Programme of the 20th Euro AD Workshop

We present the current development status in Tapenade to be able to differentiate multi-language codes (Fortran+C)

A number of tools, such as Klee-FP, CIVL, CodeThorn, offer an automated analysis of source code, and aim to prove that a given piece of code satisfies certain given properties. This talk will show how these tools can be used to find bugs in AD-generated code, and how verification can ensure that properties such as the dot-product test hold for any input or any seed vector.

In recent years Griewank and others in the AD community have worked on piecewise linearization of programs in abs-normal form. In our presentation we consider piecewise linearization for programs with general control flow branching. Like Griewank's approach the suggested method is an extension of forward mode AD. For programs that could be rewritten in abs-normal form the presented method accomplishes the same computation without having to be explicit. Control flow branching piecewise linearization does not require rewriting but it does not give the same guarantees. We discuss some uses and short comings of the presented method based on example applications.

For operator overloading AD tools it is quite simple to generate higher order derivatives by recursive use of the AD types. The number of derivatives grows exponentially and are hard to access by the users without an intuitive interface. We propose a new selection algorithm, such that the user can simply specify, that he would like to access the fifth third order derivative of the 20 third order derivatives that are available in a sixth order AD type.

Modern mesh adaptation is progressively getting rid of heuristical steps and getting closer to a well posed problem. It is formulated as a differentiable optimization problem with respect to a continuous metric representing the mesh. The user can prescribe in which norm the approximation error should be minimal. This is accounted for by the functional to minimize. Thanks to differentiation, we get a set of KKT-like optimality conditions: state system, adjoint system, stationarity. In contrast to usual optimization, the stationarity is solved analytically and a fixed point solution of the optimality system is obtained by relaxation between its three components. Application to compressible CFD are presented.

To perform an aerodynamic gradient-based shape optimization of a CAD-based model, one requires the derivatives of the cost function with respect to the design parameters of the model. A challenging part of this computation refers to the CAD derivatives, i.e., the derivatives of the surface points position with respect to the design parameters. In order to evaluate these derivatives accurately, we have developed the AD version of the open-source CAD kernel Open CASCADE Technology using the traceless forward mode of AD tool ADOL-C. The integration of the trace-based reverse mode of AD is in progress and its results will be presented. Moreover, this differentiated CAD kernel has been coupled with a discrete adjoint flow solver, thus having a complete differentiated design chain at hand. To validate it, we have performed the gradient-based optimization of two turbomachinery components: U-bend and TU Berlin TurboLab Stator.

Message Passing Interface (MPI) is a defacto programming standard for distributed parallel scientific codes. Algorithmic differentiation of MPI based scientific codes is still a manual or semi-automatic process. Therefore a complete understanding of the underlying MPI call structure is necessary to obtain the forward/reverse Algorithmic Derivatives (AD). MPI AD recipes help to circumvent this barrier by providing ready-made routines for MPI and AD MPI functions. In the present work, we provide an alternative method to manually obtain the AD MPI calls using a simple sparse matrix model. This approach suggests that the AD MPI calls are closely related to the underlying data partitioning strategy. We present examples of two data partitioning namely, (i) halo based and (ii) zero-halo based strategy.

Derivatives of financial instrument prices with respect to their underlying parameters are instrumental for risk management and highly desirable for the quick approximation of prices when underlying parameters change (either in response to real time feed events or simulation scenarios) using Taylor series expansion. The finance industry comes with a set of naturally evolving requirements that induces a set of constraints on computational graphs and derivatives computation for software builders willing to propose fast evaluations and good time to market. Those constraints include: evolving computational graphs, runtime computational graph modifications, combined evaluation, continuous evaluation, runtime derivatives control, intermediary derivatives and openness. Coarse Grain Automatic Differentiation (CGAD) is an AD-like framework that satisfies the finance industry constraints. It applies the multivariate chain rule on coarse-grained computational DAGs made of high-level business functions drawn from the ubiquitous language (see Eric Evans’ book: Domain Driven Design} shared by the software developers and users. By leveraging software and financial instrument modularity, it gives the financial software industry a practical means of computing fast and exact derivatives.

We are speaking about an open problem in the foundation of Automatic Differentiation: not yet established equivalency between two competing definitions of general elementary functions.

AD (understood here as optimized formulas of differentiation) applies only to (general) elementary functions introduced by Ramon Moore in the 1960s (as a generalization of the conventional 19th century definition by Liouville).

Moore defined so to say vector-elementariness as a property of a vector-function to satisfy a system of rational 1st order ODEs. At that, the AD and the "Unifying View on ODEs and AD" (Gofen) are based on namely this definition.

A competing definition of stand-alone elementariness is based on a property of a function to satisfy one rational ODE of order n. Are both definitions equivalent? The answer depends on the not yet resolved Conjecture discussed in this presentation.