Computational Mechanics With Deep Learning

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Computational Mechanics With Neural Networks

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Author : Genki Yagawa
language : en
Publisher: Springer Nature
Release Date : 2021-02-26

Computational Mechanics With Neural Networks written by Genki Yagawa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-26 with Technology & Engineering categories.

This book shows how neural networks are applied to computational mechanics. Part I presents the fundamentals of neural networks and other machine learning method in computational mechanics. Part II highlights the applications of neural networks to a variety of problems of computational mechanics. The final chapter gives perspectives to the applications of the deep learning to computational mechanics.

Computational Mechanics With Deep Learning

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Author : Genki Yagawa
language : en
Publisher: Springer Nature
Release Date : 2022-10-31

Computational Mechanics With Deep Learning written by Genki Yagawa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-31 with Technology & Engineering categories.

This book is intended for students, engineers, and researchers interested in both computational mechanics and deep learning. It presents the mathematical and computational foundations of Deep Learning with detailed mathematical formulas in an easy-to-understand manner. It also discusses various applications of Deep Learning in Computational Mechanics, with detailed explanations of the Computational Mechanics fundamentals selected there. Sample programs are included for the reader to try out in practice. This book is therefore useful for a wide range of readers interested in computational mechanics and deep learning.

Deep Learning In Computational Mechanics

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Author : Stefan Kollmannsberger
language : en
Publisher: Springer Nature
Release Date : 2021-08-05

Deep Learning In Computational Mechanics written by Stefan Kollmannsberger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-05 with Technology & Engineering categories.

This book provides a first course on deep learning in computational mechanics. The book starts with a short introduction to machine learning’s fundamental concepts before neural networks are explained thoroughly. It then provides an overview of current topics in physics and engineering, setting the stage for the book’s main topics: physics-informed neural networks and the deep energy method. The idea of the book is to provide the basic concepts in a mathematically sound manner and yet to stay as simple as possible. To achieve this goal, mostly one-dimensional examples are investigated, such as approximating functions by neural networks or the simulation of the temperature’s evolution in a one-dimensional bar. Each chapter contains examples and exercises which are either solved analytically or in PyTorch, an open-source machine learning framework for python.

Machine Learning Low Rank Approximations And Reduced Order Modeling In Computational Mechanics

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Author : Felix Fritzen
language : en
Publisher: MDPI
Release Date : 2019-09-18

Machine Learning Low Rank Approximations And Reduced Order Modeling In Computational Mechanics written by Felix Fritzen and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-18 with Technology & Engineering categories.

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.

Tensor Voting

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Author : Philippos Mordohai
language : en
Publisher: Springer Nature
Release Date : 2022-06-01

Tensor Voting written by Philippos Mordohai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Technology & Engineering categories.

This lecture presents research on a general framework for perceptual organization that was conducted mainly at the Institute for Robotics and Intelligent Systems of the University of Southern California. It is not written as a historical recount of the work, since the sequence of the presentation is not in chronological order. It aims at presenting an approach to a wide range of problems in computer vision and machine learning that is data-driven, local and requires a minimal number of assumptions. The tensor voting framework combines these properties and provides a unified perceptual organization methodology applicable in situations that may seem heterogeneous initially. We show how several problems can be posed as the organization of the inputs into salient perceptual structures, which are inferred via tensor voting. The work presented here extends the original tensor voting framework with the addition of boundary inference capabilities; a novel re-formulation of the framework applicable to high-dimensional spaces and the development of algorithms for computer vision and machine learning problems. We show complete analysis for some problems, while we briefly outline our approach for other applications and provide pointers to relevant sources.

Machine Learning Low Rank Approximations And Reduced Order Modeling In Computational Mechanics

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Author : Felix Fritzen
language : en
Publisher:
Release Date : 2019

Machine Learning Low Rank Approximations And Reduced Order Modeling In Computational Mechanics written by Felix Fritzen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Electronic books categories.

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.

Deep Learning And Physics

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Author : Akinori Tanaka
language : en
Publisher: Springer Nature
Release Date : 2021-02-20

Deep Learning And Physics written by Akinori Tanaka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-20 with Science categories.

What is deep learning for those who study physics? Is it completely different from physics? Or is it similar? In recent years, machine learning, including deep learning, has begun to be used in various physics studies. Why is that? Is knowing physics useful in machine learning? Conversely, is knowing machine learning useful in physics? This book is devoted to answers of these questions. Starting with basic ideas of physics, neural networks are derived naturally. And you can learn the concepts of deep learning through the words of physics. In fact, the foundation of machine learning can be attributed to physical concepts. Hamiltonians that determine physical systems characterize various machine learning structures. Statistical physics given by Hamiltonians defines machine learning by neural networks. Furthermore, solving inverse problems in physics through machine learning and generalization essentially provides progress and even revolutions in physics. For these reasons, in recent years interdisciplinary research in machine learning and physics has been expanding dramatically. This book is written for anyone who wants to learn, understand, and apply the relationship between deep learning/machine learning and physics. All that is needed to read this book are the basic concepts in physics: energy and Hamiltonians. The concepts of statistical mechanics and the bracket notation of quantum mechanics, which are explained in columns, are used to explain deep learning frameworks. We encourage you to explore this new active field of machine learning and physics, with this book as a map of the continent to be explored.

Data Driven Science And Engineering

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Author : Steven L. Brunton
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-05

Data Driven Science And Engineering written by Steven L. Brunton and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-05 with Computers categories.

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

The Principles Of Deep Learning Theory

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Author : Daniel A. Roberts
language : en
Publisher: Cambridge University Press
Release Date : 2022-05-26

The Principles Of Deep Learning Theory written by Daniel A. Roberts and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-26 with Computers categories.

This volume develops an effective theory approach to understanding deep neural networks of practical relevance.

Statistical Mechanics Of Neural Networks

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Author : Haiping Huang
language : en
Publisher: Springer Nature
Release Date : 2022-01-04

Statistical Mechanics Of Neural Networks written by Haiping Huang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Science categories.

This book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variational methods, the dynamical mean-field theory, unsupervised learning, associative memory models, perceptron models, the chaos theory of recurrent neural networks, and eigen-spectrums of neural networks, walking new learners through the theories and must-have skillsets to understand and use neural networks. The book focuses on quantitative frameworks of neural network models where the underlying mechanisms can be precisely isolated by physics of mathematical beauty and theoretical predictions. It is a good reference for students, researchers, and practitioners in the area of neural networks.