Leonid Berlyand's Books

Mathematics of Deep Learning

An Introduction

By: Leonid Berlyand,Pierre-Emmanuel Jabin

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Mathematics of Deep Learning

An Introduction

By: Leonid Berlyand,Pierre-Emmanuel Jabin

The goal of this book is to provide a mathematical perspective on some key elements of the so-called deep neural networks (DNNs). Much of the interest in deep learning has focused on the implementation of DNN-based algorithms. Our hope is that this compact textbook will offer a complementary point of view that emphasizes the underlying mathematical ideas. We believe that a more foundational perspective will help to answer important questions that have only received empirical answers so far. The material is based on a one-semester course Introduction to Mathematics of Deep Learning" for senior undergraduate mathematics majors and first year graduate students in mathematics. Our goal is to introduce basic concepts from deep learning in a rigorous mathematical fashion, e.g introduce mathematical definitions of deep neural networks (DNNs), loss functions, the backpropagation algorithm, etc. We attempt to identify for each concept the simplest setting that minimizes technicalities but still contains the key mathematics.

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Page Count

666

Publisher

Walter de Gruyter GmbH & Co KG

Published Date

ISBN 10

3111025802

ISBN 13

9783111025803

Getting Acquainted with Homogenization and Multiscale

By: Leonid Berlyand,Volodymyr Rybalko

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Getting Acquainted with Homogenization and Multiscale

By: Leonid Berlyand,Volodymyr Rybalko

The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.

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Page Count

187

Publisher

Springer

Published Date

ISBN 10

303001777X

ISBN 13

9783030017774

Introduction to the Network Approximation Method for Materials Modeling

By: Leonid Berlyand,Alexander G. Kolpakov,Alexei Novikov

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Introduction to the Network Approximation Method for Materials Modeling

By: Leonid Berlyand,Alexander G. Kolpakov,Alexei Novikov

Introduces graduate students to the state of the art in this fast-developing field of applied mathematics.

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Page Count

259

Publisher

Cambridge University Press

Published Date

ISBN 10

110702823X

ISBN 13

9781107028234

Asymptotical Mechanics of Thin-Walled Structures

By: Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch

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Asymptotical Mechanics of Thin-Walled Structures

By: Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch

In this book a detailed and systematic treatment of asymptotic methods in the theory of plates and shells is presented. The main features of the book are the basic principles of asymptotics and their applications, traditional approaches such as regular and singular perturbations, as well as new approaches such as the composite equations approach. The book introduces the reader to the field of asymptotic simplification of the problems of the theory of plates and shells and will be useful as a handbook of methods of asymptotic integration. Providing a state-of-the-art review of asymptotic applications, this book will be useful as an introduction to the field for novices as well as a reference book for specialists.

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