Introduction To Tensor Network Methods

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Introduction to Tensor Network Methods

Author : Simone Montangero
Publisher : Springer
ISBN 13 : 3030014096
Total Pages : 172 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Introduction to Tensor Network Methods by : Simone Montangero

Download or read book Introduction to Tensor Network Methods written by Simone Montangero and published by Springer. This book was released on 2018-11-28 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.

Tensor Network Contractions

Author : Shi-Ju Ran
Publisher : Springer Nature
ISBN 13 : 3030344894
Total Pages : 160 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Tensor Network Contractions by : Shi-Ju Ran

Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Emergent Phenomena in Correlated Matter

Author : Eva Pavarini
Publisher : Forschungszentrum Jülich
ISBN 13 : 3893368841
Total Pages : 562 pages
Book Rating : 4.8/5 (933 download)

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Book Synopsis Emergent Phenomena in Correlated Matter by : Eva Pavarini

Download or read book Emergent Phenomena in Correlated Matter written by Eva Pavarini and published by Forschungszentrum Jülich. This book was released on 2013 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tensors: Geometry and Applications

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821869078
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tensors: Geometry and Applications by : J. M. Landsberg

Download or read book Tensors: Geometry and Applications written by J. M. Landsberg and published by American Mathematical Soc.. This book was released on 2011-12-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Tensor Spaces and Numerical Tensor Calculus

Author : Wolfgang Hackbusch
Publisher : Springer Nature
ISBN 13 : 3030355543
Total Pages : 605 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Tensor Spaces and Numerical Tensor Calculus by : Wolfgang Hackbusch

Download or read book Tensor Spaces and Numerical Tensor Calculus written by Wolfgang Hackbusch and published by Springer Nature. This book was released on 2019-12-16 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

Tensors for Data Processing

Author : Yipeng Liu
Publisher : Academic Press
ISBN 13 : 0323859658
Total Pages : 598 pages
Book Rating : 4.3/5 (238 download)

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Book Synopsis Tensors for Data Processing by : Yipeng Liu

Download or read book Tensors for Data Processing written by Yipeng Liu and published by Academic Press. This book was released on 2021-10-21 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors for Data Processing: Theory, Methods and Applications presents both classical and state-of-the-art methods on tensor computation for data processing, covering computation theories, processing methods, computing and engineering applications, with an emphasis on techniques for data processing. This reference is ideal for students, researchers and industry developers who want to understand and use tensor-based data processing theories and methods. As a higher-order generalization of a matrix, tensor-based processing can avoid multi-linear data structure loss that occurs in classical matrix-based data processing methods. This move from matrix to tensors is beneficial for many diverse application areas, including signal processing, computer science, acoustics, neuroscience, communication, medical engineering, seismology, psychometric, chemometrics, biometric, quantum physics and quantum chemistry. Provides a complete reference on classical and state-of-the-art tensor-based methods for data processing Includes a wide range of applications from different disciplines Gives guidance for their application

Tensor Networks for Dimensionality Reduction and Large-scale Optimization

Author : Andrzej Cichocki
Publisher :
ISBN 13 : 9781680832235
Total Pages : 180 pages
Book Rating : 4.8/5 (322 download)

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Book Synopsis Tensor Networks for Dimensionality Reduction and Large-scale Optimization by : Andrzej Cichocki

Download or read book Tensor Networks for Dimensionality Reduction and Large-scale Optimization written by Andrzej Cichocki and published by . This book was released on 2016 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern applications in engineering and data science are increasingly based on multidimensional data of exceedingly high volume, variety, and structural richness. However, standard machine learning algorithms typically scale exponentially with data volume and complexity of cross-modal couplings - the so called curse of dimensionality - which is prohibitive to the analysis of large-scale, multi-modal and multi-relational datasets. Given that such data are often efficiently represented as multiway arrays or tensors, it is therefore timely and valuable for the multidisciplinary machine learning and data analytic communities to review low-rank tensor decompositions and tensor networks as emerging tools for dimensionality reduction and large scale optimization problems. Our particular emphasis is on elucidating that, by virtue of the underlying low-rank approximations, tensor networks have the ability to alleviate the curse of dimensionality in a number of applied areas. In Part 1 of this monograph we provide innovative solutions to low-rank tensor network decompositions and easy to interpret graphical representations of the mathematical operations on tensor networks. Such a conceptual insight allows for seamless migration of ideas from the flat-view matrices to tensor network operations and vice versa, and provides a platform for further developments, practical applications, and non-Euclidean extensions. It also permits the introduction of various tensor network operations without an explicit notion of mathematical expressions, which may be beneficial for many research communities that do not directly rely on multilinear algebra. Our focus is on the Tucker and tensor train (TT) decompositions and their extensions, and on demonstrating the ability of tensor networks to provide linearly or even super-linearly (e.g., logarithmically) scalable solutions, as illustrated in detail in Part 2 of this monograph.

TensorFlow for Deep Learning

Author : Bharath Ramsundar
Publisher : "O'Reilly Media, Inc."
ISBN 13 : 1491980400
Total Pages : 256 pages
Book Rating : 4.4/5 (919 download)

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Book Synopsis TensorFlow for Deep Learning by : Bharath Ramsundar

Download or read book TensorFlow for Deep Learning written by Bharath Ramsundar and published by "O'Reilly Media, Inc.". This book was released on 2018-03-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn how to solve challenging machine learning problems with TensorFlow, Google’s revolutionary new software library for deep learning. If you have some background in basic linear algebra and calculus, this practical book introduces machine-learning fundamentals by showing you how to design systems capable of detecting objects in images, understanding text, analyzing video, and predicting the properties of potential medicines. TensorFlow for Deep Learning teaches concepts through practical examples and helps you build knowledge of deep learning foundations from the ground up. It’s ideal for practicing developers with experience designing software systems, and useful for scientists and other professionals familiar with scripting but not necessarily with designing learning algorithms. Learn TensorFlow fundamentals, including how to perform basic computation Build simple learning systems to understand their mathematical foundations Dive into fully connected deep networks used in thousands of applications Turn prototypes into high-quality models with hyperparameter optimization Process images with convolutional neural networks Handle natural language datasets with recurrent neural networks Use reinforcement learning to solve games such as tic-tac-toe Train deep networks with hardware including GPUs and tensor processing units

An Introduction to Neural Network Methods for Differential Equations

Author : Neha Yadav
Publisher : Springer
ISBN 13 : 9401798168
Total Pages : 114 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis An Introduction to Neural Network Methods for Differential Equations by : Neha Yadav

Download or read book An Introduction to Neural Network Methods for Differential Equations written by Neha Yadav and published by Springer. This book was released on 2015-02-26 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field. Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.

Graph Representation Learning

Author : William L. William L. Hamilton
Publisher : Springer Nature
ISBN 13 : 3031015886
Total Pages : 141 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Graph Representation Learning by : William L. William L. Hamilton

Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

An Introduction to Neural Networks

Author : Kevin Gurney
Publisher : CRC Press
ISBN 13 : 1482286998
Total Pages : 234 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis An Introduction to Neural Networks by : Kevin Gurney

Download or read book An Introduction to Neural Networks written by Kevin Gurney and published by CRC Press. This book was released on 2018-10-08 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though mathematical ideas underpin the study of neural networks, the author presents the fundamentals without the full mathematical apparatus. All aspects of the field are tackled, including artificial neurons as models of their real counterparts; the geometry of network action in pattern space; gradient descent methods, including back-propagation; associative memory and Hopfield nets; and self-organization and feature maps. The traditionally difficult topic of adaptive resonance theory is clarified within a hierarchical description of its operation. The book also includes several real-world examples to provide a concrete focus. This should enhance its appeal to those involved in the design, construction and management of networks in commercial environments and who wish to improve their understanding of network simulator packages. As a comprehensive and highly accessible introduction to one of the most important topics in cognitive and computer science, this volume should interest a wide range of readers, both students and professionals, in cognitive science, psychology, computer science and electrical engineering.

TensorFlow Machine Learning Cookbook

Author : Nick McClure
Publisher : Packt Publishing Ltd
ISBN 13 : 1786466309
Total Pages : 370 pages
Book Rating : 4.7/5 (864 download)

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Book Synopsis TensorFlow Machine Learning Cookbook by : Nick McClure

Download or read book TensorFlow Machine Learning Cookbook written by Nick McClure and published by Packt Publishing Ltd. This book was released on 2017-02-14 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explore machine learning concepts using the latest numerical computing library — TensorFlow — with the help of this comprehensive cookbook About This Book Your quick guide to implementing TensorFlow in your day-to-day machine learning activities Learn advanced techniques that bring more accuracy and speed to machine learning Upgrade your knowledge to the second generation of machine learning with this guide on TensorFlow Who This Book Is For This book is ideal for data scientists who are familiar with C++ or Python and perform machine learning activities on a day-to-day basis. Intermediate and advanced machine learning implementers who need a quick guide they can easily navigate will find it useful. What You Will Learn Become familiar with the basics of the TensorFlow machine learning library Get to know Linear Regression techniques with TensorFlow Learn SVMs with hands-on recipes Implement neural networks and improve predictions Apply NLP and sentiment analysis to your data Master CNN and RNN through practical recipes Take TensorFlow into production In Detail TensorFlow is an open source software library for Machine Intelligence. The independent recipes in this book will teach you how to use TensorFlow for complex data computations and will let you dig deeper and gain more insights into your data than ever before. You'll work through recipes on training models, model evaluation, sentiment analysis, regression analysis, clustering analysis, artificial neural networks, and deep learning – each using Google's machine learning library TensorFlow. This guide starts with the fundamentals of the TensorFlow library which includes variables, matrices, and various data sources. Moving ahead, you will get hands-on experience with Linear Regression techniques with TensorFlow. The next chapters cover important high-level concepts such as neural networks, CNN, RNN, and NLP. Once you are familiar and comfortable with the TensorFlow ecosystem, the last chapter will show you how to take it to production. Style and approach This book takes a recipe-based approach where every topic is explicated with the help of a real-world example.

Nonnegative Matrix and Tensor Factorizations

Author : Andrzej Cichocki
Publisher : John Wiley & Sons
ISBN 13 : 9780470747285
Total Pages : 500 pages
Book Rating : 4.7/5 (472 download)

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Book Synopsis Nonnegative Matrix and Tensor Factorizations by : Andrzej Cichocki

Download or read book Nonnegative Matrix and Tensor Factorizations written by Andrzej Cichocki and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF). This includes NMF’s various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD). NMF/NTF and their extensions are increasingly used as tools in signal and image processing, and data analysis, having garnered interest due to their capability to provide new insights and relevant information about the complex latent relationships in experimental data sets. It is suggested that NMF can provide meaningful components with physical interpretations; for example, in bioinformatics, NMF and its extensions have been successfully applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining. As such, the authors focus on the algorithms that are most useful in practice, looking at the fastest, most robust, and suitable for large-scale models. Key features: Acts as a single source reference guide to NMF, collating information that is widely dispersed in current literature, including the authors’ own recently developed techniques in the subject area. Uses generalized cost functions such as Bregman, Alpha and Beta divergences, to present practical implementations of several types of robust algorithms, in particular Multiplicative, Alternating Least Squares, Projected Gradient and Quasi Newton algorithms. Provides a comparative analysis of the different methods in order to identify approximation error and complexity. Includes pseudo codes and optimized MATLAB source codes for almost all algorithms presented in the book. The increasing interest in nonnegative matrix and tensor factorizations, as well as decompositions and sparse representation of data, will ensure that this book is essential reading for engineers, scientists, researchers, industry practitioners and graduate students across signal and image processing; neuroscience; data mining and data analysis; computer science; bioinformatics; speech processing; biomedical engineering; and multimedia.

A Guide to ALGOL Programming

Author : Daniel D. McCracken
Publisher :
ISBN 13 :
Total Pages : 124 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis A Guide to ALGOL Programming by : Daniel D. McCracken

Download or read book A Guide to ALGOL Programming written by Daniel D. McCracken and published by . This book was released on 1962 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book covering ALGOL 60. An early general-audience manual on the language.

Crystal Plasticity Finite Element Methods

Author : Franz Roters
Publisher : John Wiley & Sons
ISBN 13 : 3527642099
Total Pages : 188 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Crystal Plasticity Finite Element Methods by : Franz Roters

Download or read book Crystal Plasticity Finite Element Methods written by Franz Roters and published by John Wiley & Sons. This book was released on 2011-08-04 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the leading experts in computational materials science, this handy reference concisely reviews the most important aspects of plasticity modeling: constitutive laws, phase transformations, texture methods, continuum approaches and damage mechanisms. As a result, it provides the knowledge needed to avoid failures in critical systems udner mechanical load. With its various application examples to micro- and macrostructure mechanics, this is an invaluable resource for mechanical engineers as well as for researchers wanting to improve on this method and extend its outreach.

Sustainable Interdependent Networks II

Author : M. Hadi Amini
Publisher : Springer
ISBN 13 : 3319989235
Total Pages : 304 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Sustainable Interdependent Networks II by : M. Hadi Amini

Download or read book Sustainable Interdependent Networks II written by M. Hadi Amini and published by Springer. This book was released on 2018-12-11 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book paves the way for researchers working on the sustainable interdependent networks spread over the fields of computer science, electrical engineering, and smart infrastructures. It provides the readers with a comprehensive insight to understand an in-depth big picture of smart cities as a thorough example of interdependent large-scale networks in both theory and application aspects. The contributors specify the importance and position of the interdependent networks in the context of developing the sustainable smart cities and provide a comprehensive investigation of recently developed optimization methods for large-scale networks. There has been an emerging concern regarding the optimal operation of power and transportation networks. In the second volume of Sustainable Interdependent Networks book, we focus on the interdependencies of these two networks, optimization methods to deal with the computational complexity of them, and their role in future smart cities. We further investigate other networks, such as communication networks, that indirectly affect the operation of power and transportation networks. Our reliance on these networks as global platforms for sustainable development has led to the need for developing novel means to deal with arising issues. The considerable scale of such networks, due to the large number of buses in smart power grids and the increasing number of electric vehicles in transportation networks, brings a large variety of computational complexity and optimization challenges. Although the independent optimization of these networks lead to locally optimum operation points, there is an exigent need to move towards obtaining the globally-optimum operation point of such networks while satisfying the constraints of each network properly. The book is suitable for senior undergraduate students, graduate students interested in research in multidisciplinary areas related to future sustainable networks, and the researchers working in the related areas. It also covers the application of interdependent networks which makes it a perfect source of study for audience out of academia to obtain a general insight of interdependent networks.

Introduction to Non-linear Systems

Author : J. Berry
Publisher : Hodder Education
ISBN 13 : 9780340677001
Total Pages : 212 pages
Book Rating : 4.6/5 (77 download)

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Book Synopsis Introduction to Non-linear Systems by : J. Berry

Download or read book Introduction to Non-linear Systems written by J. Berry and published by Hodder Education. This book was released on 1996 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the popularization of chaos theory, great interest has been generated in non-linear dynamical systems. This text presents an introduction to the basic mathematical concepts and techniques needed to describe and analyze these, aimed at students who have taken a first course in calculus. After reviewing the basic ideas of differential equations, matrix algebra and iteration methods, first and second order continuous systems are discussed. Chapter Four investigates discrete systems and the final chapter is a collection of investigations that can be explored as more open ended tasks.