Automatic Differentiation: Applications, Theory, and Implementations PDF Download

Author: H. Martin Bücker
Publisher: Springer Science & Business Media
ISBN: 3540284389
Category : Computers
Languages : en
Pages : 370

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Book Description
Covers the state of the art in automatic differentiation theory and practice. Intended for computational scientists and engineers, this book aims to provide insight into effective strategies for using automatic differentiation for design optimization, sensitivity analysis, and uncertainty quantification.

Author: Uwe Naumann
Publisher: SIAM
ISBN: 9781611972078
Category : Mathematics
Languages : en
Pages : 358

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Book Description
This is the first entry-level book on algorithmic (also known as automatic) differentiation (AD), providing fundamental rules for the generation of first- and higher-order tangent-linear and adjoint code. The author covers the mathematical underpinnings as well as how to apply these observations to real-world numerical simulation programs. Readers will find: examples and exercises, including hints to solutions; the prototype AD tools dco and dcc for use with the examples and exercises; first- and higher-order tangent-linear and adjoint modes for a limited subset of C/C++, provided by the derivative code compiler dcc; a supplementary website containing sources of all software discussed in the book, additional exercises and comments on their solutions (growing over the coming years), links to other sites on AD, and errata.

Author: Andreas Griewank
Publisher: SIAM
ISBN: 0898716594
Category : Mathematics
Languages : en
Pages : 448

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Book Description
This title is a comprehensive treatment of algorithmic, or automatic, differentiation. The second edition covers recent developments in applications and theory, including an elegant NP completeness argument and an introduction to scarcity.

Author: Christian H. Bischof
Publisher: Springer Science & Business Media
ISBN: 3540689427
Category : Computers
Languages : en
Pages : 366

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Book Description
The Fifth International Conference on Automatic Differentiation held from August 11 to 15, 2008 in Bonn, Germany, is the most recent one in a series that began in Breckenridge, USA, in 1991 and continued in Santa Fe, USA, in 1996, Nice, France, in 2000 and Chicago, USA, in 2004. The 31 papers included in these proceedings re?ect the state of the art in automatic differentiation (AD) with respect to theory, applications, and tool development. Overall, 53 authors from institutions in 9 countries contributed, demonstrating the worldwide acceptance of AD technology in computational science. Recently it was shown that the problem underlying AD is indeed NP-hard, f- mally proving the inherently challenging nature of this technology. So, most likely, no deterministic “silver bullet” polynomial algorithm can be devised that delivers optimum performance for general codes. In this context, the exploitation of doma- speci?c structural information is a driving issue in advancing practical AD tool and algorithm development. This trend is prominently re?ected in many of the pub- cations in this volume, not only in a better understanding of the interplay of AD and certain mathematical paradigms, but in particular in the use of hierarchical AD approaches that judiciously employ general AD techniques in application-speci?c - gorithmic harnesses. In this context, the understanding of structures such as sparsity of derivatives, or generalizations of this concept like scarcity, plays a critical role, in particular for higher derivative computations.

Author: H. L. Lukas
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 342

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Book Description
Phase diagrams are used in materials research and engineering to understand the interrelationship between composition, microstructure and process conditions. In complex systems, computational methods such as CALPHAD are employed to model thermodynamic properties for each phase and simulate multicomponent phase behavior. Written by recognized experts in the field, this is the first introductory guide to the CALPHAD method, providing a theoretical and practical approach. Building on core thermodynamic principles, this book applies crystallography, first principles methods and experimental data to computational phase behavior modeling using the CALPHAD method. With a chapter dedicated to creating thermodynamic databases, the reader will be confident in assessing, optimizing and validating complex thermodynamic systems alongside database construction and manipulation. Several case studies put the methods into a practical context, making this suitable for use on advanced materials design and engineering courses and an invaluable reference to those using thermodynamic data in their research or simulations.

Author: George Corliss
Publisher: Springer Science & Business Media
ISBN: 1461300754
Category : Computers
Languages : en
Pages : 431

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Book Description
A survey book focusing on the key relationships and synergies between automatic differentiation (AD) tools and other software tools, such as compilers and parallelizers, as well as their applications. The key objective is to survey the field and present the recent developments. In doing so the topics covered shed light on a variety of perspectives. They reflect the mathematical aspects, such as the differentiation of iterative processes, and the analysis of nonsmooth code. They cover the scientific programming aspects, such as the use of adjoints in optimization and the propagation of rounding errors. They also cover "implementation" problems.

Author: Louis B. Rall
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 194

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Book Description

Author: Masao Iri
Publisher: Springer
ISBN:
Category : Business & Economics
Languages : en
Pages : 396

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Book Description

Author: Marc Peter Deisenroth
Publisher: Cambridge University Press
ISBN: 1108569323
Category : Computers
Languages : en
Pages : 392

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Book Description
The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Author: Lynn Harold Loomis
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category : Mathematics
Languages : en
Pages : 595

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Book Description
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.