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Model order reduction using sparse coding exemplified for the lid-driven cavity

Published online by Cambridge University Press:  27 October 2016

Rohit Deshmukh ,
Jack J. McNamara ,
Zongxian Liang ,
J. Zico Kolter  and
Abhijit Gogulapati
Rohit Deshmukh
Affiliation:
Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA
Jack J. McNamara*
Affiliation:
Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA
Zongxian Liang
Affiliation:
Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA
J. Zico Kolter
Affiliation:
School of Computer Science, Carnegie Mellon University Pittsburgh, PA 15213, USA
Abhijit Gogulapati
Affiliation:
Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA
*
†Email address for correspondence: [email protected]
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Abstract

Basis identification is a critical step in the construction of accurate reduced-order models using Galerkin projection. This is particularly challenging in unsteady flow fields due to the presence of multi-scale phenomena that cannot be ignored and may not be captured using a small set of modes extracted using the ubiquitous proper orthogonal decomposition. This study focuses on this issue by exploring an approach known as sparse coding for the basis identification problem. Compared with proper orthogonal decomposition, which seeks to truncate the basis spanning an observed data set into a small set of dominant modes, sparse coding is used to identify a compact representation that spans all scales of the observed data. As such, the inherently multi-scale bases may improve reduced-order modelling of unsteady flow fields. The approach is examined for a canonical problem of an incompressible flow inside a two-dimensional lid-driven cavity. The results demonstrate that Galerkin reduction of the governing equations using sparse modes yields a significantly improved predictive model of the fluid dynamics.

JFM classification

Mathematical Foundations: Computational methods Nonlinear Dynamical Systems: Low-dimensional models Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
Papers
Information
Journal of Fluid Mechanics , Volume 808 , 10 December 2016 , pp. 189 - 223
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Copyright
© 2016 Cambridge University Press 

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