VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems
Abstract Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2024-03-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-024-56118-x |
| _version_ | 1827316029605281792 |
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| author | Thomas Simpson Konstantinos Vlachas Anthony Garland Nikolaos Dervilis Eleni Chatzi |
| author_facet | Thomas Simpson Konstantinos Vlachas Anthony Garland Nikolaos Dervilis Eleni Chatzi |
| author_sort | Thomas Simpson |
| collection | DOAJ |
| description | Abstract Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty. |
| first_indexed | 2024-04-24T23:07:40Z |
| format | Article |
| id | doaj.art-0c13ab1041f74e619a3b84be0c658379 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-24T23:07:40Z |
| publishDate | 2024-03-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-0c13ab1041f74e619a3b84be0c6583792024-03-17T12:23:16ZengNature PortfolioScientific Reports2045-23222024-03-0114112010.1038/s41598-024-56118-xVpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systemsThomas Simpson0Konstantinos Vlachas1Anthony Garland2Nikolaos Dervilis3Eleni Chatzi4Department of Civil, Environmental, and Geomatic Engineering, ETH ZürichDepartment of Civil, Environmental, and Geomatic Engineering, ETH ZürichSandia National LaboratoriesDynamics Research Group, Department of Mechanical Engineering, University of SheffieldDepartment of Civil, Environmental, and Geomatic Engineering, ETH ZürichAbstract Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.https://doi.org/10.1038/s41598-024-56118-xParametric reductionReduced Order Models (ROMs)Conditional VAEsUncertainty |
| spellingShingle | Thomas Simpson Konstantinos Vlachas Anthony Garland Nikolaos Dervilis Eleni Chatzi VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems Scientific Reports Parametric reduction Reduced Order Models (ROMs) Conditional VAEs Uncertainty |
| title | VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems |
| title_full | VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems |
| title_fullStr | VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems |
| title_full_unstemmed | VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems |
| title_short | VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems |
| title_sort | vprom a novel variational autoencoder boosted reduced order model for the treatment of parametric dependencies in nonlinear systems |
| topic | Parametric reduction Reduced Order Models (ROMs) Conditional VAEs Uncertainty |
| url | https://doi.org/10.1038/s41598-024-56118-x |
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