• The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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## 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.

• Evolution of the adjoint AD model to keep in pace with with modern programming languages constructs.

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