A comparison of neural network architectures for data-driven reduced-order modeling

The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other netw...

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Vydané v:	Computer methods in applied mechanics and engineering Ročník 393; s. 114764
Hlavní autori:	Gruber, Anthony, Gunzburger, Max, Ju, Lili, Wang, Zhu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Amsterdam Elsevier B.V 01.04.2022 Elsevier BV Elsevier
Predmet:	Computer architecture Convolutional autoencoder ENGINEERING Graph convolution Modelling Neural networks Nonlinear dimensionality reduction Parametric PDEs Reduced order models Reduced-order modeling System effectiveness Reduced-order modeling Parametric PDEs 65M60 Graph convolution 65M22 Convolutional autoencoder Nonlinear dimensionality reduction
ISSN:	0045-7825, 1879-2138
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Abstract	The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other network-based methods in all modeling scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark experiments, it is shown that the superior autoencoder architecture for a given ROM application is highly dependent on the size of the latent space and the structure of the snapshot data, with the proposed architecture demonstrating benefits on data with irregular connectivity when the latent space is sufficiently large. •Autoencoder neural networks facilitate effective nonlinear methods for reduced-order modeling (ROM).•Many popular ROMs employ a standard convolutional autoencoder which is only suitable for regular data.•A new ROM architecture is proposed which uses a graph convolutional autoencoder suitable for irregular data.•The proposed architecture is compared to ROMs based on POD, standard convolutional, and fully connected architectures.•Experiments show that the notion of best architecture is task-dependent, with the proposed ROM producing superior results in several cases.
AbstractList	The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other network-based methods in all modeling scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark experiments, it is shown that the superior autoencoder architecture for a given ROM application is highly dependent on the size of the latent space and the structure of the snapshot data, with the proposed architecture demonstrating benefits on data with irregular connectivity when the latent space is sufficiently large. The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other network-based methods in all modeling scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark experiments, it is shown that the superior autoencoder architecture for a given ROM application is highly dependent on the size of the latent space and the structure of the snapshot data, with the proposed architecture demonstrating benefits on data with irregular connectivity when the latent space is sufficiently large. •Autoencoder neural networks facilitate effective nonlinear methods for reduced-order modeling (ROM).•Many popular ROMs employ a standard convolutional autoencoder which is only suitable for regular data.•A new ROM architecture is proposed which uses a graph convolutional autoencoder suitable for irregular data.•The proposed architecture is compared to ROMs based on POD, standard convolutional, and fully connected architectures.•Experiments show that the notion of best architecture is task-dependent, with the proposed ROM producing superior results in several cases.
ArticleNumber	114764
Author	Wang, Zhu Ju, Lili Gruber, Anthony Gunzburger, Max
Author_xml	– sequence: 1 givenname: Anthony orcidid: 0000-0001-7107-5307 surname: Gruber fullname: Gruber, Anthony email: agruber@fsu.edu organization: Department of Scientific Computing, Florida State University, 400 Dirac Science Library, Tallahassee, 32306, FL, USA – sequence: 2 givenname: Max surname: Gunzburger fullname: Gunzburger, Max email: mgunzburger@fsu.edu organization: Department of Scientific Computing, Florida State University, 400 Dirac Science Library, Tallahassee, 32306, FL, USA – sequence: 3 givenname: Lili orcidid: 0000-0002-6520-582X surname: Ju fullname: Ju, Lili email: ju@math.sc.edu organization: Department of Mathematics, University of South Carolina, 1523 Greene Street, Columbia, 29208, SC, USA – sequence: 4 givenname: Zhu surname: Wang fullname: Wang, Zhu email: wangzhu@math.sc.edu organization: Department of Mathematics, University of South Carolina, 1523 Greene Street, Columbia, 29208, SC, USA
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Snippet	The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale...
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SubjectTerms	Computer architecture Convolutional autoencoder ENGINEERING Graph convolution Modelling Neural networks Nonlinear dimensionality reduction Parametric PDEs Reduced order models Reduced-order modeling System effectiveness
Title	A comparison of neural network architectures for data-driven reduced-order modeling
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