Automatic Differentiation of Algorithms: From Simulation to Optimization

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George Corliss, Christele Faure, Andreas Griewank, Laurent Hascoet, Uwe Naumann
Springer Science & Business Media, Jan 8, 2002 - Computers - 432 pages
Automatic Differentiation (AD) is a maturing computational technology and has become a mainstream tool used by practicing scientists and computer engineers. The rapid advance of hardware computing power and AD tools has enabled practitioners to quickly generate derivative-enhanced versions of their code for a broad range of applications in applied research and development. "Automatic Differentiation of Algorithms" provides a comprehensive and authoritative survey of all recent developments, new techniques, and tools for AD use. The book covers all aspects of the subject: mathematics, scientific programming ( i.e., use of adjoints in optimization) and implementation (i.e., memory management problems). A strong theme of the book is the relationships between AD tools and other software tools, such as compilers and parallelizers. A rich variety of significant applications are presented as well, including optimum-shape design problems, for which AD offers more efficient tools and techniques. Topics and features: * helpful introductory AD survey chapter for brief overview of the field *extensive applications chapters, i.e., for circuit simulation, optimization and optimal-control shape design, structural mechanics, and multibody dynamical systems modeling *comprehensive bibliography for all current literature and results for the field *performance issues *optimal control sensitivity analysis *AD use with object oriented software tool kits The book is an ideal and accessible survey of recent developments and applications of AD tools and techniques for a broad scientific computing and computer engineering readership. Practitioners, professionals, and advanced graduates working in AD development will find the book a useful reference and essential resource for their work.
 

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Contents

Difierentiation Methods for Industrial Strength Problems
3
AD Tools in Optimization Software
25
Using Automatic Differentiation for SecondOrder
35
Performance Issues in Automatic Differentiation
51
A Case Study of Computational Differentiation
69
Automatic Differentiation for Modern Nonlinear
83
Electron Paramagnetic Resonance Optimization
99
Continuous Optimal Control Sensitivity Analysis
109
A Parallel Hierarchical Approach for Automatic
231
New Results on Program Reversals
237
Elimination Techniques for Cheap J acobians
247
AD Tools and Prospects for Optimal AD
255
Reducing the Number of AD Passes for Computing
263
Verifying J acobian Sparsity
271
Recomputations in Reverse Mode AD
283
Minimizing the Tape Size
293

Application of Automatic Difierentiation
117
Globalization of Pantojas Optimal Control Algorithm
125
Analytical Aspects and Practical Pitfalls
131
Nonlinear Observer Design Using Automatic
137
On the Iterative Solution of Aclioint Equations
145
Aerofoil Optimisation via AD of a Multigrid
153
Automatic Diflerentiation and the Adjoint
161
Efficient Operator Overloading AD for Solving
167
Integrating AD with ObjectOriented Toolkits
173
Optimal Sizing of Industrial Structural Mechanics
181
Second Order Exact Derivatives to Perform Optimization
189
Accurate Gear Tooth Contact and Sensitivity
197
Optimal Laser Control of Chemical Reactions Using AD
205
Sensitivity Analysis Using Parallel ODE Solvers
223
Adjoining Independent Computations
299
Complexity Analysis of Automatic Differentiation
305
Expression Templates and Forward Mode
311
Application of AD to a Family of Periodic Functions
319
FAD Method to Compute Second Order Derivatives
327
Application of Higher Order Derivatives
335
Efficient HighOrder Methods for ODEs and DAEs
343
From Rounding Error Estimation to Automatic
351
New Applications of Taylor Model Methods
359
Taylor Models in Deterministic Global Optimization
365
Towards a Universal Data Type for Scientific
373
Bibliography
383
Index
427
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