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: 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: Shaun Forth
Publisher: Springer Science & Business Media
ISBN: 3642300235
Category : Mathematics
Languages : en
Pages : 356

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Book Description
The proceedings represent the state of knowledge in the area of algorithmic differentiation (AD). The 31 contributed papers presented at the AD2012 conference cover the application of AD to many areas in science and engineering as well as aspects of AD theory and its implementation in tools. For all papers the referees, selected from the program committee and the greater community, as well as the editors have emphasized accessibility of the presented ideas also to non-AD experts. In the AD tools arena new implementations are introduced covering, for example, Java and graphical modeling environments or join the set of existing tools for Fortran. New developments in AD algorithms target the efficiency of matrix-operation derivatives, detection and exploitation of sparsity, partial separability, the treatment of nonsmooth functions, and other high-level mathematical aspects of the numerical computations to be differentiated. Applications stem from the Earth sciences, nuclear engineering, fluid dynamics, and chemistry, to name just a few. In many cases the applications in a given area of science or engineering share characteristics that require specific approaches to enable AD capabilities or provide an opportunity for efficiency gains in the derivative computation. The description of these characteristics and of the techniques for successfully using AD should make the proceedings a valuable source of information for users of AD tools.

Author: Thomas F. Coleman
Publisher: SIAM
ISBN: 1611974356
Category : Science
Languages : en
Pages : 114

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Book Description
The calculation of partial derivatives is a fundamental need in scientific computing. Automatic differentiation (AD) can be applied straightforwardly to obtain all necessary partial derivatives (usually first and, possibly, second derivatives) regardless of a code?s complexity. However, the space and time efficiency of AD can be dramatically improved?sometimes transforming a problem from intractable to highly feasible?if inherent problem structure is used to apply AD in a judicious manner. Automatic Differentiation in MATLAB using ADMAT with Applications discusses the efficient use of AD to solve real problems, especially multidimensional zero-finding and optimization, in the MATLAB environment. This book is concerned with the determination of the first and second derivatives in the context of solving scientific computing problems with an emphasis on optimization and solutions to nonlinear systems. The authors focus on the application rather than the implementation of AD, solve real nonlinear problems with high performance by exploiting the problem structure in the application of AD, and provide many easy to understand applications, examples, and MATLAB templates.

Author: Nicholas N. Olenev
Publisher: Springer Nature
ISBN: 3030927113
Category : Mathematics
Languages : en
Pages : 291

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Book Description
This book constitutes the refereed proceedings of the 12th International Conference on Optimization and Applications, OPTIMA 2021, held in Petrovac, Montenegro, in September - October 2021. Due to the COVID-19 pandemic the conference was partially held online. The 19 revised full papers presented were carefully reviewed and selected from 38 submissions. The papers are organized in topical sections on ​​mathematical programming; global optimization; stochastic optimization; optimal control; mathematical economics; optimization in data analysis; applications.

Author: Mats G. Larson
Publisher: Springer Science & Business Media
ISBN: 3642332870
Category : Computers
Languages : en
Pages : 403

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Book Description
This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

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: Dimitrios V. Papavassiliou
Publisher: Elsevier
ISBN: 0128176830
Category : Technology & Engineering
Languages : en
Pages : 370

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Book Description
Nanocomposites with Carbon-based nanofillers (e.g., carbon nanotubes, graphene sheets and nanoribbons etc.) form a class of extremely promising materials for thermal applications. In addition to exceptional material properties, the thermal conductivity of the carbon-based nanofillers can be higher than any other known material, suggesting the possibility to engineer nanocomposites that are both lightweight and durable, and have unique thermal properties. This potential is hindered by thermal boundary resistance (TBR) to heat transfer at the interface between nanoinclusions and the matrix, and by the difficulty to control the dispersion pattern and the orientation of the nanoinclusions. Thermal Behaviour and Applications of Carbon-Based Nanomaterials: Theory, Methods and Applications explores heat transfer in nanocomposites, discusses techniques predicting and modeling the thermal behavior of carbon nanocomposites at different scales, and methods for engineering applications of nanofluidics and heat transfer. The chapters combine theoretical explanation, experimental methods and computational analysis to show how carbon-based nanomaterials are being used to optimise heat transfer. The applications-focused emphasis of this book makes it a valuable resource for materials scientists and engineers who want to learn more about nanoscale heat transfer. Offers an informed overview of how carbon nanomaterials are currently used for nanoscale heat transfer Discusses the major applications of carbon nanomaterials for heat transfer in a variety of industry sectors Details the major computational methods for the analysis of the thermal properties of carbon nanomaterials

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

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Book Description

Author: Alexander A. Kokhanovsky
Publisher: Springer Science & Business Media
ISBN: 354074276X
Category : Science
Languages : en
Pages : 516

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Book Description
This fourth volume of Light Scattering Reviews is composed of three parts. The ?rstpartisconcernedwiththeoreticalandexperimentalstudiesofsinglelightsc- tering by small nonspherical particles. Light scattering by small particles such as, for instance, droplets in the terrestrial clouds is a well understood area of physical optics. On the other hand, exact theoretical calculations of light scattering p- terns for most of nonspherical and irregularly shaped particles can be performed only for the restricted values of the size parameter, which is proportional to the ratio of the characteristic size of the particle to the wavelength?. For the large nonspherical particles, approximations are used (e. g. , ray optics). The exact th- retical techniques such as the T-matrix method cannot be used for extremely large particles, such as those in ice clouds, because then the size parameter in the v- iblex=2?a/???,wherea is the characteristic size (radius for spheres), and the associated numerical codes become unstable and produce wrong answers. Yet another problem is due to the fact that particles in many turbid media (e. g. , dust clouds) cannot be characterized by a single shape. Often, refractive indices also vary. Because of problems with theoretical calculations, experimental (i. e. , la- ratory) investigations are important for the characterization and understanding of the optical properties of such types of particles. The ?rst paper in this volume, written by B. Gustafson, is aimed at the descr- tionofscaledanalogueexperimentsinelectromagneticscattering.