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

Author: Felix Fritzen

Publisher: MDPI

Published: 2019-09-18

Total Pages: 254

ISBN-13: 3039214098

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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.

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

Author: Felix Fritzen

Publisher:

Published: 2019

Total Pages: 1

ISBN-13: 9783039214105

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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.

Numerical Analysis meets Machine Learning
Numerical Analysis meets Machine Learning

Author:

Publisher: Elsevier

Published: 2024-06-13

Total Pages: 590

ISBN-13: 0443239851

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Numerical Analysis Meets Machine Learning series, highlights new advances in the field, with this new volume presenting interesting chapters. Each chapter is written by an international board of authors. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Numerical Analysis series - Updated release includes the latest information on the Numerical Analysis Meets Machine Learning

Reduced Order Methods for Modeling and Computational Reduction
Reduced Order Methods for Modeling and Computational Reduction

Author: Alfio Quarteroni

Publisher: Springer

Published: 2014-06-05

Total Pages: 338

ISBN-13: 3319020900

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This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

Machine Learning Methods with Noisy, Incomplete or Small Datasets
Machine Learning Methods with Noisy, Incomplete or Small Datasets

Author: Jordi Solé-Casals

Publisher: MDPI

Published: 2021-08-17

Total Pages: 316

ISBN-13: 3036512888

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Over the past years, businesses have had to tackle the issues caused by numerous forces from political, technological and societal environment. The changes in the global market and increasing uncertainty require us to focus on disruptive innovations and to investigate this phenomenon from different perspectives. The benefits of innovations are related to lower costs, improved efficiency, reduced risk, and better response to the customers’ needs due to new products, services or processes. On the other hand, new business models expose various risks, such as cyber risks, operational risks, regulatory risks, and others. Therefore, we believe that the entrepreneurial behavior and global mindset of decision-makers significantly contribute to the development of innovations, which benefit by closing the prevailing gap between developed and developing countries. Thus, this Special Issue contributes to closing the research gap in the literature by providing a platform for a scientific debate on innovation, internationalization and entrepreneurship, which would facilitate improving the resilience of businesses to future disruptions. Order Your Print Copy

Mathematics for Machine Learning
Mathematics for Machine Learning

Author: Marc Peter Deisenroth

Publisher: Cambridge University Press

Published: 2020-04-23

Total Pages: 392

ISBN-13: 1108569323

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The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Data-Driven Science and Engineering
Data-Driven Science and Engineering

Author: Steven L. Brunton

Publisher: Cambridge University Press

Published: 2022-05-05

Total Pages: 615

ISBN-13: 1009098489

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A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Encyclopedia of Computational Mechanics
Encyclopedia of Computational Mechanics

Author: Erwin Stein

Publisher:

Published: 2004

Total Pages: 870

ISBN-13:

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The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.

Reduced Basis Methods for Partial Differential Equations
Reduced Basis Methods for Partial Differential Equations

Author: Alfio Quarteroni

Publisher: Springer

Published: 2015-08-19

Total Pages: 305

ISBN-13: 3319154311

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This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit