = {Multiscale Model. Simul.}, year = 2006, volume = 5, number = 3, pages = {802--827 (electronic)}, fjournal = {Multiscale Modeling \& Simulation. A SIAM Interdisciplinary Journal}, issn = {1540-3459} } @Article{morHosB08, author = {M.-S. Hossain and P. Benner}, title = {Projection-Based Model Reduction for {LTV} Descriptor System Using Multipoint {K}rylov-Subspace Projectors}, journal = PAMM, year = 2008, volume = 8, number = 1, pages = {10081--10084}, month = dec, organization = {GAMM} } @InProceedings{morHosB12, author = {Hossain, M.-S. and Benner, P.}, title = {Iterative solvers for periodic matrix equations and model reduction for periodic control systems}, booktitle = {7th International Conference on Electrical and Computer Engineering}, year = 2012, pages = {791--794}, publisher = {IEEE}, isbn = {978-1-4673-1436-7}, doi = {10.1109/ICECE.2012.6471669} } @InProceedings{morHosB14, author = {M.-S. Hossain and P. Benner}, title = {Generalized inverses of periodic matrix pairs and model reduction for periodic control systems}, booktitle = {Proc. of 1st International Conference on Electrical Engineering and Information \& Communication Technology (ICEEICT)}, year = 2014, pages = {1--6}, address = {Dhaka, Bangladesh}, publisher = {IEEE}, isbn = {978-1-4799-4820-8}, doi = {10.1109/ICEEICT.2014.6919033} } @InProceedings{morHsuDC83, author = {Hsu, C.~S. and Desai, U.~B. and Crawley, C.~A.}, title = {Realization algorithms and approximation methods of bilinear systems}, booktitle = {The 22nd {IEEE} Conference on Decision and Control, San Antonio, TX, USA}, year = 1983, pages = {783--788}, doi = {10.1109/CDC.1983.269628} } @Article{morHuaJX20, author = {Huang, Y. and Jiang, Y.-L. and Xu, K.-L.}, title = {Structure-preserving model reduction of port-{H}amiltonian systems based on projection}, journal = {Asian J. Control}, volume = {}, pages = {}, year = {2020}, doi = {10.1002/asjc.2332} } @Article{morHuaLHetal03, author = {L. Zhang and J. Lam and B. Huang and G.~H. Yang}, title = {On gramians and balanced truncation of discrete-time bilinear systems}, journal = IntControl, year = 2003, volume = 76, number = 4, pages = {414--427} } @MastersThesis{morHun15, author = {Hund, Manuela}, title = {{Z}eitbereichs-{M}odellreduktion und {S}ylvester-{G}leichungen}, school = OVGU, year = 2015, address = {Magdeburg, Germany}, note = {available from: \url{http://nbn-resolving.de/urn:nbn:de:gbv:ma9:1-7794}}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:ma9:1-7794} } @Article{morHunMMetal22, author = {Hund, M. and Mitchell, T. and Mlinari{\'c}, P. and Saak, J.}, title = {Optimization-based Parametric Model Order Reduction via $\mathcal{H}_2 \otimes \mathcal{L}_2$ First-order Necessary Conditions}, journal = SIAMSciComp, year = 2022, volume = 44, number = 3, pages = {A1554--A1578}, doi = {10.1137/21M140290X} } @Article{morHunMS18, author = {Hund, M. and Mlinari{\'c}, P. and Saak, J.}, title = {An \(\mathcal{H}_2 \otimes \mathcal{L}_2\)-Optimal Model Order Reduction Approach for Parametric Linear Time-Invariant Systems}, journal = PAMM, year = 2018, volume = 18, number = 1, pages = {e201800084}, doi = {10.1002/pamm.201800084} } @InProceedings{morHunS14, author = {M. Hund and J. Saak}, title = {Numerische {A}spekte der {Zeitbereichs-MOR} mittels orthogonaler {P}olynome}, booktitle = {Tagungsband des GMA-Fachausschusses 1.30 "Modellbildung, Identifikation und Simulation in der Automatisierungstechnik"}, year = 2014, editor = {Sawodny, O. and Adamy, J.}, pages = {176--185}, organization = {Institut f{\"{u}}r Automatisierungstechnik und Mechatronik}, publisher = {Technische Universit{\"{a}}t Darmstadt} } @Article{morHunS16, author = {Hund, M. and Saak, J.}, title = {A Connection between Time Domain Model Order Reduction and Moment Matching}, journal = PAMM, year = 2016, volume = 16, number = 1, pages = {727--728}, month = oct, publisher = WileyVCH, issn = {1617-7061}, doi = {10.1002/pamm.201610352} } @Article{morHunS18, author = {Hund, M. and Saak, J.}, title = {A Connection Between Time Domain Model Order Reduction and Moment Matching for {LTI} Systems}, journal = MCMDS, year = 2018, volume = 24, number = 5, pages = {455--484}, doi = {10.1080/13873954.2018.1488742} } @Article{morHuyKCetal10, author = {Huynh, D.~B.~P. and Knezevic, D.~J. and Chen, Y. and Hesthaven, J.~S. and Patera, A.~T.}, title = {A natural-norm Successive Constraint Method for inf-sup lower bounds}, journal = CompMethAppMechEng, year = 2010, volume = 199, number = 29, pages = {1963--1975}, doi = {10.1016/j.cma.2010.02.011} } @Article{morHuyRSetal07, author = {Huynh, D.~B.~P. and Rozza, G. and Sen, S. and Patera, A.~T.}, title = {A successive constraint linear optimization method for lower bounds of parametric coercivity and inf-sup lower bounds}, journal = CRAcadSciParis, year = 2007, volume = 345, number = 8, pages = {473--478}, doi = {10.1016/j.crma.2007.09.019} } @InCollection{morIapTV16, author = {Iapichino, L. and Trenz, S. and Volkwein, S.}, title = {Reduced-Order Multiobjective Optimal Control of Semilinear Parabolic Problems}, booktitle = {Numerical Mathematics and Advanced Applications ENUMATH 2015}, publisher = {Springer International Publishing}, year = 2016, editor = {Karas{\"{o}}zen, B. and Manguo{\u g}lu, M. and Tezer-Sezgin, M. and G{\"{o}}ktepe, S. and U{\u g}ur, {\"{o}}}, series = LNCSE, pages = {389--397}, address = {Cham}, doi = {10.1007/978-3-319-39929-4_37} } @Article{morIapUV17, author = {Iapichino, L. and Ulbrich, S. and Volkwein, S.}, title = {Multiobjective PDE-constrained Optimization using the Reduced-Basis Method}, journal = AdvComputMath, year = 2017, doi = {10.1007/s10444-016-9512-x} } @Article{morIapVW16, author = {Iapichino, L. and Volkwein, S. and Wesche, A.}, title = {A-posteriori error analysis for lithium-ion concentrations in batteries utilizing the reduced-basis method}, journal = MCMDS, year = 2016, volume = 22, number = 4, pages = {362--379}, doi = {10.1080/13873954.2016.1198387} } @Article{morIglFBetal26, author = {Iglesias-Tesouro, C. and Feng, L. and Balicki, L. and Romano, D. and Gugercin, S. and Antonini, G. and Gosea I.~V. and Benner, P.}, title = {Learning Multivariate Matrix-Valued Electromagnetic Transfer Functions using p-{AAA}}, journal = {Research in the Mathematical Science}, year = 2026, note = {submitted} } @Article{morImrG15, author = {Imran, M. and Ghafoor, A.}, title = {Model reduction of descriptor systems using frequency limited {G}ramians}, journal = {J. Franklin Inst.}, year = 2015, volume = 352, number = 1, pages = {33--51}, doi = {10.1016/j.jfranklin.2014.10.013} } @InProceedings{morImu12, author = {Imura, J.-i.}, title = {Clustered model reduction of large-scale complex networks}, booktitle = {Proceedings of the 20th International Symposium on Mathematical Theory of Networks and Systems, Melbourne, Australia}, year = 2012, url = {http://www.mtns2012.conference.net.au/Full\%20Paper/MTNS2012_0311_paper.pdf} } @Article{morIonA14, author = {Ionita, A.~C. and Antoulas, A.~C.}, title = {Data-Driven Parametrized Model Reduction in the {L}oewner Framework}, journal = SIAMSciComp, year = 2014, volume = 36, number = 3, pages = {A984--A1007}, doi = {10.1137/130914619} } @InProceedings{morIonFS09, author = {Ionescu, T.~C. and Fujimoto, K. and Scherpen, J.~M.~A.}, title = {The Cross Operator and the Singular Value Analysis for Nonlinear Symmetric Systems}, booktitle = {Proc. Eur. 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Moosmann and J.~G. Korvink}, title = {Automatic parametric {MOR} for {MEMS} design}, booktitle = {Tagungsband GMA-FA 1.30, 'Modellbildung, Identifizierung und Simulation in der Automatisierungstechnik', Workshop am Bostalsee, 27.-29.9.2009}, year = 2006, pages = {89--99} } @InProceedings{morMooRGetal04, author = {C. Moosmann and E.~B. Rudnyi and A. Greiner and J.~G. Korvink}, title = {Model Order Reduction for Linear Convective Thermal Flow}, booktitle = {THERMINIC 2004}, year = 2004, pages = {317--321}, address = {Sophia Antipolis, France}, url = {http://modelreduction.rudnyi.ru/doc/papers/moosmann04THERMINIC.pdf} } @InProceedings{morMooRGetal05, author = {C. Moosmann and E.~B. Rudnyi and A. Greiner and J.~G. Korvink and M. 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Penzl}, title = {Algorithms for model reduction of large dynamical systems}, institution = {Sonderforschungsbereich 393 {\itshape Numerische Simulation auf massiv parallelen Rechnern}, TU Chem\-nitz}, year = 1999, type = {Technical report}, number = {SFB393/99-40}, address = {09107 Chem\-nitz, FRG}, note = {Available from \url{http://www.tu-chemnitz.de/sfb393/sfb99pr.html}.} } @ARTICLE{morPenM16, author = {Peng, L. and Mohseni, K.}, title = {Symplectic Model Reduction of {H}amiltonian Systems}, journal = SIAMSciComp, volume = 38, number = 1, pages = {A1--A27}, year = 2016, doi = {10.1137/140978922}, } @Article{morPer16, author = {Perev, K.}, title = {The Unifying Feature of Projection in Model Order Reduction}, journal = {Information Technologies and Control}, year = 2016, volume = 12, number = {3--4}, pages = {17--27}, doi = {10.1515/itc-2016-0003} } @Article{morPerS82, author = {Pernebo, L. and Silverman, L.~M.}, title = {Model reduction via balanced state space representations.}, journal = IEEETransAC, year = 1982, volume = 27, number = 2, pages = {382--387}, doi = {10.1109/TAC.1982.1102945} } @PhdThesis{morPet13, author = {Petersson, D.}, title = {A Nonlinear Optimization Approach to {$\mathcal{H}_{2}$}-Optimal Modeling and Control}, school = {Link{\"{o}}ping University}, year = 2013, type = {Dissertation}, url = {http://liu.diva-portal.org/smash/get/diva2:647068/FULLTEXT01.pdf}, isbn = {978-91-7519-567-4}, issn = {0345-7524} } @InProceedings{morPetBFetal25, author = {Peterson, L. and B{\"{u}}ttner, M. and Forootani, A. and Gosea, I.~V. and Benner, P. and Sundmacher, K.}, title = {Greedy Sampling Neural Network {SINDy} with Control for a Catalytic CO$_2$ Methanation Reactor}, booktitle = LNCS, year = 2025, publisher = {Springer}, note = {full paper, presented at the 15th International Conference on Large-Scale Scientific Computations (LSSC), Sozopol, Bulgaria, June 16 - 20} } @Article{morPetFSetal25, author = {Peterson, L. and Forootani, A. and Sanchez Medina, E.~I. and Gosea, I.~V. and Sundamcher, K. and Benner, P.}, title = {Towards {D}igital {T}wins for {P}ower-to-{X}: Comparing Surrogate Models for a Catalytic {CO}$_2$ {M}ethanation Reactor}, journal = {IEEE Trans. Autom. Sci. Eng.}, year = 2025, volume = {}, number = {}, pages = {}, doi = {10.1109/TASE.2025.3564637} } @InCollection{morPetG20, author = {Petreczky, M. and Gosea, I.~V.}, title = {Model reduction and realization theory of linear switched systems}, booktitle = {Realization and Model Reduction of Dynamical Systems - A Festschrift in Honor of the 70th Birthday of Thanos Antoulas}, editors = {Beattie, C. and Benner, P. and Embree, M. and Gugercin, S. and Lefteriu, S.}, publisher = {Springer}, year = {2020}, note = {accepted July 2020} } @Article{morPetGBetal25, author = {Peterson, L. and Gosea, I.~V. and Benner, P. and Sundmacher, K.}, title = {Digital Twins in Process Engineering: An Overview on Computational and Numerical Methods}, journal = {Computers $\&$ Chemical Engineering}, year = 2025, volume = 193, pages = 108917, doi = {10.1016/j.compchemeng.2024.108917} } @InCollection{morPetGGetal24, author = {Peterson, L. and Goyal, P. and Gosea, I.~V. and Bremer, J. and Benner, P. and Sundmacher, K.}, title = {Learning reduced-order models for dynamic {CO}$_2$ methanation using operator inference}, booktitle = {34th European Symposium on Computer Aided Process Engineering / 15th International Symposium on Process Systems Engineering}, publisher = {Elsevier}, year = 2024, editor = {Flavio Manenti and Gintaras V. Reklaitis}, volume = 53, series = {Computer Aided Chemical Engineering}, pages = {3319--3324}, issn = {1570-7946}, doi = {10.1016/B978-0-443-28824-1.50554-8} } @InProceedings{morPetGGetal25, author = {Peterson, L. and Goyal, P. and and Gosea, I.~V. and Benner, P. and Sundmacher, K.}, title = {Reduced-order modeling for a methanation reactor by harnessing the effectiveness of nonlinear decoders}, booktitle = {7th International Workshop on Model Order Reduction Techniques (MORTech 2025), Zaragoza, Spain, November 26 - 28}, year = 2025, note = {extended abstract, accepted for presentation} } @Article{morPetWL13, author = {M. Petreczky and R. Wisniewski and J. 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Control Signals Systems}, year = 2004, volume = 16, number = 4, pages = {297--319}, fjournal = {Mathematics of Control, Signals, and Systems}, issn = {0932-4194}, doi = {10.1007/s00498-004-0141-4} } @Article{morSty06, author = {Stykel, T.}, title = {Balanced truncation model reduction for semidiscretized {S}tokes equation}, journal = LinAlgApp, year = 2006, volume = 415, number = {2--3}, pages = {262--289}, doi = {10.1016/j.laa.2004.01.015} } @Article{morSuC91, author = {Su, T.-J. and Craig~Jr., R.~R.}, title = {Model reduction and control of flexible structures using {K}rylov vectors}, journal = {Journal of Guidance, Control, and Dynamics}, year = 1991, volume = 14, number = 2, pages = {260--267}, doi = {10.2514/3.20636} } @Book{morSun08, author = {Sun, Kai}, title = {Model order reduction and domain decomposition for large-scale dynamical systems}, publisher = {ProQuest LLC, Ann Arbor, MI}, year = 2008, note = {Thesis (Ph.D.)--Rice University}, pages = 169, isbn = {978-1109-21236-5}, url = {https://search.proquest.com/docview/304507831?accountid=104761} } @Article{morSunFB26, author = {Sun, Shuwen and Feng, Lihong and Benner, Peter}, title = {Data-augmented predictive deep neural network: {E}nhancing the extrapolation capabilities of non-intrusive surrogate models}, journal = CMAME, year = 2026, volume = 450, pages = {Paper No. 118604}, ISSN = {0045-7825,1879-2138}, DOI = {10.1016/j.cma.2025.118604} } @TechReport{morSunFCetal23, author = {Sun, S. and Feng, L. and Chan, H. and Mili{\v{c}}i{\'c}, T. and Vidakovi{\'c}-Koch, T. and Benner, P.}, title = {Parametric Dynamic Mode Decomposition for nonlinear parametric dynamical systems}, institution = {arXiv}, year = 2023, type = {e-print}, number = {2305.06197}, note = {math.NA}, doi = {10.48550/arXiv.2305.06197} } @Article{morSunH05, author = {Sun, C. and Hahn, J.}, title = {Reduction of stable differential-algebraic equation systems via projections and system identification}, journal = {J. Process Control}, year = 2005, volume = 15, number = 6, pages = {639--650}, doi = {10.1016/j.jprocont.2005.01.003} } @Article{morSunH06, author = {Sun, C. and Hahn, J.}, title = {Parameter reduction for stable dynamical systems based on {H}ankel singular values and sensitivity analysis}, journal = {Chem. Eng. Sci.}, year = 2006, volume = 61, number = 16, pages = {5393--5403}, doi = {10.1016/j.ces.2006.04.027} } @Article{morSunH06a, author = {Sun, C. and Hahn, J.}, title = {Model reduction in the presence of uncertainty in model parameters}, journal = {J. 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Tan and L. He}, title = {Advanced Model Order Reduction Techniques in {VLSI} Design}, publisher = {Cambridge University Press}, year = 2007, address = {New York, NY, USA} } @Article{morTanLAetal04, author = {Tang, D. and Li, A. and Attar, P. and Dowell, E.~H.}, title = {Reduced order dynamic model for polysaccharides molecule attached to an atomic force microscope}, journal = JComputPhys, year = 2004, volume = 201, number = 2, pages = {723--752}, publisher = {Elsevier} } @InProceedings{morTaoZYetal06, author = {Tao, J. and Zeng, X. and Yang, F. and Su, Y. and Feng, L. and Cai, W. and Zhou, D. and Chiang, C.}, title = {A {O}ne-shot {P}rojection {M}ethod for {I}nterconnects with {P}rocess {V}ariations}, booktitle = {Proc. IEEE International Symposium on Circuits and Systems}, year = 2006, month = may } @PhdThesis{morTen04, author = {Teng, Cong}, title = {Model Order Reduction of Second-Order Linear Dynamical Systems}, school = RICE, year = 2004, address = {Houston, Texas}, month = jun } @Article{morTen12, author = {Teng, C.}, title = {Second-Order Model Reduction Based on Gramians}, journal = {J. Control Sci. Eng.}, year = 2012, volume = 2012, pages = {1--9}, doi = {10.1155/2012/302498} } @InProceedings{morThaGK16, author = {Thakallapelli, A. and Ghosh, S. and Kamalasadan, S.}, title = {Real-time frequency based reduced order modeling of large power grid}, booktitle = {2016 IEEE Power and Energy Society General Meeting (PESGM)}, pages = {16464882}, year = {2016}, doi = {10.1109/PESGM.2016.7741877} } @Article{morTinGK08, author = {Tin, L.~D. and Greiner, A. and Korvink, J.~G.}, title = {Model Order Reduction for Circuit Level Simulation of {RF MEMS} Frequency Selective Devices}, journal = {Sensor Letters}, year = 2008, volume = 6, number = 1, pages = {1--8}, publisher = {American Scientific Publishers} } @Article{morTolA17, author = {Tolks, C. and Ament, C.}, title = {Model Order Reduction of Glucose-Insulin Homeostasis Using Empirical {G}ramians and Balanced Truncation}, journal = {IFAC-PapersOnline (Proceedings of the 20th IFAC World Congress)}, year = 2017, volume = 50, number = 1, pages = {14735--14740}, doi = {10.1016/j.ifacol.2017.08.2576} } @PhdThesis{morTom11, author = {Tomljanovi{\'c}, Z.}, title = {Optimal damping for vibrating systems using dimension reduction}, school = JJSUO, year = 2011, url = {https://hrcak.srce.hr/68645} } @Article{morTomBG18, author = {Tomljanovi{\'c}, Z. and Beattie, C. and Gugercin, S.}, title = {Damping optimization of parameter dependent mechanical systems by rational interpolation}, journal = AdvComputMath, year = 2018, volume = 44, number = 6, pages = {1797--1820}, doi = {10.1007/s10444-018-9605-9} } @Article{morTomP87, author = {Tombs, M.~S. and Postlethwaite, I.}, title = {Truncated balanced realization of a stable non-minimal state-space system}, journal = IntControl, year = 1987, volume = 46, number = 4, pages = {1319--1330}, doi = {10.1080/00207178708933971} } @article{morTomV20, author = {Tomljanovi{\'c}, Z. and Voigt, M.}, title = {Semi-active $\mathcal{H}_\infty$ damping optimization by adaptive interpolation}, journal = NumAlgAppl, volume = {27}, number = {4}, pages = {e2300}, year = 2020, doi = {10.1002/nla.2300} } @Article{morTorLMetal23, author = {Torchio, R. and Lucchini, F. and Filippini, M. and Romano, D. and Feng, L. and Benner, P. and Antonini, G.}, title = {A reduced order modelling approach for full-{M}axwell lightning strike analyses in layered backgrounds}, journal = IEEETransPD, year = 2023, volume = 38, number = 3, pages = {1949--1957}, doi = {10.1109/TPWRD.2022.3228900} } @Article{morTroMF92, author = {I. Troch and P.~C. M{\"{u}}ller and K.-H. Fasol}, title = {Modellreduktion f{\"{u}}r {S}imulation und {R}eglerentwurf}, journal = atAutom, year = 1992, volume = 40, number = 4, pages = {132--141} } @Article{morTroV09, author = {Tr{\"{o}}ltzsch, F. and Volkwein, S.}, title = {{POD} a-posteriori error estimates for linear-quadratic optimal control problems}, journal = {Comput. Optim. Appl.}, year = 2009, volume = 44, number = 1, pages = {83--115} } @Article{morTuRLetal14, author = {Tu, J.~H. and Rowley, C.~W. and Luchtenburg, D.~M. and Brunton, S.~L. and Kutz, J.~N.}, title = {On dynamic mode decomposition: Theory and applications}, journal = {Journal of Computational Dynamics}, year = 2014, volume = 1, number = 2, pages = {391--421}, doi = {10.3934/jcd.2014.1.391} } @MastersThesis{morUdd11, author = {Uddin, M.~M.}, title = {Model Reduction for Piezo-Mechanical Systems using {B}alanced {T}runcation}, school = {Stockholm University}, year = 2011, type = {Master's thesis}, address = {Stockholm, Sweden}, url = {http://www.qucosa.de/fileadmin/data/qucosa/documents/7822/Master_Thesis_Uddin.pdf} } @PhdThesis{morUdd15, author = {Uddin, M.~M.}, title = {Computational Methods for Model Reduction of Large-Scale Sparse Structured Descriptor Systems}, type = {{D}issertation}, school = OVGU, address = {Magdeburg, Germany}, year = 2015, url = {http://nbn-resolving.de/urn:nbn:de:gbv:ma9:1-6535} } @Article{morUddSKetal12, author = {Uddin, M.~M. and Saak, J. and Kranz, B. and Benner, P.}, title = {Computation of a compact state space model for an adaptive spindle head configuration with piezo actuators using balanced truncation}, journal = {Production Engineering}, year = 2012, volume = 6, pages = {577--586}, issn = {0944-6524}, issue = 6, doi = {10.1007/s11740-012-0410-x}, publisher = Springer } @InCollection{morUzuK17, author = {Uzunca, M. and Karas{\"{o}}zen, B.}, title = {Energy stable model order reduction for the {A}llen-{C}ahn equation}, booktitle = {Model Reduction of Parametrized Systems}, publisher = {Springer}, year = 2017, editor = {Benner, P. and Ohlberger, M. and Patera, A.~T. and Rozza, G. and Urban, K.}, volume = 17, series = {Modeling, Simulation and Applications}, pages = {403--419}, address = {Cham}, doi = {10.1007/978-3-319-58786-8_25} } @InProceedings{morVakK99, author = {Vakilian, M. and Ketabi, A.}, title = {A method for reduction of power system transient model}, booktitle = {1999 IEEE Transmission and Distribution Conference}, pages = {198--205}, year = {1999}, doi = {10.1109/TDC.1999.755340} } @InProceedings{morVan00, author = {Van~Dooren, P.}, title = {Gramian Based Model Reduction of Large-Scale Dynamical Systems}, booktitle = {Numerical Analysis 1999. Proc. 18th Dundee Biennial Conference on Numerical Analysis}, year = 2000, editor = {D.~F. Griffiths and G.~A. 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Varga}, title = {Model Reduction Software in the {SLICOT} Library}, booktitle = {Applied and Computational Control, Signals, and Circuits}, publisher = {Kluwer Academic Publishers}, year = 2001, editor = {B.~N. Datta}, volume = 629, series = {The Kluwer International Series in Engineering and Computer Science}, pages = {239--282}, address = {Boston, MA} } @InProceedings{morVar91, author = {Varga, A.}, title = {Efficient minimal realization procedure based on balancing}, booktitle = {Prepr. of the IMACS Symp. on Modelling and Control of Technological Systems}, volume = 2, pages = {42--47}, year = 1991 } @InProceedings{morVar91a, author = {A. Varga}, title = {Balancing-free square-root algorithm for computing singular perturbation approximations}, booktitle = {Proc. 30th IEEE Conf. Dec. Control, Brighton, UK}, year = 1991, pages = {1062--1065}, doi = {10.1109/CDC.1991.261486} } @InCollection{morVar91b, author = {A. 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Varga}, title = {Model reduction routines for {SLICOT}}, institution = {The Working Group on Software (WGS)}, year = 1999, type = {NICONET Report}, number = {1999--8}, month = jun, note = {Available from \url{www.slicot.org}} } @Article{morVar99a, author = {A. Varga}, title = {Balancing related methods for minimal realization of periodic systems}, journal = SCL, year = 1999, volume = 36, pages = {339--349} } @TechReport{morVar99b, author = {A. Varga}, title = {Task {II.~B.1} -- Selection of Software for Controller Reduction}, institution = {The Working Group on Software (WGS)}, year = 1999, type = {SLICOT Working Note}, number = {1999--18}, month = dec, note = {Available from \url{www.slicot.org}} } @Article{morVarA03, author = {Varga, A. and Anderson, B.~D.~O.}, title = {Accuracy-enhancing methods for balancing-related frequency-weighted model and controller reduction}, journal = Automatica, year = 2003, volume = 39, pages = {919--927} } @InProceedings{morVarF93, author = {A. Varga and K.~H. Fasol}, title = {A new square--root balancing--free stochastic truncation model reduction algorithm}, booktitle = {Prepr. 12th {IFAC} World Congress}, year = 1993, volume = 7, pages = {153--156}, address = {Sydney, Australia} } @Article{morVerP05, author = {Veroy, K. and Patera, A.~T.}, title = {Certified real-time solution of the parametrized steady incompressible {N}avier-{S}tokes equations: rigorous reduced-basis a posteriori error bounds}, journal = {Internat. J. Numer. 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Volkwein}, title = {Model Reduction using Proper Orthogonal Decomposition}, institution = {University of Konstanz}, year = 2013, type = {Lecture notes}, annote = {Script in English language, 41 pages} } @Article{morVolH08, author = {Volkwein, S. and Hepberger, A.}, title = {Impedance Identification by {POD} Model Reduction Techniques {(Impedanz-Identifikation mittels POD Modellreduktion)}}, journal = atAutom, year = 2008, volume = 56, number = {8/2008}, pages = {437--446}, publisher = {Oldenbourg} } @MastersThesis{morVos05, author = {Vo{\ss}, T.}, title = {Model reduction for nonlinear differential algebraic equations}, school = {Universit{\"{a}}t Wuppertal}, year = 2005, type = {Diploma Thesis}, address = {Wuppertal} } @Article{morVosPMetal07, author = {Vo{\ss}, T. and Pulch, R. and Maten, E.~J.~W. and {El~Guennouni}, A.}, title = {Trajectory Piecewise Linear Approach for Nonlinear Differential-Algebraic Equations in circuit simulation}, journal = {Mathematics in industry}, year = 2007, volume = 11, pages = {167--174}, editor = {Ciuprina, G. and Ioan, D.}, publisher = {Springer} } @PhdThesis{morVui14, author = {Vuillemin, P.}, title = {Frequency-limited model approximation of large-scale dynamical models}, school = {Universit{\'e} de Toulouse}, year = 2014, url = {http://www.pierre-vuillemin.fr/publi/vuillemin_thesis_2014.pdf} } @Article{morWalH12, author = {S. Waldherr and B. Haasdonk}, title = {Efficient Parametric Analysis of the Chemical Master Equation through Model Order Reduction}, journal = {BMC Systems Biology}, year = 2012, volume = 6, pages = 81, doi = {10.1186/1752-0509-6-81} } @InProceedings{morWanFLetal24, author = {C. Wang and L. Feng and W. Lu and W. Bian and Z. You and P. Benner}, title = {Active learning enhanced deep-learning surrogate model for fast {MEMS} design with high-dimensional design parameter spaces}, booktitle = {19th IEEE International Conference on Nano/Micro Engineered and Molecular Systems (IEEE NEMS 2024)}, year = 2024, note = {accepted} } @InProceedings{morWanGV04, author = {Wang, J. and Ghanta, P. and Vrudhula, S.}, title = {Stochastic analysis of interconnect performance in the presence of process variations}, booktitle = {Computer Aided Design, 2004. ICCAD-2004. 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Autom. Control}, year = 2016, volume = 61, number = 11, pages = {3438--3451}, month = nov, doi = {10.1109/TAC.2016.2521361}, issn = {2334-3303} } @PhdThesis{morWol15, author = {Wolf, T.}, title = {${H}_2$ Pseudo-Optimal Model Order Reduction}, school = TUM, year = 2015, type = {{D}issertation}, address = {Munich, Germany} } @Article{morWolP16, author = {T. Wolf and H.K.F. Panzer}, title = {The {ADI} iteration for {L}yapunov equations implicitly performs {H2} pseudo-optimal model order reduction}, journal = IntControl, year = 2016, volume = 89, number = 3, pages = {481--493}, publisher = {Taylor \& Francis}, doi = {10.1080/00207179.2015.1081985} } @Article{morWolPL11, author = {Wolf, T. and Panzer, H. and Lohmann, B.}, title = {{G}ramian-based error bound in model reduction by {K}rylov subspace methods}, journal = {IFAC Proceedings Volumes (18th IFAC World Congress)}, year = 2011, volume = 44, number = 1, pages = {3587--3592}, doi = {10.3182/20110828-6-IT-1002.02809} } @Article{morWolPL13, author = {Wolf, T. and Panzer, H.~K.~F. and Lohmann, B.}, title = {Model Order Reduction by Approximate Balanced Truncation: A Unifying Framework}, journal = atAutom, year = 2013, volume = 61, number = 8, pages = {545--556}, doi = {10.1524/auto.2013.1007} } @Article{morWon08, author = {Wong, N.}, title = {Efficient Positive-Real Balanced Truncation of Symmetric Systems Via Cross-{R}iccati Equations}, journal = IEEETransCADCS, year = 2008, volume = 27, number = 3, pages = {470--480}, doi = {10.1109/TCAD.2008.915534} } @Article{morWonB07, author = {Wong, N. and Balakrishnan, V.}, title = {Fast Positive-Real Balanced Truncation Via Quadratic Alternating Direction Implicit Iteration}, journal = IEEETransCADCS, year = 2007, volume = 26, number = 9, pages = {1725--1731}, month = sep, doi = {10.1109/TCAD.2007.895617} } @Article{morWonBKetal06, author = {Wong, N. and Balakrishnan, V. and Koh, C.-K. and Ng, T.-S.}, title = {Two Algorithms for Fast and Accurate Passivity-Preserving Model Order Reduction}, journal = {IEEE Trans. Comput. Aided. Des. Integr. Circuits Syst.}, year = 2006, volume = 25, number = 10, pages = {2062--2075}, month = oct, doi = {10.1109/TCAD.2006.873893} } @PhdThesis{morWor94, author = {P.~M.~R. Wortelboer}, title = {Frequency-weighted Balanced Reduction of Closed-loop Mechanical Servo-systems: Theory and Tools}, school = {Delft University of Technology}, year = 1994, type = {{Ph.D. Thesis}}, address = {Delft, NL} } @PhdThesis{morWya12, author = {Wyatt, S.}, title = {Issues in Interpolatory Model Reduction: Inexact Solves, Second-order Systems and {DAE}s}, school = VTech, year = 2012, address = {Blacksburg, Virginia, USA}, month = may, url = {http://hdl.handle.net/10919/27668} } @Article{morXiaJ14, author = {Xiao, Zhi-Hua and Jiang, Yao-Lin}, title = {Dimension reduction for second-order systems by general orthogonal polynomials}, journal = MCMDS, year = 2014, volume = 20, number = 4, pages = {414--432}, doi = {10.1080/13873954.2013.867274} } @Article{morXuJ20, author = {Xu, K. and Jiang, Y.}, title = {Structure-preserving interval-limited balanced truncation reduced models for port-{H}amiltonian systems}, journal = {IET Control Theory \& Applications}, volume = {14}, number = {3}, pages = {405--414}, year = {2020}, doi = {10.1049/iet-cta.2019.0566} } @Article{morXuLBetal25, author = {Xu, Kang-Li and Li, Zhen and Benner, Peter}, title = {Parametric Interpolation Model Order Reduction on {Grassmann} Manifolds by Parallelization}, journal = IEEETransCSII, year = 2025, volume = 72, number = 1, pages = {198--202}, doi = {10.1109/TCSII.2024.3460171} } @Article{morXuZ11, author = {Xu, Y. and Zeng, T.}, title = {Optimal {$\mathcal{H}_2$} Model Reduction for Large Scale {MIMO} Systems via Tangential Interpolation}, journal = {Int. J. Numer. Anal. 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Passive-Order Reduction of {RLCK} Circuits}, journal = IEEETransCSII, year = 2008, volume = 55, number = 9, pages = {942--946}, month = sep } @InProceedings{morYanWT08, author = {Yan, B. and Wang, H. and Tan, S.~X.~D.}, title = {A Survey of RLCK Reduction and Simulation Methods by Fast Truncated Balanced Realization}, booktitle = {Solid-State and Integrated-Circuit Technology}, year = 2008, volume = 9, pages = {2236--2239}, doi = {10.1109/ICSICT.2008.4735035} } @InProceedings{morYaoDY08, author = {Yao, S. and Deng, Y. and Yu, Z.}, title = {Balanced Truncation on Empirical Gramians for Model-Order-Reduction of Non-Quasi-Static Effects in {MOSFET}s}, booktitle = {9th International Conference on Solid-State and Integrated-Circuit Technology}, year = 2008, pages = {309--312}, doi = {10.1109/ICSICT.2008.4734525} } @TechReport{morYeuLH17, author = {Yeung, E. and Liu, Z. and Hodas, N.~O.}, title = {A {K}oopman Operator Approach for Computing and Balancing {G}ramians for Discrete Time 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Astronautics}, year = 2008, volume = 34, number = 12, pages = {1437--1440}, url = {http://en.cnki.com.cn/Article_en/CJFDTOTAL-BJHK200812017.htm} } @Article{morZhaFLetal14, author = {Zhang, Y. and Feng, L. and Li, S. and Benner, P.}, title = {Accelerating {PDE} constrained optimization by the reduced basis method: application to batch chromatography}, journal = IntNumerEng, year = 2015, volume = 104, number = 11, pages = {983--1007}, doi = {10.1002/nme.4950}, publisher = {Wiley Online Library} } @Article{morZhaFLetal15, author = {Zhang, Y. and Feng, L. and Li, S. and Benner, P.}, title = {An efficient output error estimation for model order reduction of parametrized evolution equations}, journal = SIAMSciComp, year = 2015, volume = 37, number = 6, pages = {B910--B936}, doi = {10.1137/140998603} } @Article{morZhaFLetal15a, author = {Zhang, Y. and Feng, L. and Li, S. and Benner, P.}, title = {Accelerating PDE constrained optimization by the reduced basis method: application to batch 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Zilouchian}, title = {Balanced structures and model reduction of unstable systems}, booktitle = {IEEE Proceedings of the SOUTHEASTCON '91}, year = 1991, volume = 2, pages = {1198--1201}, month = apr, doi = {10.1109/SECON.1991.147956} } @InProceedings{morZuyG23, author = {Zuyev, A. and Gosea, I.~V.}, title = {Approximating a flexible beam model in the {L}oewner framework}, booktitle = {21st European Control Conference (ECC)}, year = 2023, pages = {1--7}, doi = {10.23919/ECC57647.2023.10178203} } @Article{mordelCFetal22, author = {de la Rubia, V. and Chellappa, S. and Feng, L. and Benner, P.}, title = {Fast A Posteriori State Error Estimation for Reliable Frequency Sweeping in Microwave Circuits via the Reduced-Basis Method}, journal = IEEETransMTT, year = 2022, volume = 70, number = 11, pages = {5172--5184}, doi = {10.1109/TMTT.2022.3203726} } @Misc{morembsweb, title = {{MOREMBS} (Model Order Reduction of Elastic Multibody Systems)}, howpublished = {\url{https://www.itm.uni-stuttgart.de/en/software/morembs/}}, key = {MOREMBS}, organization = {Institute of Engineering and Computational Mechanics, University of Stuttgart} } @Misc{morpackweb, title = {{MORPACK} (Model Order Reduction PACKage)}, howpublished = {\url{https://tu-dresden.de/ing/maschinenwesen/ifkm/dmt/forschung/projekte/morpack}}, key = {MORPACK}, organization = {Chair of Dynamics and Mechanism Design, TU Dresden} } @Misc{morpymorrepo, author = {{pyMOR developers and contributors}}, title = {{pyMOR} - Model Order Reduction with {P}ython}, howpublished = {\url{https://github.com/pymor/pymor}}, key = {pymor} } @Misc{morpymorweb, author = {{pyMOR developers and contributors}}, title = {{pyMOR} - Model Order Reduction with {P}ython}, howpublished = {\url{https://pymor.org}}, key = {pymor} } % abbreviations from MR http://www.ams.org/msnhtml/serials.pdf % Mathematical Reviews (MR) generally follows the ISO 4 standard for % abbreviating journal titles. % all IEEE abbrev. from http://www.ieee.org/documents/trans_journal_names.pdf @String { Academic = {Academic Press} } @String { ACMMathSoft = {{ACM} Trans. Math. Software} } @String { ACMPress = {{ACM} Press} } @String { AdamHilger = {Adam Hilger} } @String { AddisonWesley = {Addison-Wesley} } @String { AdvComputMath = {Adv. Comput. Math.} } @String { AIAA = {AIAA J.} } @String { AdvParComp = {Advances in Parallel Computing} } @String { AeroQuart = {Aeronaut. Quart.}} @String { AllynBacon = {Allyn and Bacon} } @String { AmerMathMonthly = {Amer. Math. Monthly} } @String { AmerSocio = {Amer. J. Sociology} } @String { AmerStatAssoc = {J. Amer. Statist. Assoc.} } @String { AMS = {American Mathematical Society} } @String { AMSES = {Adv. Model. and Simul. in Eng. Sci.} } @String { AMSTrans = {Amer. Math. Soc. Transl.} } @String { ApplMathComp = {Appl. Math. Comput.} } @String { ApplMathLett = {Appl. Math. Lett.} } @String { ApplMathModel = {Appl. Math. Model.} } @String { ApplMathOptim = {Appl. Math. Optim.} } @String { ApplNumMath = {Appl. Numer. Math.} } @String { ArchCompEng = {Arch. Comput. Methods Eng.}} @String { atAutom = {at-Auto\-mati\-sie\-rungs\-tech\-nik} } @String { Automatica = {Automatica J. IFAC} } @String { Birkhauser = {Birkh{\"{a}}user} } @String { BIT = {{BIT}} } @String { BritStatPsych = {Brit. J. Math. Statist. Psych.} } @String { BullAMS = {Bull. Amer. Math. Soc.} } @String { CACM = {Comm. {ACM}} } @String { CambridgePress = {Cambridge University Press} } @String { CAMWA = {Comput. Math. Appl.} } @String { CanMathBull = {Canad. Math. Bull.} } @String { Chelsea = {Chelsea} } @String { ClarendonPress = {Clarendon Press} } @String { CMAM = {Comput. Meth. Appl. Math.} } @String { CMAME = {Comput. Meth. Appl. Mech. Eng.} } @String { CommMathSci = {Commun. Math. Sci.} } @String { CompApplMath = {J. Comput. Appl. Math.} } @String { CompJour = {Comput. J.} } @String { CompMethAppMechEng = {Comp. Meth. Appl. Mech. Eng.} } @String { CompOptimApp = {Comput. Optim. Appl.} } @String { CompServ = {Comput. Surveys} } @String { CompStruct = {Comput. \& Structures} } @String { CompSysSci = {J. Comput. System Sci.} } @String { Computer = {{IEEE} Computer} } @String { Computing = {Computing} } @String { CompVisSci = {Comput. Vis. Sci.} } @String { ContempMath = {Contemp. Math.} } @String { CPE = {Concurrency and Comput.: Pract. Exper.} } @String { CRAcadSciParis = {C.~R. Acad. Sci. Paris} } @String { Crelle = {Crelle's J.} } @String { DAC = {In Proc. Design Automation Conference} } @String { DeGruyter = {Walter de Gruyter GmbH \& Co. KG} } @String { DoverPub = {Dover Publications} } @String { ETNA = {Electron. Trans. Numer. Anal.} } @String { EuropJCon = {Eur. J. Control} } @String { Eyolles = {Eyolles} } @String { FinEl = {Finite Elem. Anal. Des.}} @String { GAMMMit = {GAMM-Mitt.} } @String { GiornaleMath = {Giorn. Mat.} } @String { Harvard = {Harvard University Press} } @String { HoltRinehartWinston = {Holt, Rinehart and Winston} } @String { ICCAD = {In Proc. 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Indust. Appl. Math.} } @String { JSIAMB = {J. Soc. Indust. Appl. Math. Ser. B Numer. Anal.} } @String { JSUPER = {J. Supercomput.} } @String { Kibernetika = {Kibernetika} } @String { LinAlgApp = {Linear Algebra Appl.} } @String { LNCIS = {Lect. Notes Control Inf. Sci.} } @String { LNCS = {Lecture Notes in Comput. Sci.} } @String { LNCSE = {Lect. Notes Comput. Sci. Eng.} } @String { LNEE = {Lect. Notes Electr. Eng.} } @String { LNM = {Lecture Notes in Math.} } @String { LNNS = {Lect. Notes Netw. Syst.} } @String { LNPE = {Lect. N. Prod. Eng.} } @String { Macmillan = {Macmillan} } @String { MathAnaAppl = {J. Math. Anal. Appl.} } @String { MathAnnalen = {Math. Ann.} } @String { MathComp = {Math. Comp.} } @String { MathPhys = {J. Math. Phys.} } @String { MathProg = {Math. Program.} } @String { MathScand = {Math. Scand.} } @String { MathWorks = {The Math Works Inc.} } @String { MathZ = {Math. Z.} } @String { McGrawHill = {McGraw-Hill} } @String { MCMDS = {Math. Comput. Model. Dyn. 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