Publication: A Case Study of Computational Differentiation Applied to Neutron Scattering
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A Case Study of Computational Differentiation Applied to Neutron Scattering

- incollection -
 

Area
Chemistry

Author(s)
Christian H. Bischof , H. Martin Bücker , Dieter an Mey

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
In a neutron scattering application, an unconstrained nonlinear minimization problem is used for the fitting of model parameters to experimental data. Automatic differentiation enables, in a completely mechanical fashion, algorithmic changes by switching from a quasi-Newton method, where first order derivatives are approximated by finite differences, to a modified Gauss--Newton method using exact first order derivatives. Compared to the original code, the code generated by this black box approach produces reliable results rather than results of dubious quality. This approach also is faster in terms of execution time. Its performance is improved further by replacing the most time-consuming subroutine involved in the derivative evaluation by a surprisingly simple, hand-coded implementation of the corresponding analytic expression.

Cross-References
Corliss2002ADo

AD Tools
ADIFOR

AD Theory and Techniques
Integration of Analytic Derivatives

Related Applications
- Parameter Fitting in Neutron Scattering

BibTeX
@INCOLLECTION{
         Bischof2002ACS,
       author = "Christian H. Bischof and H. Martin B{\"u}cker and an Mey, Dieter",
       title = "A Case Study of Computational Differentiation Applied to Neutron Scattering",
       pages = "69--74",
       chapter = "6",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       abstract = "In a neutron scattering application, an unconstrained nonlinear minimization
         problem is used for the fitting of model parameters to experimental data. Automatic differentiation
         enables, in a completely mechanical fashion, algorithmic changes by switching from a quasi-Newton
         method, where first order derivatives are approximated by finite differences, to a modified
         Gauss--Newton method using exact first order derivatives. Compared to the original code, the code
         generated by this black box approach produces reliable results rather than results of dubious
         quality. This approach also is faster in terms of execution time. Its performance is improved
         further by replacing the most time-consuming subroutine involved in the derivative evaluation by a
         surprisingly simple, hand-coded implementation of the corresponding analytic expression.",
       referred = "[Klein2002DMf].",
       ad_area = "Chemistry",
       ad_tools = "ADIFOR",
       ad_theotech = "Integration of Analytic Derivatives"
}


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