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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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Abstract

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

Entropy in Dynamic Systems

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ISBN: 9783039216161 9783039216178 Year: Pages: 172 DOI: 10.3390/books978-3-03921-617-8 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Technology (General) --- General and Civil Engineering
Added to DOAB on : 2019-12-09 11:49:16
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In order to measure and quantify the complex behavior of real-world systems, either novel mathematical approaches or modifications of classical ones are required to precisely predict, monitor, and control complicated chaotic and stochastic processes. Though the term of entropy comes from Greek and emphasizes its analogy to energy, today, it has wandered to different branches of pure and applied sciences and is understood in a rather rough way, with emphasis placed on the transition from regular to chaotic states, stochastic and deterministic disorder, and uniform and non-uniform distribution or decay of diversity. This collection of papers addresses the notion of entropy in a very broad sense. The presented manuscripts follow from different branches of mathematical/physical sciences, natural/social sciences, and engineering-oriented sciences with emphasis placed on the complexity of dynamical systems. Topics like timing chaos and spatiotemporal chaos, bifurcation, synchronization and anti-synchronization, stability, lumped mass and continuous mechanical systems modeling, novel nonlinear phenomena, and resonances are discussed.

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2019 (2)