Introduction To Tensor Network Methods

Author : Simone Montangero
Publisher : Springer
Page : 172 pages
File Size : 49,6 Mb
Release : 2018-11-28
Category : Science
ISBN : 9783030014094

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Introduction to Tensor Network Methods by Simone Montangero Pdf

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.

Author : Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein
Publisher : Springer Nature
Page : 160 pages
File Size : 50,9 Mb
Release : 2020-01-27
Category : Science
ISBN : 9783030344894

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Tensor Network Contractions by Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein Pdf

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.

Author : Eva Pavarini,Erik Koch,Ulrich Schollwöck
Publisher : Forschungszentrum Jülich
Page : 562 pages
File Size : 53,7 Mb
Release : 2013
Category : Electronic
ISBN : 9783893368846

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Emergent Phenomena in Correlated Matter by Eva Pavarini,Erik Koch,Ulrich Schollwöck Pdf

Author : Mukund Rangamani,Tadashi Takayanagi
Publisher : Springer
Page : 246 pages
File Size : 40,7 Mb
Release : 2017-05-08
Category : Science
ISBN : 9783319525730

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Holographic Entanglement Entropy by Mukund Rangamani,Tadashi Takayanagi Pdf

This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.

Author : Andrzej Cichocki,Namgil Lee,Ivan Oseledets,Anh-Huy Phan,Qibin Zhao,Danilo P. Mandic
Publisher : Unknown
Page : 196 pages
File Size : 49,7 Mb
Release : 2016-12-19
Category : Computers
ISBN : 1680832220

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Tensor Networks for Dimensionality Reduction and Large-Scale Optimization by Andrzej Cichocki,Namgil Lee,Ivan Oseledets,Anh-Huy Phan,Qibin Zhao,Danilo P. Mandic Pdf

This monograph provides a systematic and example-rich guide to the basic properties and applications of tensor network methodologies, and demonstrates their promise as a tool for the analysis of extreme-scale multidimensional data. It demonstrates the ability of tensor networks to provide linearly or even super-linearly, scalable solutions.

Author : Yipeng Liu
Publisher : Academic Press
Page : 598 pages
File Size : 45,5 Mb
Release : 2021-10-21
Category : Technology & Engineering
ISBN : 9780323859653

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Tensors for Data Processing by Yipeng Liu Pdf

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

Author : William L. William L. Hamilton
Publisher : Springer Nature
Page : 141 pages
File Size : 41,9 Mb
Release : 2022-06-01
Category : Computers
ISBN : 9783031015885

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Graph Representation Learning by William L. William L. Hamilton Pdf

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.

Author : Bharath Ramsundar,Reza Bosagh Zadeh
Publisher : "O'Reilly Media, Inc."
Page : 256 pages
File Size : 54,9 Mb
Release : 2018-03-01
Category : Computers
ISBN : 9781491980408

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TensorFlow for Deep Learning by Bharath Ramsundar,Reza Bosagh Zadeh Pdf

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

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 40,7 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780821869079

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Tensors: Geometry and Applications by J. M. Landsberg Pdf

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.

Author : Neha Yadav,Anupam Yadav,Manoj Kumar
Publisher : Springer
Page : 114 pages
File Size : 47,6 Mb
Release : 2015-02-26
Category : Mathematics
ISBN : 9789401798167

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An Introduction to Neural Network Methods for Differential Equations by Neha Yadav,Anupam Yadav,Manoj Kumar Pdf

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.

Author : Johan A.K. Suykens,Joos P.L. Vandewalle
Publisher : Springer Science & Business Media
Page : 265 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461557036

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Nonlinear Modeling by Johan A.K. Suykens,Joos P.L. Vandewalle Pdf

Nonlinear Modeling: Advanced Black-Box Techniques discusses methods on Neural nets and related model structures for nonlinear system identification; Enhanced multi-stream Kalman filter training for recurrent networks; The support vector method of function estimation; Parametric density estimation for the classification of acoustic feature vectors in speech recognition; Wavelet-based modeling of nonlinear systems; Nonlinear identification based on fuzzy models; Statistical learning in control and matrix theory; Nonlinear time-series analysis. It also contains the results of the K.U. Leuven time series prediction competition, held within the framework of an international workshop at the K.U. Leuven, Belgium in July 1998.

Author : Leticia González,Roland Lindh
Publisher : John Wiley & Sons
Page : 52 pages
File Size : 41,5 Mb
Release : 2021-02-01
Category : Science
ISBN : 9781119417750

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Quantum Chemistry and Dynamics of Excited States by Leticia González,Roland Lindh Pdf

An introduction to the rapidly evolving methodology of electronic excited states For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry. An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems. Readers will learn: ● Essential theoretical techniques to describe the properties and dynamics of chemical systems ● Electronic Structure methods for stationary calculations ● Methods for electronic excited states from both a quantum chemical and time-dependent point of view ● A breakdown of the most recent developments in the past 30 years For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.

Author : N. V. Balasubramanian,J. W. Lynn,D. P. Sen Gupta
Publisher : Elsevier
Page : 200 pages
File Size : 52,7 Mb
Release : 2013-10-22
Category : Technology & Engineering
ISBN : 9781483103242

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Differential Forms on Electromagnetic Networks by N. V. Balasubramanian,J. W. Lynn,D. P. Sen Gupta Pdf

Differential Forms on Electromagnetic Networks deals with the use of combinatorial techniques in electrical circuit, machine analysis, and the relationship between circuit quantities and electromagnetic fields. The monograph is also an introduction to the organization of field equations by the methods of differential forms. The book covers topics such as algebraic structural relations in an electric circuit; mesh and node-pair analysis; exterior differential structures; generalized Stoke's theorem and tensor analysis; and Maxwell's electromagnetic equation. Also covered in the book are the applications for the field network model; oscillatory behavior of electric machines; and the rotation tensor in machine differential structures. The text is recommended for engineering students who would like to be familiarized with electromagnetic networks and its related topics.

Author : John Watrous
Publisher : Unknown
Page : 599 pages
File Size : 50,7 Mb
Release : 2018-04-26
Category : Computers
ISBN : 9781107180567

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The Theory of Quantum Information by John Watrous Pdf

Formal development of the mathematical theory of quantum information with clear proofs and exercises. For graduate students and researchers.

Author : Delip Rao,Brian McMahan
Publisher : O'Reilly Media
Page : 256 pages
File Size : 45,7 Mb
Release : 2019-01-22
Category : Computers
ISBN : 9781491978207

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Natural Language Processing with PyTorch by Delip Rao,Brian McMahan Pdf

Natural Language Processing (NLP) provides boundless opportunities for solving problems in artificial intelligence, making products such as Amazon Alexa and Google Translate possible. If you’re a developer or data scientist new to NLP and deep learning, this practical guide shows you how to apply these methods using PyTorch, a Python-based deep learning library. Authors Delip Rao and Brian McMahon provide you with a solid grounding in NLP and deep learning algorithms and demonstrate how to use PyTorch to build applications involving rich representations of text specific to the problems you face. Each chapter includes several code examples and illustrations. Explore computational graphs and the supervised learning paradigm Master the basics of the PyTorch optimized tensor manipulation library Get an overview of traditional NLP concepts and methods Learn the basic ideas involved in building neural networks Use embeddings to represent words, sentences, documents, and other features Explore sequence prediction and generate sequence-to-sequence models Learn design patterns for building production NLP systems