Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics
The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the...
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| Format: | Online |
| Idioma: | anglès |
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MDPI - Multidisciplinary Digital Publishing Institute
2021
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| Accés en línia: | 42525 |
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| _version_ | 1869522061528924160 |
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| author | Fritzen, Felix Ryckelynck, David |
| author_browse | Fritzen, Felix Ryckelynck, David |
| author_facet | Fritzen, Felix Ryckelynck, David |
| author_sort | Fritzen, Felix |
| collection | Directory of Open Access Books |
| description | The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics. |
| format | Online |
| id | doab-20.500.12854ir-52520 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | MDPI - Multidisciplinary Digital Publishing Institute |
| publisherStr | MDPI - Multidisciplinary Digital Publishing Institute |
| record_format | ojs |
| spelling | doab-20.500.12854ir-525202024-04-11T15:10:18Z Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics Fritzen, Felix Ryckelynck, David TA1-2040 T1-995 supervised machine learning proper orthogonal decomposition (POD) PGD compression stabilization nonlinear reduced order model gappy POD symplectic model order reduction neural network snapshot proper orthogonal decomposition 3D reconstruction microstructure property linkage nonlinear material behaviour proper orthogonal decomposition reduced basis ECSW geometric nonlinearity POD model order reduction elasto-viscoplasticity sampling surrogate modeling model reduction enhanced POD archive modal analysis low-rank approximation computational homogenization artificial neural networks unsupervised machine learning large strain reduced-order model proper generalised decomposition (PGD) a priori enrichment elastoviscoplastic behavior error indicator computational homogenisation empirical cubature method nonlinear structural mechanics reduced integration domain model order reduction (MOR) structure preservation of symplecticity heterogeneous data reduced order modeling (ROM) parameter-dependent model data science Hencky strain dynamic extrapolation tensor-train decomposition hyper-reduction empirical cubature randomised SVD machine learning inverse problem plasticity proper symplectic decomposition (PSD) finite deformation Hamiltonian system DEIM GNAT thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues::TBX History of engineering and technology The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics. 2021-02-11T18:29:39Z 2021-02-11T18:29:39Z 2019-12-09 11:49:15 2019 book 42525 9783039214099 9783039214105 https://directory.doabooks.org/handle/20.500.12854/52520 eng application/octet-stream Attribution-NonCommercial-NoDerivatives 4.0 International https://mdpi.com/books/pdfview/book/1551 MDPI - Multidisciplinary Digital Publishing Institute 10.3390/books978-3-03921-410-5 10.3390/books978-3-03921-410-5 46cabcaa-dd94-4bfe-87b4-55023c1b36d0 9783039214099 9783039214105 254 open access |
| spellingShingle | TA1-2040 T1-995 supervised machine learning proper orthogonal decomposition (POD) PGD compression stabilization nonlinear reduced order model gappy POD symplectic model order reduction neural network snapshot proper orthogonal decomposition 3D reconstruction microstructure property linkage nonlinear material behaviour proper orthogonal decomposition reduced basis ECSW geometric nonlinearity POD model order reduction elasto-viscoplasticity sampling surrogate modeling model reduction enhanced POD archive modal analysis low-rank approximation computational homogenization artificial neural networks unsupervised machine learning large strain reduced-order model proper generalised decomposition (PGD) a priori enrichment elastoviscoplastic behavior error indicator computational homogenisation empirical cubature method nonlinear structural mechanics reduced integration domain model order reduction (MOR) structure preservation of symplecticity heterogeneous data reduced order modeling (ROM) parameter-dependent model data science Hencky strain dynamic extrapolation tensor-train decomposition hyper-reduction empirical cubature randomised SVD machine learning inverse problem plasticity proper symplectic decomposition (PSD) finite deformation Hamiltonian system DEIM GNAT thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues::TBX History of engineering and technology Fritzen, Felix Ryckelynck, David Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics |
| title | Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics |
| title_full | Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics |
| title_fullStr | Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics |
| title_full_unstemmed | Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics |
| title_short | Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics |
| title_sort | machine learning low rank approximations and reduced order modeling in computational mechanics |
| topic | TA1-2040 T1-995 supervised machine learning proper orthogonal decomposition (POD) PGD compression stabilization nonlinear reduced order model gappy POD symplectic model order reduction neural network snapshot proper orthogonal decomposition 3D reconstruction microstructure property linkage nonlinear material behaviour proper orthogonal decomposition reduced basis ECSW geometric nonlinearity POD model order reduction elasto-viscoplasticity sampling surrogate modeling model reduction enhanced POD archive modal analysis low-rank approximation computational homogenization artificial neural networks unsupervised machine learning large strain reduced-order model proper generalised decomposition (PGD) a priori enrichment elastoviscoplastic behavior error indicator computational homogenisation empirical cubature method nonlinear structural mechanics reduced integration domain model order reduction (MOR) structure preservation of symplecticity heterogeneous data reduced order modeling (ROM) parameter-dependent model data science Hencky strain dynamic extrapolation tensor-train decomposition hyper-reduction empirical cubature randomised SVD machine learning inverse problem plasticity proper symplectic decomposition (PSD) finite deformation Hamiltonian system DEIM GNAT thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues::TBX History of engineering and technology |
| topic_facet | TA1-2040 T1-995 supervised machine learning proper orthogonal decomposition (POD) PGD compression stabilization nonlinear reduced order model gappy POD symplectic model order reduction neural network snapshot proper orthogonal decomposition 3D reconstruction microstructure property linkage nonlinear material behaviour proper orthogonal decomposition reduced basis ECSW geometric nonlinearity POD model order reduction elasto-viscoplasticity sampling surrogate modeling model reduction enhanced POD archive modal analysis low-rank approximation computational homogenization artificial neural networks unsupervised machine learning large strain reduced-order model proper generalised decomposition (PGD) a priori enrichment elastoviscoplastic behavior error indicator computational homogenisation empirical cubature method nonlinear structural mechanics reduced integration domain model order reduction (MOR) structure preservation of symplecticity heterogeneous data reduced order modeling (ROM) parameter-dependent model data science Hencky strain dynamic extrapolation tensor-train decomposition hyper-reduction empirical cubature randomised SVD machine learning inverse problem plasticity proper symplectic decomposition (PSD) finite deformation Hamiltonian system DEIM GNAT thema EDItEUR::T Technology, Engineering, Agriculture, Industrial processes::TB Technology: general issues::TBX History of engineering and technology |
| url | 42525 |
| work_keys_str_mv | AT fritzenfelix machinelearninglowrankapproximationsandreducedordermodelingincomputationalmechanics AT ryckelynckdavid machinelearninglowrankapproximationsandreducedordermodelingincomputationalmechanics |