Recent Advances in Algorithmic Differentiation

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Shaun Forth, Paul Hovland, Eric Phipps, Jean Utke, Andrea Walther
Springer Science & Business Media, Jul 30, 2012 - Mathematics - 362 pages
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.
 

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Contents

A Leibniz Notation for Automatic Differentiation
1
Sparse Jacobian Construction for Mapped Grid ViscoResistive Magnetohydrodynamics
10
Combining Automatic Differentiation Methods for HighDimensional Nonlinear Models
23
Application of Automatic Differentiation to an Incompressible URANS Solver
34
Applying Automatic Differentiation to the Community Land Model
47
Using Automatic Differentiation to Study the Sensitivity of a Crop Model
58
Efficient Automatic Differentiation of Matrix Functions
71
Native Handling of MessagePassing Communication in DataFlow Analysis
82
Using Directed Edge Separators to Increase Efficiency in the Determination of Jacobian Matrices via Automatic Differentiation
208
An Integer Programming Approach to Optimal DerivativeAccumulation
221
The Relative Cost of Function and Derivative Evaluations in the CUTEr Test Set
232
Java Automatic Differentiation Tool Using Virtual OperatorOverloading
241
HighOrder Uncertainty Propagation Enabled by Computational Differentiation
251
Generative Programming for Automatic Differentiation
261
AD in Fortran Implementation via Prepreprocessor
273
An ADEnabled Optimization ToolBox in LabVIEW
285

Increasing Memory Locality by Executing Several Model Instances Simultaneously
93
Adjoint Mode Computation of Subgradients for McCormickRelaxations
103
Evaluating an Element of the Clarke Generalized Jacobian of a Piecewise Differentiable Function
114
The Impact of Dynamic Data Reshaping on Adjoint Code Generation for WeaklyTyped Languages Such as Matlab
127
On the Efficient Computation of Sparsity Patterns for Hessians
139
Exploiting Sparsity in Automatic Differentiation on Multicore Architectures
150
Automatic Differentiation Through the Use of HyperDual Numbers for Second Derivatives
163
Connections Between Power Series Methods and Automatic Differentiation
174
Hierarchical Algorithmic Differentiation A Case Study
187
Storing Versus Recomputation on Multiple DAGs
197
CasADi A Symbolic Package for Automatic Differentiation and Optimal Control
296
Efficient Expression Templates for Operator OverloadingBased Automatic Differentiation
309
Computing Derivatives in a Meshless Simulation Using Permutations in ADOLC
320
Lazy KWay Linear Combination Kernels for Efficient Runtime Sparse Jacobian Matrix Evaluations in C++
333
Implementation of Partial Separability in a SourcetoSource Transformation AD Tool
343
Editorial Policy
354
Lecture Notesin Computational Science and Engineering
356
Monographs in Computational Science and Engineering
360
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