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Randomized dynamic mode decomposition for nonintrusive reduced order modelling
Author(s) -
Bistrian Diana Alina,
Navon Ionel Michael
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5499
Subject(s) - dynamic mode decomposition , model order reduction , reduction (mathematics) , basis (linear algebra) , basis function , interpolation (computer graphics) , projection (relational algebra) , galerkin method , mathematics , computation , computer science , decomposition , mathematical optimization , algorithm , finite element method , mathematical analysis , artificial intelligence , engineering , geometry , motion (physics) , ecology , machine learning , biology , structural engineering
Summary This paper focuses on a new framework for obtaining a nonintrusive (i.e., not requiring projecting of the governing equations onto the reduced basis modes) reduced order model for two‐dimensional fluid problems. To overcome the shortcomings of intrusive model order reduction usually derived by combining the Proper Orthogonal Decomposition and the Galerkin projection methods, we developed a novel technique on the basis of randomized dynamic mode decomposition (DMD) as a fast and accurate option in model order reduction. Our approach utilizes an adaptive randomized DMD to obtain a reduced basis in the offline stage, and then the temporal values of the reduced order model are obtained in the online stage through an interpolation using radial basis functions. The rank of the reduced DMD model is given as the unique solution of a constrained optimization problem. The Saint‐Venant (shallow water) equations in a channel on the rotating earth are employed to provide the numerical data. We emphasize the excellent behavior of the nonintrusive reduced order model by performing a qualitative analysis. In addition, we gain a significantly reduction of CPU time in computation of the reduced order models compared with the classical DMD method. Copyright © 2016 John Wiley & Sons, Ltd.