
Programme of the Sixth Euro AD Workshop
Thursday, November 15, 2007
 10^{00} –11^{00} Registration and welcome coffee
 11^{00} –12^{30} Session 1: AD tools
 Massimiliano Martinelli (INRIA SophiaAntipolis, France)
Second derivatives via TangentonTangent and TangentonReverse
Secondorder derivatives of PDEconstrained functionals can be obtained
through an adjoint formulation and using two differents AD approaches:
TangentonTangent and TangentonReverse. The two strategies return the same derivatives but differ about their computational cost.
I will present the two algorithms with some estimates about their
computational costs and some examples of applications using a 3D Euler
solver.
 Johannes Willkomm (Institute for scientific computing, Aachen University, Germany)
AD tools from a user's perspective
AD tools using the operator overloading technique are easy to use in
principle, since they only require a change of the datatype of the code
(activation). An effective method for the concurrent development and
maintenance of the regular and activated version of a source code is the use
of generic programming (templates). We take a look at the feasibility of this
approach using various AD tools.
 Marina Menshikova (Cranfield University, Shrivenham Campus, UK)
Branch Detection and Sparsity Estimation in Matlab
Some computations performed by automatic differentiation can be
performed more effectively if we can be assured that the control flow of
the program does not change from one call of the program to the next.
This is the case with: uncertainty estimation via Taylor series,
Jacobian sparsity estimation, or reverse mode AD implemented via taping.
We present an overloaded branch detection algorithm for the MAD package
for AD in Matlab that enables one to automatically check whether any
relational operators are evaluated and/or whether their evaluation
changes from one call of the program to the next. In the absence of the
controlflow analysis facilitated by sourcetransformation, detection of
relational operators is taken to indicate the presence of a branch in
the program and hence potential changes in control flow. We further
present a sparsity detection class for MAD which gives tight
overestimates of Jacobian sparsity patterns even in the presence of
program computations involving sparse matrices. The sparsity patterns
may then be used for Jacobian compression.
 12^{30} –14^{00} Lunch break
 14^{00} –15^{30} Session 2: Earth Sciences (I)
 Monika Krysta (IMAG, projects LEGI & LKJ, Grenoble, France)
Data assimilation :variations on Kalman Filtering approach
Data assimilation is a method of coupling models and observations. It aims
to produce an optimal state of a physical system. The method is widely used in
geoscience, namely in physics and chemistry of the atmosphere and ocean. In
fact, both a chaotic character of these phenomena and an inherent model error
require to periodically constrain a model with observations.
In this presentation we shall focus on Kalman Filtering approach to data assimilation.
Firstly, the bases of the standard Kalman Filter algorithm shall
be presented. Next, in view of practical applications, the necessity of order
reduction shall be raised. The foundations of the Reduced Rank Square
Root(RRSQRT) KalmanFilter and Singular Evolutive Extended/Interpolated
Kalman(SEEK/SEIK) Filter shall be given. The presence of the tangent linear
and adjoint models in the algorithms shall be stressed and the currently
used ways of circumventing them discussed. Furthermore, Kalman Filterbased
methods (Ensemble Kalman Filter and Particle Filter) which enable tackling
nonlinearities in the models shall be discussed. Finally, the differences between
Kalman Filtering and variational method shall be emphasised. The equivalence
of the latter one and a fixed interval smoother issued from Kalman Filter shall
also be mentioned.
 Michael Vossbeck (FastOpt, Hamburg, Germany)
TAF and TAC++ applications to earth sciences
Transformation of Algorithms in Fortran (TAF) and Transformation of
Algorithms in C++ (TAC++) are FastOpt's Automatic Differentiation tools
for code written in Fortran and C, respectively.
We will give a brief overview on the tools and their applications.
Successful largescale applications cover all components of state of the
art earth system models,such as atmospheric and ocean general
circulation, terrestrial and marine biogeochemistry, atmospheric
transport and chemistry, seaice and the radiative transfer.
 Olivier Titaud (IMAG, Grenoble, France)
Observation operators in image assimilation
Satellite images represent a large amount of data which are currently
underused in numerical forecast systems. Extending assimilation techniques
to image data become of primary importance to improve the quality of the analysis.
Assimilating dynamical informations included in image sequences requires,
among other things, the construction of observation operators
which map the model state variables space onto a given image space.
This mapping will probably induce some difficulties in automatic differentiation.
This work is supported by the ANR in the framework of the ADDISA
project ( http://addisa.gforge.inria.fr).
 15^{30} –16^{00} Coffee break
 16^{00} –18^{00} Session 3: AD algorithms
 John Pryce (Cranfield University, Shrivenham Campus, UK)
DAETS: a DifferentialAlgebraic Equation code in C++ for high index and high accuracy
Ned Nedialkov and John Pryce are the authors of DAETS, a C++ code for
solving differentialalgebraic equations (DAEs). It uses Pryce's
structural analysis theory, and expands the solution in Taylor series
using AD. Version 1 is now available. DAETS is especially good when
high accuracy is required, and at solving problems of high index (we
have solved artificial DAEs of index up to 47). It is versatile:
higherorder systems do not have to be cast in firstorder form; it
can solve explicit and implicit ODEs; it can solve purely algebraic
(continuation) problems, by simple or by arclength continuation. The
talk will outline the design of the algorithm and the code, and give
examples of the code's performance. This includes some puzzling
phenomena, e.g. why, on one stiff ODE from a standard test set, does
tightening the tolerance give a *decrease* in CPU time and number of
steps, uniformly over a range of tolerances from 1e4 to 1e12?
 Andrew Lyons (Argonne National Laboratory, USA)
Optimal Derivative Accumulation on SeriesParallel Dags
I will present an algorithm for optimal chain rulebased derivative
accumulation on a subclass of directed acyclic graphs. The algorithm
is based on the seriesparallel decomposition tree, which can be
constructed in linear time.
 Jean Utke (Argonne National Laboratory, USA)
Toward adjoinable MPI
In the past, various approaches have been taken to make AD tools aware
of MPI calls and generate the proper adjoint code. Considering the
correctness of the adjoint and its performance there is so far no
generic recipe for source transformation tools. We will look at some
of the problems and discuss first ideas how to arrive at an MPI code
that can be adjoined, is guaranteed to be correct and does not loose
too much performance.
 19^{45} Banquet Dinner

Friday, November 16, 2007
 9^{00} –10^{30} Session 4: AD applications (I)
 Andreas Griewank (Humboldt University, Berlin, Germany)
Evaluating and Bounding Cross Derivatives
In several (potential) applications of algorithmic differentiation
one needs to evaluate or bound crossderivatives, i.e. mixed
partials that are obtained by differentiating with respect to each
one of <i>n</i> variables at most once. We observe that the 2<sup>n</sup>
crossderivatives of a scalar function <i>f</i> can be evaluated in the forward
mode with an operation count of no more than 3<sup>n</sup> times that for
evaluating <i>f</i> by itself. For the error estimation and design of
certain quasimulti Carlo quadratures it is sufficient to bound
the crossderivatives by products of 2,n order and variable
weights. We demonstrate how they can be calculated with an effort
that grows at worst quadratically with respect to the dimension
<i>n</i>, again relative to the cost of evaluating <i>f</i> by itself.
 Michael Luelfesmann (Institute for scientific computing, Aachen University, Germany)
Sensitivity of the Optimal Geometry of a Blood Pump
For identifying the blood model which is appropriate for the shape
optimization of a blood pump we want to get the sensitivities of the
optimal geometry with respect to the parameters of different blood
models. For getting this information we want to differentiate
through an optimization algorithm. In this talk the first
results of differentiating the optimizer DonLP2 will be shown.
 Samuel Buis (INRA Avignon, France)
Some applications of AD for the study of vegetation
The study of vegetation at landspace scale often implies the use of simulation models, observed data
and the resolution of inverse problems.
We will briefly present several applications based on adjoint methods and using the AD tool TAPENADE.
We will particularly focus on the interest of using spatial and /or temporal constraints in the resolution of inverse problems and on the experience of using TAPENADE on different models.
 10^{30} –11^{00} Coffee break
 11^{00} –12^{30} Session 5: Earth Sciences (II)
 Patrick Heimbach (MIT, USA)
Of tiles, tools and topologies: Adjoint applications of the MIT general circulation model
Rigorous use of automatic differentiation with the AD tool TAF has
enabled numerous applications of the MITgcm adjoint modeling framework.
They include state estimation and sensitivity studies in an oceanonly,
coupled oceanbiogeochemistry and coupled oceanseaice context,
at coarse and high (eddyermitting) resolution for various domains and
grid topologies of the world ocean. Applications ran on various HPC
platforms, some of which scaled up to 600 processors.
Successful MITgcm adjoint code generation with the new opensource
tool OpenAD has enabled us to compare adjoint code reliability among
different AD tools in the complex framwork of a fullyfledged GCM.
 Hicham Tber (INRIA SophiaAntipolis, France)
AD of Ocenagraphy code OPA
We present the construction by Tapenade of the adjoint code of the oceanography code OPA. OPA 9.0 is a major rewrite of OPA, now written in FORTRAN 95. We discuss some techniques used to improve the adjoint code, such as binomial checkpointing and a specific differentiation strategy for the iteative solver. We present validation results and some preliminary applications.
 Franz Schreier (DLR, Oberpfaffenhofen, Germany)
Automatic differentiation of an infrared radiative transfer code for atmospheric remote sensing
Accurate yet efficient computation of derivatives is essential for
solution of inverse problems in atmospheric remote sensing. A
linebyline radiative transfer code has been developed for high
resolution infrared and microwave atmospheric sounding. Derivatives
of spectra with respect to atmospheric state parameters
(e.g. molecular concentration or temperature) are obtained by means of
automatic differentiation using ADIFOR. Currently the code is
converted to modern Fortran. Experience with ADIFOR and TAPENADE is
discussed.
 12^{30} –14^{00} Lunch break
 14^{00} –15^{30} Session 6: AD applications (II)
 Petre Enciu (ENSIEEG, Grenoble, France)
AD applied for the design of electrical devices
In electrical engineering (electromechanical devices, power
electronics converters, electrical drives, microsystems, etc.),
analytical models are usually used for fast computation, mainly in
sizing processes. Such a process is often a constrained optimization
problem with numerous constraints (some tens to some hundreds). So,
gradient optimization algorithms are useful. However, such a model may
contain algorithms, complex equations (not real), specific routines
such as nonlinear implicit equations, differential and integral
equations, etc. which require numerical solving methods. In the
presentation, the authors will present an approach with the use of
ADOLC to derive symbolic sizing model described in C, and specifically
equations and simple algorithms. The authors will focus on the
mathematical aspects of their work. The computation results are
compared with results obtained by derivatives provided by a symbolic
approach (when it is possible). The approach with ADOLC is integrated
in CADES framework (developed in our laboratory for device sizing), to
be used by researchers in electrical engineering.
 Dagmar Monett Diaz (DFG Research Center MATHEON, Humboldt University, Berlin, Germany)
Index Determination in DAEs using AD techniques
 15^{30} End of workshop

