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Reverse automatic differentiation for optimum design:
from adjoint state assembly to gradient computation

*Francois Courty*
*Alain Dervieux*
*Bruno Koobus*
*Laurent Hascoët*
*(INRIA, BP93, 06902 Sophia-Antipolis, France)*

Article in Optimization Methods and Software Journal, 2003 (13 pages)

**Abstract:**
Gradient descent is a key technique in Optimal Design problems.
We describe a method to compute the gradient of a optimization criterion
with respect to design parameters. This method is hybrid, using
Automatic Differentiation to compute the residual of the adjoint
system, and using this residual in a hand-written solver that computes
the adjoint state and then the gradient. Automatic Differentiation
is here used in its so-called reverse mode, with a special
refinement for gather-scatter loops. The hand-written solver
uses a matrix-free algorithm, preconditioned by the first-order
derivative of the flux function. This method was tested on
a typical optimal design problem, for which we give validation
and performance results.

**Keywords:**
Computational Fluid Dynamics, Optimum Design, Euler Equations, Adjoint Equations,
Automatic Differentiation, Checkpointing, Data Dependence Analysis

Full text (pdf)
`
@article{CDKH03,
author = {Courty, F. and Dervieux, A. and Koobus, B. and Hasco{\"e}t, L.},
title = {Reverse automatic differentiation for optimum design:
from adjoint state assembly to gradient computation},
journal = {Optimization Methods and Software},
publisher = {Taylor \& Francis},
volume = 18,
number = 5,
pages = "615-627",
year = 2003
}
`