Machine Learning Phases in Statistical Physics
Machine Learning Phases in Statistical Physics

Author: Qi Chen (Ph. D.)

Publisher:

Published: 2017

Total Pages: 126

ISBN-13:

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Conventionally, the study of phases in statistical mechan- ics is performed with the help of random sampling tools. Among the most powerful are Monte Carlo simulations consisting of a stochastic importance sampling over state space and evaluation of estimators for physical quantities. The ability of modern machine learning techniques to classify, identify, or in- terpret massive data sets provides a complementary paradigm to the above approach to analyze the exponentially large number of states in statistical physics. In this report, it is demonstrated by application on Ising-type models that deep learning has potential wide applications in solving many-body statis- tical physics problems. In application of supervised learning, we showed that the feed-forward neural network can identify phases and phase transitions in the ferromagnetic Ising model and the convolutional neural network (CNN) is extremely powerful in classifying T = 0 and T = ∞ phases in the Ising gauge model; In application of unsupervised learning, we illustrated that a deep auto-encoder constructed by stacked restricted Boltzmann machines (RBM) is closely related to the renormalization group (RG) method well understood in modern physics and our reconstruction of Ising spin configurations in the ferromagnetic Ising model is similar to the hand-written digits reconstruction.

Deep Learning and Physics
Deep Learning and Physics

Author: Akinori Tanaka

Publisher: Springer Nature

Published: 2021-03-24

Total Pages: 207

ISBN-13: 9813361085

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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.

Brain-Inspired Computing
Brain-Inspired Computing

Author: Katrin Amunts

Publisher: Springer Nature

Published: 2021-07-20

Total Pages: 159

ISBN-13: 3030824276

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This open access book constitutes revised selected papers from the 4th International Workshop on Brain-Inspired Computing, BrainComp 2019, held in Cetraro, Italy, in July 2019. The 11 papers presented in this volume were carefully reviewed and selected for inclusion in this book. They deal with research on brain atlasing, multi-scale models and simulation, HPC and data infra-structures for neuroscience as well as artificial and natural neural architectures.

Phase Transitions in Machine Learning
Phase Transitions in Machine Learning

Author: Lorenza Saitta

Publisher: Cambridge University Press

Published: 2011-06-16

Total Pages: 401

ISBN-13: 1139496530

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Phase transitions typically occur in combinatorial computational problems and have important consequences, especially with the current spread of statistical relational learning as well as sequence learning methodologies. In Phase Transitions in Machine Learning the authors begin by describing in detail this phenomenon, and the extensive experimental investigation that supports its presence. They then turn their attention to the possible implications and explore appropriate methods for tackling them. Weaving together fundamental aspects of computer science, statistical physics and machine learning, the book provides sufficient mathematics and physics background to make the subject intelligible to researchers in AI and other computer science communities. Open research issues are also discussed, suggesting promising directions for future research.

Geometric Structures of Statistical Physics, Information Geometry, and Learning
Geometric Structures of Statistical Physics, Information Geometry, and Learning

Author: Frédéric Barbaresco

Publisher: Springer Nature

Published: 2021-06-27

Total Pages: 466

ISBN-13: 3030779572

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Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.

Statistical Mechanics of Learning
Statistical Mechanics of Learning

Author: A. Engel

Publisher: Cambridge University Press

Published: 2001-03-29

Total Pages: 346

ISBN-13: 9780521774796

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Learning is one of the things that humans do naturally, and it has always been a challenge for us to understand the process. Nowadays this challenge has another dimension as we try to build machines that are able to learn and to undertake tasks such as datamining, image processing and pattern recognition. We can formulate a simple framework, artificial neural networks, in which learning from examples may be described and understood. The contribution to this subject made over the last decade by researchers applying the techniques of statistical mechanics is the subject of this book. The authors provide a coherent account of various important concepts and techniques that are currently only found scattered in papers, supplement this with background material in mathematics and physics and include many examples and exercises to make a book that can be used with courses, or for self-teaching, or as a handy reference.

From Statistical Physics to Statistical Inference and Back
From Statistical Physics to Statistical Inference and Back

Author: P. Grassberger

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 351

ISBN-13: 9401110689

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Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

The Statistical Physics of Data Assimilation and Machine Learning
The Statistical Physics of Data Assimilation and Machine Learning

Author: Henry D. I. Abarbanel

Publisher: Cambridge University Press

Published: 2022-02-17

Total Pages: 208

ISBN-13: 1009021702

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Data assimilation is a hugely important mathematical technique, relevant in fields as diverse as geophysics, data science, and neuroscience. This modern book provides an authoritative treatment of the field as it relates to several scientific disciplines, with a particular emphasis on recent developments from machine learning and its role in the optimisation of data assimilation. Underlying theory from statistical physics, such as path integrals and Monte Carlo methods, are developed in the text as a basis for data assimilation, and the author then explores examples from current multidisciplinary research such as the modelling of shallow water systems, ocean dynamics, and neuronal dynamics in the avian brain. The theory of data assimilation and machine learning is introduced in an accessible and unified manner, and the book is suitable for undergraduate and graduate students from science and engineering without specialized experience of statistical physics.

Molecular Networking
Molecular Networking

Author: Caroline Desgranges

Publisher: CRC Press

Published: 2024-01-29

Total Pages: 249

ISBN-13: 1003832431

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The book builds on the analogy between social groups and assemblies of molecules to introduce the concepts of statistical mechanics, machine learning and data science. Applying a data analytics approach to molecular systems, we show how individual (molecular) features and interactions between molecules, or "communication" processes, allow for the prediction of properties and collective behavior of molecular systems - just as polling and social networking shed light on the behavior of social groups. Applications to systems at the cutting-edge of research for biological, environmental, and energy applications are also presented. Key features: Draws on a data analytics approach of molecular systems Covers hot topics such as artificial intelligence and machine learning of molecular trends Contains applications to systems at the cutting-edge of research for biological, environmental and energy applications Discusses molecular simulation and links with other important, emerging techniques and trends in computational sciences and society Authors have a well-established track record and reputation in the field