Automatic Differentiation Applications Theory And Implementations
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Automatic Differentiation: Applications, Theory, and Implementations by H. Martin Bücker,George Corliss,Paul Hovland,Uwe Naumann,Boyana Norris Pdf
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.
Advances in Automatic Differentiation by Christian H. Bischof,H. Martin Bücker,Paul Hovland,Uwe Naumann,Jean Utke Pdf
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.
Recent Advances in Algorithmic Differentiation by Shaun Forth,Paul Hovland,Eric Phipps,Jean Utke,Andrea Walther Pdf
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.
Evaluating Derivatives by Andreas Griewank,Andrea Walther Pdf
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.
Advances in Optimization and Applications by Nicholas N. Olenev,Yuri G. Evtushenko,Milojica Jaćimović,Michael Khachay,Vlasta Malkova Pdf
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.
Algorithmic Differentiation in Finance Explained by Marc Henrard Pdf
This book provides the first practical guide to the function and implementation of algorithmic differentiation in finance. Written in a highly accessible way, Algorithmic Differentiation Explained will take readers through all the major applications of AD in the derivatives setting with a focus on implementation. Algorithmic Differentiation (AD) has been popular in engineering and computer science, in areas such as fluid dynamics and data assimilation for many years. Over the last decade, it has been increasingly (and successfully) applied to financial risk management, where it provides an efficient way to obtain financial instrument price derivatives with respect to the data inputs. Calculating derivatives exposure across a portfolio is no simple task. It requires many complex calculations and a large amount of computer power, which in prohibitively expensive and can be time consuming. Algorithmic differentiation techniques can be very successfully in computing Greeks and sensitivities of a portfolio with machine precision. Written by a leading practitioner who works and programmes AD, it offers a practical analysis of all the major applications of AD in the derivatives setting and guides the reader towards implementation. Open source code of the examples is provided with the book, with which readers can experiment and perform their own test scenarios without writing the related code themselves.
The Finite Element Method: Theory, Implementation, and Applications by Mats G. Larson,Fredrik Bengzon Pdf
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.
Automatic Differentiation in MATLAB Using ADMAT with Applications by Thomas F. Coleman,Wei Xu Pdf
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 Applicationsödiscusses 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.ö
Thermal Behaviour and Applications of Carbon-Based Nanomaterials by Dimitrios V. Papavassiliou,Hai M. Duong,Feng Gong Pdf
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
Automatic Differentiation of Algorithms by George Corliss,Christele Faure,Andreas Griewank,Laurent Hascoet,Uwe Naumann Pdf
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.
Mathematical Software - ICMS 2006 by Andres Iglesias,Nobuki Takayama Pdf
This book constitutes the refereed proceedings of the Second International Congress on Mathematical Software, ICMS 2006. The book presents 45 revised full papers, carefully reviewed and selected for presentation. The papers are organized in topical sections on new developments in computer algebra packages, interfacing computer algebra in mathematical visualization, software for algebraic geometry and related topics, number-theoretical software, methods in computational number theory, free software for computer algebra, and general issues.
Computational Techniques And Applications - Proceedings Of The Sixth Biennial Conference by Henry J Gardner,David Singleton,David Stewart Pdf
This volume contains papers on computational mathematics, development, implementation, and application of numerical algorithms, the development and application of computational systems, and numerical modelling. Also featured are reports on applications of advanced computer architectures and innovative visualisation techniques. It will be a help for developers and implementors of computational methods who wish to find out more about the work of those applying the technology to problems in engineering and science, and vice versa.
Light Scattering Reviews 4 by Alexander A. Kokhanovsky Pdf
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.
