Advances in Automatic Differentiation
:
Timothy J. Barth, Michael Griebel, David E. Keyes, Risto M. Nieminen, Dirk Roose, Tamar Schlick, Chr
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Christian H. Bischof, H. Martin Bücker, Paul Hovland, Uwe Naumann, Jean Utke
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Advances in Automatic Differentiation
:
Springer-Verlag
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9783540689423
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1
:
CHF 123.80
:
:
Allgemeines, Lexika
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English
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368
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Wasserzeichen/DRM
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PC/MAC/eReader/Tablet
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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.
Preface
5
Contents
8
List of Contributors
11
Reverse Automatic Differentiation of Linear Multistep Methods
17
1 Introduction
17
2 Linear Multistep Methods
19
3 Zero-Stability of the Discrete Adjoints
23
4 Derivatives at the Initial Time
24
5 Numerical Experiments
26
6 Conclusions
27
References
27
Call Tree Reversal is NP-Complete
29
1 Background
29
2 Data-Flow Reversal is NP-Complete
32
3 Call Tree Reversal is NP-Complete
34
4 Conclusion
36
References
36
A Reference Code for Result Checkpointing
38
On Formal Certification of AD Transformations
39
1 Introduction
39
2 Background and Problem Statement
40
3 Unifying PCC and AD Validation
42
4 Foundational Certification of AD Transformations
44
5 Related Work
47
6 Conclusions and Future Work
47
References
48
Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation
50
1 Introduction
50
2 Matrix Product, Inverse and Determinant
51
3 MLE and the Dwyer/Macphail Paper
56
4 Validation
57
5 Conclusions
58
References
58
A Modification of WeeksÌ Method for Numerical Inversion of the Laplace Transform in the Real Case Based on Automatic Differentiation
60
1 Introduction
60
2 Preliminaries
62
3 Remarks on Automatic Differentiation
63
4 Numerical Experiments
65
5 Conclusions
69
References
69
A Low Rank Approach to Automatic Differentiation
70
1 Introduction
70
2 Methodology
72
3 Case Study
76
4 Conclusions and Future Work
79
References
80
Algorithmic Differentiation of Implicit Functions and Optimal Values
81
1 Introduction
81
2 Jacobians of an Implicit Function
83
3 Differentiating an Optimal Value Function
84
4 Example
86
5 Conclusion
89
6 Appendix
90
References
91
Using Programming Language Theory to Make Automatic Differentiation Sound and Efficient
92
1 Introduction
92
2 Functional Programming and Modularity in AD
94
3 The AD Transforms Are Higher-Order Functions
95
4 AD and Differential Geometry
97
5 Migration to Compile Time
98
6 Some Preliminary Performance Results
99
7 Discussion and Conclusion
102
References
103
A Polynomial-Time Algorithm for Detecting Directed Axial Symmetry in Hessian Computational Graphs
104
1 Introduction
104
2 Mathematical Definitions
105
3 Symmetry Detection Algorithm
106
4 Analysis of the Algorithm
111
5 Results and Discussion
112
6 Conclusions and Future Work
114
References
114
On the Practical Exploitation of Scarsity
116
1 Introduction
116
2 Scarsity
118
3 Test Examples
124
4 Conclusions and Outlook
126
References
126
Design and Implementation of a Context-Sensitive, Flow- Sensitive Activity Analysis Algorithm for Automatic Differentiation
128
1 Introduction
128
2 Background
130
3 Algorithm
132
4 Experiment
134
5 Related Work
137
6 Conclusion
137
References
138
Efficient Higher-Order Derivatives of the Hypergeometric Function
139
1 Introduction
139
2 Taylor Coefficient Propagation
142
3 Double Ionization Application
144
4 Conclusions
148
References
148
The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic Numerical Method
150
1 Introduction
150
2 Asymptotic Numerical Method (ANM)
151
3 Applying AD to the ANM Computations
154
4 Diamant: An AD Tool Devoted to the ANM
156
5 Application to a Nonlinear PDE Problem in Structural Mechanics
157
6 Conclusion
159
References
160
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