Programme of the 16th Euro AD Workshop

Parametrised functions occur in various applications. A function is parametrised in this context, if it depends on certain model constants, however either no derivatives with respect to these constants are ever required or these derivatives are known to be trivial and need not be computed using algorithmic differentiation tools like ADOL-C. From the beginning ADOL-C stores such passive constants on a separate trace, the value trace, and does not compute any derivatives with respect to such constants. The problem in this approach is the fact that if one changes the model constants, one would need to recreate the trace, which could be rather expensive. Recently interfaces have been added to ADOL-C to mark interchangeable parameters during the tracing process, so that their values can be easily changed by the user before a forward or reverse evaluation of the trace. A very obvious application is the interface for optimisation software like IpOpt, which requires the computation of derivatives of the Lagrangian with respect to the primal variables at varying values for the Lagrange multipliers. One need not compute derivatives with respect to the multipliers as they enter only linearly. This reduces the computation time for the Hessian of the Lagrangian considerably, since the number of independent variables is greatly reduced using this approach in comparison to the previous implementation.

Adjoint based methods are an effective way for obtaining cheap gradients in CFD optimization problems even with a large number of degrees of freedom when traditional methods like Finite Difference becomes too expensive. Here we present a discrete adjoint model of foam-extend (v3.1) [1], which is kind of a fork of OpenFOAM, the open source library for CFD, retaining a lot of its structural features with some additional extensions and performance improvements. It is obtained using Algorithmic Differentiation tool, dco/c++.

Adjoint methods come in two variations, discrete and continuous. The former has the distinct advantage of robustness and flexibility over the later but at the cost of increased spatial and temporal complexities. Often in the case of large size industrial problems, these limitations prove to be the bottleneck. Strategies like checkpointing [2] and analytical treatment of linear solvers help to assuage this problem, however further improvement is required.

Therefore our coupled adjoint solver based on pUCoupledFoam [3], an incompressible pressure-velocity coupled solver based on an explicit use of Rhie-Chow interpolation is presented. The objective is to exploit the faster rate of convergence of the flow equations (and hopefully, faster computations) to decrease the overall time for the computation of the gradients.

[1]                   http://www.extend-project.de/

[2] A.Griewank and A.Walther, Algorithm 799: revolve: an implementation of checkpointing for the reverse or adjoint mode of computational differentiation, ACM Transactions on Mathematical Software, Vol. 26, pp. 19-45 , (2000).

[3] K.Jareteg, V.Vukcevic and H.Jasak, pUCoupledFoam - an open source coupled incompressible pressure-velocity solver based on foam-extend, 9th OpenFOAM wokshop., 2014.

In this talk we discuss the development of a discrete adjoint solver, which enables the computation of consistent gradients in a robust way based on the exploitation of the fixed-point structure of the flow solver. All occurring derivatives in this formulation can be calculated using advanced techniques of AD so that the extension to arbitrary complex flow models can be performed along with the development of the primal code. We will then show some recent results of aerodynamic shape optimization problems in turbulent flows that make use of this adjoint solver.

Originally piecewise linearisation was conceived as a way to locally approximate piecewise smooth functions with second order error. However, once we have given up the extreme simplicity of linear models and accepted some combinatorial hassles we might as well preserve some global characteristics of elementary functions like evenness and non-negativity by 'clipping' their tangent lines or planes appropriately. The results are rather astounding even when the underlying model is smooth and have not yet been fully explored.

Joint work with Andrea Walther, Andreas Griewank

Joint work with A. Geletu, S. Hopfgarten, and P. Li.

A new feature for Tapenade is presented that enables multiple activities for a given procedure in both adjoint and tangent mode. The benefits are twofold. First, derivative routines can be specialized automatically by Tapenade, so that at each call site, a variant of the derivative routine is called that will only calculate the derivative variables needed in this context, improving the performance of the generated code. Second, the user has more flexibility by defining several differentiation contexts for any given routine. As a case-study, the mgopt flow solver developed at Queen Mary University of London is differentiated. The new multi-activity feature removes the need for any pre- and postprocessing in the build process of mgopt and thus reduces complexity and build time. Furthermore, it improves the runtime performance of the final executable in adjoint mode.

Joint work with Steve Merschel, Stefan Schuster, Pu Li, Christoph Kaleta

The community website autodiff.org was set up almost 15 years ago. What is the functionality that is appreciated today? What is not really critical? This talk is intended to stimulate a discussion.