Convolutional autoencoders, clustering, and POD for low-dimensional parametrization of flow equations
Simulations of large-scale dynamical systems require expensive computations and large amounts of storage. Low-dimensional representations of high-dimensional states such as in reduced order models deriving from, say, Proper Orthogonal Decomposition (POD) trade in a reduced model complexity against a...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) Jg. 175; S. 49 - 61 |
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| Abstract | Simulations of large-scale dynamical systems require expensive computations and large amounts of storage. Low-dimensional representations of high-dimensional states such as in reduced order models deriving from, say, Proper Orthogonal Decomposition (POD) trade in a reduced model complexity against accuracy and can be a solution to lessen the computational burdens. However, for really low-dimensional parametrizations of the states as they may be needed for example for controller design, linear methods like the POD come to their natural limits so that nonlinear approaches will be the methods of choice. In this work, we propose a convolutional autoencoder (CAE) consisting of a nonlinear encoder and an affine linear decoder and consider a deep clustering model where a CAE is integrated with k-means clustering for improved encoding performance. The proposed set of methods is compared to the standard POD approach in three scenarios: single- and double-cylinder wakes modeled by incompressible Navier-Stokes equations and flow setup described by viscous Burgers' equations. |
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| AbstractList | Simulations of large-scale dynamical systems require expensive computations and large amounts of storage. Low-dimensional representations of high-dimensional states such as in reduced order models deriving from, say, Proper Orthogonal Decomposition (POD) trade in a reduced model complexity against accuracy and can be a solution to lessen the computational burdens. However, for really low-dimensional parametrizations of the states as they may be needed for example for controller design, linear methods like the POD come to their natural limits so that nonlinear approaches will be the methods of choice. In this work, we propose a convolutional autoencoder (CAE) consisting of a nonlinear encoder and an affine linear decoder and consider a deep clustering model where a CAE is integrated with k-means clustering for improved encoding performance. The proposed set of methods is compared to the standard POD approach in three scenarios: single- and double-cylinder wakes modeled by incompressible Navier-Stokes equations and flow setup described by viscous Burgers' equations. |
| Author | Kim, Yongho Heiland, Jan |
| Author_xml | – sequence: 1 givenname: Jan orcidid: 0000-0003-0228-8522 surname: Heiland fullname: Heiland, Jan email: heiland@mpi-magdeburg.mpg.de organization: Department of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106, Magdeburg, Germany – sequence: 2 givenname: Yongho orcidid: 0000-0003-4181-7968 surname: Kim fullname: Kim, Yongho email: ykim@mpi-magdeburg.mpg.de organization: Department of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106, Magdeburg, Germany |
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| Cites_doi | 10.1016/j.jcp.2019.108973 10.1109/5.726791 10.1051/m2an/2015029 10.2514/1.J058462 10.1016/j.ipm.2004.10.005 10.1016/j.cma.2023.116072 10.1016/j.jcp.2019.05.026 10.1007/s10589-022-00359-x 10.1016/j.camwa.2022.08.006 10.1016/j.patrec.2020.07.028 10.1016/j.cma.2021.114181 10.1017/jfm.2019.959 10.1016/j.ifacol.2022.11.091 10.1007/s10915-020-01294-x 10.1109/LCSYS.2023.3291231 10.3389/fams.2022.879140 10.1146/annurev.fl.25.010193.002543 10.1016/j.jcp.2020.110079 10.1016/j.neucom.2017.06.053 |
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| Keywords | Linear parameter varying (LPV) systems Model order reduction Convolutional autoencoders Clustering |
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| SubjectTerms | Clustering Convolutional autoencoders Linear parameter varying (LPV) systems Model order reduction |
| Title | Convolutional autoencoders, clustering, and POD for low-dimensional parametrization of flow equations |
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