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Projection-Based Clustering through Self-Organization and Swarm Intelligence: Combining Cluster Analysis with the Visualization of High-Dimensional Data

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ISBN: 9783658205393 9783658205409 Year: Pages: 201 DOI: https://doi.org/10.1007/978-3-658-20540-9 Language: English
Publisher: Springer Nature Grant: Philipps-Universität Marburg
Subject: Mathematics
Added to DOAB on : 2018-06-29 15:12:23
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Abstract

This book covers aspects of unsupervised machine learning used for knowledge discovery in data science and introduces a data-driven approach to cluster analysis, the Databionic swarm (DBS). DBS consists of the 3D landscape visualization and clustering of data. The 3D landscape enables 3D printing of high-dimensional data structures.The clustering and number of clusters or an absence of cluster structure are verified by the 3D landscape at a glance. DBS is the first swarm-based technique that shows emergent properties while exploiting concepts of swarm intelligence, self-organization and the Nash equilibrium concept from game theory. It results in the elimination of a global objective function and the setting of parameters. By downloading the R package DBS can be applied to data drawn from diverse research fields and used even by non-professionals in the field of data mining.

Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics

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ISBN: 9783039214099 9783039214105 Year: Pages: 254 DOI: 10.3390/books978-3-03921-410-5 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:15
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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.

Keywords

parameter-dependent model --- surrogate modeling --- tensor-train decomposition --- gappy POD --- heterogeneous data --- elasto-viscoplasticity --- archive --- model reduction --- 3D reconstruction --- inverse problem plasticity --- data science --- model order reduction --- POD --- DEIM --- gappy POD --- GNAT --- ECSW --- empirical cubature --- hyper-reduction --- reduced integration domain --- computational homogenisation --- model order reduction (MOR) --- low-rank approximation --- proper generalised decomposition (PGD) --- PGD compression --- randomised SVD --- nonlinear material behaviour --- machine learning --- artificial neural networks --- computational homogenization --- nonlinear reduced order model --- elastoviscoplastic behavior --- nonlinear structural mechanics --- proper orthogonal decomposition --- empirical cubature method --- error indicator --- symplectic model order reduction --- proper symplectic decomposition (PSD) --- structure preservation of symplecticity --- Hamiltonian system --- reduced order modeling (ROM) --- proper orthogonal decomposition (POD) --- enhanced POD --- a priori enrichment --- modal analysis --- stabilization --- dynamic extrapolation --- computational homogenization --- large strain --- finite deformation --- geometric nonlinearity --- reduced basis --- reduced-order model --- sampling --- Hencky strain --- microstructure property linkage --- unsupervised machine learning --- supervised machine learning --- neural network --- snapshot proper orthogonal decomposition

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