Recent Advances in Algorithmic Differentiation

Name: Recent Advances in Algorithmic Differentiation
Brand: Springer
Price: 96.29 EUR
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Shaun Forth Paul Hovland Eric Phipps Jean Utke Andrea Walther(Herausgeber*in)

Springer (Verlag)

Erschienen am 30. Juli 2012

XVIII, 362 Seiten

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Intro
Recent Advances in Algorithmic Differentiation
Preface
Contents
Contributors
A Leibniz Notation for Automatic Differentiation
1 Historical Background
2 The Leibniz Notation
2.1 The Forward Mode
2.2 The Reverse Mode
2.3 Forward over Forward
2.4 Forward over Reverse
3 Second Order Approaches Involving Reverse Mode
3.1 Forward over Reverse
3.2 Reverse over Forward
3.3 Reverse over Reverse
4 The Equivalence Theorem
References
Sparse Jacobian Construction for Mapped Grid Visco-Resistive Magnetohydrodynamics
1 Introduction
1.1 Model
1.2 Implicit Solver Framework
2 Preconditioner Construction
2.1 Code Reconfiguration
2.2 OpenAD Usage
2.3 Code Integration
3 Results
3.1 Conclusions and Future Work
References
Combining Automatic Differentiation Methods for High-Dimensional Nonlinear Models
1 Introduction
2 Methodology
3 Implementation
3.1 Gradients with OpenAD
3.2 Higher-Order Derivatives with Rapsodia
4 Test Cases
References
Application of Automatic Differentiation to an Incompressible URANS Solver
1 Introduction
2 Incompressible URANS Equations and Flow Solver
3 Generation of a Discrete Adjoint Solver
3.1 Reversal of the Time Loop
3.2 Adjoining the Outer Iterations
3.3 Parallelization of the Adjoint Solver
4 Validation of the Adjoint Solver
References
Applying Automatic Differentiation to the Community Land Model
1 Introduction
2 Background
3 Automatic Differentiation and OpenAD
4 AD Development Process
4.1 Code Comprehension
4.2 Preprocessing
4.3 Transformation
4.4 Postprocessing
5 Results
6 Conclusion
References
Using Automatic Differentiation to Study the Sensitivity of a Crop Model
1 The Application Domain: The Agronomic Crop Model STICS
2 Sensitivity Analysis
3 Automatic Differentiation of STICS
3.1 The TAPENADE Automatic Differentiation Tool
3.2 STICS Adjoint : The Pains and Sufferings of an AD End-User
3.3 Validation of the Adjoint Model
4 Results: Sensitivity Analysis of STICS
4.1 Selection of Input Parameters for Sensitivity Analysis of Output Variables
4.2 Sensitivity Results of LAI and Biomass
5 Conclusion and Outlook
References
Efficient Automatic Differentiation of Matrix Functions
1 Introduction
1.1 Terminology
1.2 Matrix Derivatives in Matrix Form
2 Kronecker Products
3 Box Products
3.1 Box Products of Identity Matrices
4 Differentiation Rules
4.1 A Simple Example
4.2 The Hessian and Newton's Method
4.3 An Example Taylor Series
5 Future Work
References
Native Handling of Message-Passing Communication in Data-Flow Analysis
1 Introduction
2 Context-Sensitive and Flow-Sensitive Data-Flow Analysis
3 Impact of Message-Passing on Data-Flow Analysis
4 Data-Flow Analysis with Flow Graph Local Restart
5 Performance Discussion
6 Choosing a Good Set of Channels
7 Implementation and Outlook
References
Increasing Memory Locality by Executing Several Model Instances Simultaneously
1 Introduction
2 Cloning
3 Applications
4 Conclusions
References
Adjoint Mode Computation of Subgradients for McCormickRelaxations
1 Introduction
2 Tangent-Linear Mode Computation of Subgradients of McCormick Relaxations
3 Adjoint Mode Computation of Subgradients of McCormick Relaxations
4 Numerical Results
5 Conclusion and Outlook
References
Evaluating an Element of the Clarke Generalized Jacobian of a Piecewise Differentiable Function
1 Introduction
2 Mathematical Background
2.1 Piecewise Differentiable Functions
2.2 Automatic Differentiation
3 Generalized Jacobian Element Evaluation
4 Concluding Remarks
References
The Impact of Dynamic Data Reshaping on Adjoint Code Generation for Weakly-Typed Languages Such as Matlab
1 Introduction
2 Implicit Scalar Expansion and Array Reshape
2.1 Binary Component-Wise Operators
2.2 General Expressions
2.3 Matrix Multiplication
2.4 One-to-Many Index Assignment and Implicit Array Reshape
3 Performance of the Adjred Mechanism
4 Implicit Array Enlargement
5 Performance of the push_index/pop_index Mechanism
6 Conclusion
References
On the Efficient Computation of Sparsity Patterns for Hessians
1 Introduction
2 Algorithms for Exact and Overestimated Sparsity Patterns
3 New Data Structures and Corresponding Set Operations
4 Numerical Examples
5 Conclusions and Outlook
References
Exploiting Sparsity in Automatic Differentiation on Multicore Architectures
1 Introduction
2 Parallel Derivative Computation in ADOL-C
3 Parallel Sparse Derivative Computation
3.1 Sparsity Pattern Detection
3.2 Seed Matrix Determination
3.3 Derivative Calculation
4 Experimental Results
4.1 Test Cases
4.2 Runtime Results
5 Conclusion
References
Automatic Differentiation Through the Use of Hyper-Dual Numbers for Second Derivatives
1 Introduction
2 First Derivative Calculations
3 Second Derivative Calculations
4 Hyper-Dual Number Implementation and Results
4.1 Application to a Computational Fluid Dynamics Code
4.2 Computational Cost
5 Conclusion
References
Connections Between Power Series Methods and Automatic Differentiation
1 Introduction
2 Applying PSM
2.1 Example 1: PSM and AD Applied to an IVODE
2.2 Example 2: Root-Finding
2.3 Example 3: The Maclaurin Polynomial for an Inverse Function
3 PSM Theory and AD
4 Conclusion
References
Hierarchical Algorithmic Differentiation A Case Study
1 Introduction
2 Problem Description
3 Structure of JURASSIC2
4 Performance Analysis
5 Numerical Results
6 Summary and Conclusion
References
Storing Versus Recomputation on Multiple DAGs
1 Introduction
2 A Use Case for Storing Edge Labels
3 Computational Graphs Share Value Restoration
4 Problem Formulation
4.1 A Cost Function
4.2 A Search Strategy
4.3 Algorithm
5 Observations and Summary
References
Using Directed Edge Separators to Increase Efficiency in the Determination of Jacobian Matrices via Automatic Differentiation
1 Introduction
1.1 Automatic Differentiation and the Edge Separator
2 On Finding Separators to Increase Efficiency in the Application of Automatic Differentiation
2.1 Minimum Weighted Separator
2.2 Natural Order Edge Separator
2.3 Multiple Separators
3 Experiments
3.1 Thin Computational Graphs
3.2 Fat Computational Graphs
4 Accelerating the Calculation of the Jacobian matrix
5 Concluding Remarks
References
An Integer Programming Approach to Optimal DerivativeAccumulation
1 Introduction
2 Integer Programming Formulations
2.1 IP Formulation
2.2 Computational Consideration for Solving (MinFlops)
3 Computational Experiments
4 Conclusion
References
The Relative Cost of Function and Derivative Evaluations in the CUTEr Test Set
1 Introduction
2 Numerical Results
2.1 Problem Dimension and Ratio
2.2 Run-Time and Run-Time Ratios
2.3 Sparsity
3 Conclusion
References
Java Automatic Differentiation Tool Using Virtual OperatorOverloading
1 Introduction
1.1 Java AD Tool
1.2 Requirements for System Design Optimization
2 Virtual Operator Overloading
2.1 Forward Model Principle
2.2 Using Jacobian and Partial Derivatives
2.3 Management of External Functions
3 JAP Architecture
3.1 Lexical and Syntax Analysis
3.2 Source Class Decomposition
3.3 Adding Forward Propagation Method
3.4 JAP Limits
4 JAP Performance
5 Conclusions and Perspectives
References
High-Order Uncertainty Propagation Enabled by Computational Differentiation
1 Introduction
2 Computational Differentiation
3 State Transition Tensor Models
4 Probability Distribution Function
4.1 Approximate Solutions to the Liouville's Equation
4.2 Data Structures for Numerical Integration
5 Applications
5.1 Unforced Duffing Oscillator
5.2 Two-Body Problem
6 Summary and Conclusion
References
Generative Programming for Automatic Differentiation
1 Introduction
2 Related Work
3 Implementation
3.1 Implementation Details
3.1.1 Expression Tree
3.1.2 Code Generation
4 Experimental Results
5 Conclusion and Future Work
References
AD in Fortran: Implementation via Prepreprocessor
1 Introduction
2 Language Extensions
2.1 Extension 1: AD Syntax
2.2 Extension 2: Nested Subprograms
2.3 Concrete Example
3 Implementation
3.1 Nested Subprograms in Detail
3.2 AD Syntax in Detail
3.3 Performance
4 Conclusion
References
An AD-Enabled Optimization ToolBox in LabVIEWT
1 Introduction
2 Implementation of AD in LabVIEW: The LVAD Package
2.1 LVAD Class
2.2 Operator Overloading
2.3 Examples
3 Implementation of a LabVIEW Optimization Toolbox
3.1 Root Finding: The fzero subVI
3.2 Minimization: The fmin subVI
4 Results
4.1 Simple Example
4.2 Performance Testing
5 Conclusions
References
CasADi: A Symbolic Package for Automatic Differentiation and Optimal Control
1 Introduction and Motivation
2 Background: Eight Flavors of Automatic Differentiation
2.1 Operator Overloading versus Source Code Transformation
2.2 Scalar versus Matrix-Valued Atomic Operations
3 Structure of CasADi
3.1 Two Different Expression Graph Representations
3.1.1 Scalar-Valued Atomic Operations
3.1.2 Sparse, Matrix-Valued Atomic Operations
3.2 Three Different Symbolic Types
3.3 Function Objects
3.4 Sparsity Pattern Detection and Graph Coloring for Jacobians
3.5 External Solver Interfaces
3.6 Python and Octave Front-Ends
4 Numerical Results
5 Conclusion
References
Efficient Expression Templates for Operator Overloading-Based Automatic Differentiation
1 Introduction
2 Expression Templates for Forward Mode AD
3 Improving Performance of Expression Templates
4 Application to Differentiation of a Fluid Dynamics Simulation
5 Concluding Remarks
References
Computing Derivatives in a Meshless Simulation Using Permutations in ADOL-C
1 Introduction
2 Finite Pointset Method
3 Permutations and Selections
3.1 Active rvalue and lvalue Subscripting
3.2 Permutations in Finite Pointset Method
4 Numerical Simulation with Finite Pointset Method
5 Other Applications
6 Conclusions
References
Lazy K-Way Linear Combination Kernels for Efficient Runtime Sparse Jacobian Matrix Evaluations in C++
1 Introduction
1.1 This Work
2 Lazy Evaluation Techniques for Dynamic Sparsity
3 K-Way SPLC Evaluation Kernels
3.1 K-Way SPLC Kernel 1: Caching Nodal Binary Tree
3.2 K-Way SPLC Kernel 2: Prolong-and-Restrict Dense Accumulation
3.3 Summary
4 Computational Examples
4.1 Model SPLC Numerical Experiments
4.2 Model Problem Simulation Jacobian
5 Summary
References
Implementation of Partial Separability in a Source-to-Source Transformation AD Tool
1 Introduction
1.1 ADIC2
1.2 ColPack
2 Related Work
3 Implementation
4 Experimental Results
5 Conclusion
References
Editorial Policy
Lecture Notesin Computational Science and Engineering
Monographs in Computational Science and Engineering
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