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:
- 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)