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)


INRIA Research Report #4363, january 2002 (33 pages)

Abstract: The utilization of reverse mode Automatic Differentiation to the adjoint method for solving an Optimal Design problem is described. Using the reverse mode, we obtain the adjoint system residual in a rather efficient way. But memory requirements may be very large. The family of programs to differentiate involves many independant calculations, typically in parallel loops. Then we propose to apply a reverse differentiation "by iteration". This demands much less memory storage. This methods is used for the computing of the adjoint state and gradient related to the Optimal Design problem.

Keywords: Automatic Differentiation, Optimal shape design, Computational Fluid Dynamics, Euler Equations, Compressible flow, Adjoint, Gradient, Reverse mode, Checkpointing, Data Dependence Analysis, Memory optimization

Full text (pdf)

@techreport{CDKH02,
  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},
  institution = {INRIA},
  type = {Research Report},
  number=4363,
  url = "http://www.inria.fr/rrrt/rr-4363.html",
  year=2001
}