Selected Introductory Works

Following is a list of selected works introducing the field of model order reduction. A comprehensive list of journal articles, conference proceedings, collection chapters, and PhD theses can be found on the Publications page.

Books

• L. Fortuna, G. Nunnari, A. Gallo. "Model Order Reduction Techniques with Applications in Electrical Engineering". Springer, 1992. ISBN 9781447132004

• P. Benner, V. L. Mehrmann, D. C. Sorensen. "Dimension Reduction of Large-scale Systems". Springer, 2005. ISBN 9783540279099

• S.X.-D. Tan and L. Hei. "Advanced Model Order Reduction Techniques in VLSI Design". Cambridge University Press, 2007. ISBN 9780511541117

• W. H. Schilders, H. A. van der Vorst, J. Rommes. "Model Order Reduction: Theory, Research Aspects and Applications". Springer - Mathematics in Industry Vol. 13, 2008. ISBN 9783540788416

• A. C. Antoulas. "Approximation of large-scale dynamical systems". SIAM - Advances in Design and Control Vol. 6, 2009. ISBN 9780898715293

• P. Benner, M. Hinze, E. J. W. ter Maten. "Model Reduction for Circuit Simulation". Springer - Lecture Notes in Electrical Engineering Vol. 74, 2011. ISBN 9789400700895

• G. Obinata, B. D. O. Anderson. "Model Reduction for Control System Design". Springer - Communications and Control Engineering, 2012. ISBN 9781447102830

• A. Quarteroni, G. Rozza (Editors). "Reduced Order Methods for Modeling and Computational Reduction". Springer - Modeling, Simulation & Application Vol. 9, 2014. ISBN 9783319020907

• J. S. Hesthaven, G. Rozza, B. Stamm. "Certified Reduced Basis Methods for Parametrized Partial Differential Equations". Springer - Briefs in Mathematics, 2015. ISBN 9783319224701

• A. Quarteroni, A. Manzoni, F. Negri. "Reduced Basis Methods for Partial Differential Equations: An Introduction". Springer - La Mathematica Per Il 3+2, 2015. ISBN 9783319154312

• P. Benner, M. Ohlberger, A. Cohen and K. Willcox (Editors). "Model Reduction and Approximation: Theory and Algorithms". SIAM - Computational Science & Engineering, 2017. ISBN 9781611974812

• P. Benner, M. Ohlberger, A. Patera, G. Rozza and K. Urban (Editors). "Model Reduction of Parametrized Systems". Springer - Modeling, Simulation & Application, Vol. 17, 2017. ISBN 9783319587851

• P. Benner, T. Breiten, H. Faßbender, M. Hinze, T. Stykel, R. Zimmermann (Editors). "Model Reduction of Complex Dynamical Systems". Springer - International Series of Numerical Mathematics, Vol. 171, 2021. ISBN 9783030729820

• A. C. Antoulas , C. A. Beattie and S. Gugercin. "Interpolatory Methods for Model Reduction". SIAM - Computational Science & Engineering, 2020. ISBN 9781611976076

• "Model Order Reduction" Handbook Series (UPCOMING):
  • P. Benner, W. Schilders, S. Grivet-Talocia, A. Quarteroni, G. Rozza and L. M. Silveira. "Model Order Reduction, Volume 1: System- and Data-Driven Methods and Algorithms". De Gruyter, 2021. ISBN 9783110500431
  • P. Benner, W. Schilders, S. Grivet-Talocia, A. Quarteroni, G. Rozza and L. M. Silveira. "Model Order Reduction, Volume 2: Snapshot-Based Methods and Algorithms". De Gruyter, 2021. ISBN 9783110671407
  • P. Benner, W. Schilders, S. Grivet-Talocia, A. Quarteroni, G. Rozza and L. M. Silveira. "Model Order Reduction, Volume 3: Applications". De Gruyter, 2021. ISBN 9783110500448

Surveys

• A.C. Antoulas, D.C. Sorensen and S. Gugercin. "A survey of model reduction methods for large-scale systems". Contemporary Mathematics, 280: 193--219, 2001.

• A.C. Antoulas. "An overview of approximation methods for large-scale dynamical systems". Annual Reviews in Control, 29(2): 181--190, 2005.

• M. Frangos, Y. Marzouk, K. Willcox, and B. van Bloemen Waanders. "Surrogate and Reduced-Order Modeling: A Comparison of Approaches for Large-Scale Statistical Inverse Problems". In: Large-Scale Inverse Problems and Quantification of Uncertainty: 123--149. John Wiley & Sons, 2010.

• U. Baur, P. Benner, L. Feng. "Model Order Reduction for Linear and Nonlinear Systems: A System-Theoretic Perspective". Archives of Computational Methods in Engineering, 21(4): 331--358, 2014.

• P. Benner and H. Fassbender. "Model Order Reduction: Techniques and Tools". In: Encyclopedia of Systems and Control, pages 1--10. Springer, 2014.

• P. Benner, S. Gugercin, and K. Willcox. "A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems". SIAM Review, 57(4): 483--531, 2015.

• C.W. Rowley and S.T.M. Dawson. "Model Reduction for Flow Analysis and Control". Annual Review of Fluid Mechanics, 49: 387--417, 2017.

Lectures

• C. Moler. "Eigenvalues and Singular Values". Chapter 10, Numerical Computing with MATLAB.

• S. Lall "Robust Control Analysis and Synthesis", 2001.

• H. Sandberg "Applications: Controller and Nonlinear Model Order Reduction", 2008.

• S. Volkwein "Model Reduction Using Proper Orthogonal Decomposition", 2011.

• S. Volkwein "POD a-posteriori error estimation for PDE constrained optimization", CIRM Model Reduction and Approximation for Complex Systems, 2013. (video)

• P. Benner "Matrix Equations and Model Reduction", 2013. (video: Part 1, Part 2, Part 3, Part 4, Part 5)

• V. Mehrmann "Model Reduction: Analysis, Numerical Solution and Real World Applications", 2015. (video: Model Reduction, a Survey, Preservation of Physical Properties in Model Reduction Methods, Model Reduction in Real World and Industrial Applications )

• N. Kutz "Reduced Order Modelling", 2016. (video: ROM, POD 1, POD 2, POD 3)

• K. Carlberg "Reduced Order Modelling", 2016. (video: part 1,part 2, part 3, part 4, part 5)

• M. Hinze "Proper Orthogonal Decomposition - mathematics and practical aspects". LMS - EPSRC Durham Symposium on Model Order Reduction, 2017. (slides: part 1, part 2, part 3; video: part 1, part 2, part 3)

• B. Haasdonk. "Reduced Basis Methods for Parametrized Partial Differential Equations". LMS - EPSRC Durham Symposium on Model Order Reduction, 2017. (slides: part 1, part 2, part 3; video: part 1, part 2, part 3)

• T. Stykel. "Balanced truncation model reduction". LMS - EPSRC Durham Symposium on Model Order Reduction, 2017. (slides: part 1, part 2, part 3)

• S. Gugercin, C. Beattie, and A. C. Antoulas. "Model Reduction via Interpolation". LMS - EPSRC Durham Symposium on Model Order Reduction, 2017. (slides: part 1, part 2; video part 1, part 2, part 3)

• T. Damm. "Model order reduction for stochastic systems". LMS - EPSRC Durham Symposium on Model Order Reduction, 2017. (slides: part 1, part 2, part 3; video: part 1, part 2, part 3)

• P. Benner. "Parameter-preserving model order reduction of dynamical systems". LMS - EPSRC Durham Symposium on Model Order Reduction, 2017. (slides: part 1, part 2, part 3; video: part 1, part 2, part 3)

• C. Beattie, P. Benner, S. Gugercin "An Introduction to System-theoretic Methods for Model Reduction". ICERM - Model and dimension reduction in uncertain and dynamic systems, 2020. (videos:

part 1A, part 1B, part 1C, part 2A, part 2B, part 3A, part 3B, part 4, part 5)

News

• P Benner. "Solving large-scale control problems", IEEE Control Systems Magazine 24(1): 44--59, 2004.

• M. Gunzburger and K. Willcox. "Reduced-Order Models of Large-Scale Computational Systems", SIAM News 38(5): 2005.

• P. Benner. "Numerical Linear Algebra for Model Reduction in Control and Simulation", GAMM Mitteilungen 29(2): 275--296, 2006.

• P. Benner. "Model Reduction at ICIAM '07", SIAM News 40(8): 2007.

• M. Ohlberger and B. Haasdonk. "Wenn die Probleme zahlreicher werden: Reduzierte Basis Methoden für effiziente und gesicherte numerische Simulation", GAMM Rundbrief 2014(1): 6--13, 2014.

• R. Brueckner. "Predictive Data Science for Physical Systems: From Model Reduction to Scientific Machine Learning", Inside HPC, 2020.