Advances in Automatic Differentiation

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.

Includes supplementary material: sn.pub/extras

Reverse Automatic Differentiation of Linear Multistep Methods.- Call Tree Reversal is NP-Complete.- On Formal Certification of AD Transformations.- Collected Matrix Derivative Results for Forward and Reverse Mode Algorithmic Differentiation.- A Modification of Weeks' Method for Numerical Inversion of the Laplace Transform in the Real Case Based on Automatic Differentiation.- A Low Rank Approach to Automatic Differentiation.- Algorithmic Differentiation of Implicit Functions and Optimal Values.- Using Programming Language Theory to Make Automatic Differentiation Sound and Efficient.- A Polynomial-Time Algorithm for Detecting Directed Axial Symmetry in Hessian Computational Graphs.- On the Practical Exploitation of Scarsity.- Design and Implementation of a Context-Sensitive, Flow-Sensitive Activity Analysis Algorithm for Automatic Differentiation.- Efficient Higher-Order Derivatives of the Hypergeometric Function.- The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic Numerical Method.- Tangent-on-Tangent vs. Tangent-on-Reverse for Second Differentiation of Constrained Functionals.- Parallel Reverse Mode Automatic Differentiation for OpenMP Programs with ADOL-C.- Adjoints for Time-Dependent Optimal Control.- Development and First Applications of TAC++.- TAPENADE for C.- Coping with a Variable Number of Arguments when Transforming MATLAB Programs.- Code Optimization Techniques in Source Transformations for Interpreted Languages.- Automatic Sensitivity Analysis of DAE-systems Generated from Equation-Based Modeling Languages.- Index Determination in DAEs Using the Library indexdet and the ADOL-C Package for Algorithmic Differentiation.- Automatic Differentiation for GPU-Accelerated 2D/3D Registration.- Robust Aircraft Conceptual Design UsingAutomatic Differentiation in Matlab.- Toward Modular Multigrid Design Optimisation.- Large Electrical Power Systems Optimization Using Automatic Differentiation.- On the Application of Automatic Differentiation to the Likelihood Function for Dynamic General Equilibrium Models.- Combinatorial Computation with Automatic Differentiation.- Exploiting Sparsity in Jacobian Computation via Coloring and Automatic Differentiation: A Case Study in a Simulated Moving Bed Process.- Structure-Exploiting Automatic Differentiation of Finite Element Discretizations.- Large-Scale Transient Sensitivity Analysis of a Radiation-Damaged Bipolar Junction Transistor via Automatic Differentiation.