Methods for the differentiation of non-smooth physical parameterizations
by
Fabrice Veersé
projet IDOPT, LMC, BP 53, F-38041 Grenoble Cedex 9
Coauthors: Isabelle Charpentier (projet Idopt)

Understanding complex physical processes often relies on numerical simulations with models solved on large discretization spaces and requiring sometimes non-differentiable parameterizations. The latter involve for example threshold processes and positivity constraints. Non-differentiable routines cannot be treated in a straightforward manner. A solution is to perform modifications on the source code in order to replace non-differentiable routines by differentiable ones having a similar physical behavior.
In that context, physicists use their knowledge of the physical behavior of the model of interest to create differentiable sets of parameterizations. Such a method is tedious since each parameterization has to be studied, and it cannot be systematic. We propose to test differentiable spline-based approximations of non-smooth parameterizations. The physical knowledge on the behavior of the system is introduced here via an optimization process involving observations.
The layout of the presentation is the following. Different kinds of non-differentiabilities encountered in numerical codes and some solutions by physicists are first discussed. In a second part, alternate methods to perform systematic modifications of the code are proposed. These are demonstrated by numerical experiments with a bio-physical estuarine ecosystem model.

http://www-lmc.imag.fr/lmc-edp/Fabrice.Veerse/AD2000/e_abstract.ps

Date received: December 7, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cads-08.