Section: Overall Objectives

Overall Objectives

Team Ecuador studies Algorithmic Differentiation (AD) of computer programs, blending :

• AD theory: We study software engineering techniques, to analyze and transform programs mechanically. Algorithmic Differentiation (AD) transforms a program P that computes a function $F$, into a program P' that computes analytical derivatives of $F$. We put emphasis on the adjoint mode of AD, a sophisticated transformation that yields gradients for optimization at a remarkably low cost.

• AD application to Scientific Computing: We adapt the strategies of Scientific Computing to take full advantage of AD. We validate our work on real-size applications.

We want to produce AD code that can compete with hand-written sensitivity and adjoint programs used in the industry. We implement our algorithms into the tool Tapenade, one of the most popular AD tools now.

Our research directions :

• Efficient adjoint AD of frequent dialects e.g. Fixed-Point loops.

• Development of the adjoint AD model towards Dynamic Memory Management.

• Development of the adjoint AD model towards Parallel Languages.

• Optimal shape design and optimal control for steady and unsteady simulations. Higher-order derivatives for uncertainty quantification.

• Adjoint-driven mesh adaptation.