Section: New Results

Automatic Differentiation and iterative processes

Participants : Laurent Hascoet, Ala Taftaf.

Adjoint codes naturally propagate partial gradients backwards from the result of the simulation. However, this uses the data flow of the simulation in reverse order, at a cost that increases with the length of the simulation. AD research looks for strategies to reduce this cost, taking advantage of the structures of the given program. One such structure is iterative fixed point loops, commonplace in numerical computation. They occur at the topmost level of steady-state simulations, as well as in unsteady simulations. They may also occur deeper in the simulation, for instance in linear solvers.

It clear that the first iterations of a fixed-point search operate on a meaningless state vector, and that reversing the corresponding data-flow is wasted effort. An adapted adjoint strategy for the iterative process should consider only the last or the few last iterations. Furthermore, there is a discrete component to an iterative algorithm, namely the number of iterations, and this makes differentiability questionnable. For these reasons we are looking for a specific strategy for the adjoint, that reverses only the necessary data-flow, and that restores confidence in the validity of the derivative.

We seek inspiration in the strategies proposed by two authors  [19] , [27] to design one strategy that is amenable to implementation in a source-transformation AD tool such as tapenade . This will be triggered by user-given differentiation directives. We are also selecting example codes (a steady-state flow solver and a Newton solver) to benchmark and experiment.

Ala Taftaf presented her preliminary results at Queen Mary University in september, and at the 13th EuroAD workshop in Oxford, december 9-10. She attended a training on the CFD code OpenFOAM at Queen Mary, september 3-6.