Section: Overall Objectives

Overall Objectives

The TROPICS team studies Automatic Differentiation (AD) of algorithms and programs. We work at the junction of two research domains:

• AD theory: On the one hand, we study software engineering techniques, to analyze and transform programs mechanically. Automatic 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 so-called reverse or adjoint mode of AD, a sophisticated transformation that yields gradients for optimization at a remarkably low cost.

• AD application to Scientific Computing: On the other hand, we study application of the adjoint mode of AD to e.g. Computational Fluid Dynamics. We adapt the strategies used in Scientific Computing in order to take full advantage of AD. This work is applied to several real-size applications.

Each aspect of our work benefit to the other. We want to produce AD code that can compete with hand-written sensitivity and adjoint programs that are used in the industry. We implement our algorithms into our tool tapenade , which is now one of the most popular AD tools.

Our research directions are :

• Modern numerical methods for finite elements or finite differences : multigrid methods, mesh adaptation.

• Optimal shape design or optimal control in fluid dynamics for steady and unsteady simulations. Higher-order derivatives needed by robust optimization.

• Automatic Differentiation : AD-specific static data-flow analysis, strategies to reduce runtime and memory consumption of the reverse mode in the case of very large codes. Improved models for reverse AD, in particular coping with message-passing parallellism.