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

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@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
}