Advances in Computational Mathematics

, Volume 45, Issue 3, pp 1251–1271 | Cite as

Randomized model order reduction

  • Alessandro AllaEmail author
  • J. Nathan Kutz


The singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensional model which is then evaluated cheaply. It constitutes a building block for many techniques such as the proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD). The aim of this work is to provide an efficient computation of low-rank POD and/or DMD modes via randomized matrix decompositions. This is possible due to the randomized singular value decomposition (rSVD) which is a fast and accurate alternative of the SVD. Although this is considered an offline stage, this computation may be extremely expensive; therefore, the use of compressed techniques drastically reduce its cost. Numerical examples show the effectiveness of the method for both POD and DMD.


Nonlinear dynamical systems Proper orthogonal decomposition Dynamic mode decomposition Randomized linear algebra 

Mathematics Subject Classification (2010)

65L02 65M02 37M05 62H25 


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Funding information

This study is supported by the Department of Energy (grant no. DE-SC0009324) and the U.S. Air Force Office of Scientific Research (FA9550-15-1-0385).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPUC-RioRio de JaneiroBrazil
  2. 2.Department of Applied MathematicsUniversity of WashingtonSeattleUSA

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