Publication: Automatic Sensitivity Analysis of DAE-systems Generated from Equation-Based Modeling Languages
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Automatic Sensitivity Analysis of DAE-systems Generated from Equation-Based Modeling Languages

- incollection -
 

Area
Differential-Algebraic Equation

Author(s)
Atya Elsheikh , Wolfgang Wiechert

Published in
Advances in Automatic Differentiation

Editor(s)
Christian H. Bischof, H. Martin Bücker, Paul D. Hovland, Uwe Naumann, J. Utke

Year
2008

Publisher
Springer

Abstract
This paper aims at sensitivity analysis of differential algebraic equation (DAE) systems, generated from mathematical models, specified in equation-based modeling languages. Modern simulation languages (e.g. Modelica) use an equation-based syntax enriched by facilities for object-oriented modeling, hierarchical system decomposition and code reuse in libraries. Sophisticated compiler tools exist for generating efficient run-time code from a given model specification. These tools rely on powerful algorithms for code optimization and equations rearrangement. Particularly, automatic differentiation (ad) is already used, though for the different task of DAE- index reduction. Clearly, the mentioned facilities should be exploited as far as possible in a new ad tool for sensitivity analysis. In this paper, three possible levels at which ad can be applied are discussed. These are given by ad on run time code, flat model and library level. Then the new source-to-source ad tool (ADModelica) is introduced which takes the second approach. Particularly, it is shown that there are several differences between ad methods for classical procedural languages and equation-based modeling languages.

Cross-References
Bischof2008AiA

BibTeX
@INCOLLECTION{
         Elsheikh2008ASA,
       author = "Atya Elsheikh and Wolfgang Wiechert",
       title = "Automatic Sensitivity Analysis of {DAE}-systems Generated from Equation-Based Modeling
         Languages",
       doi = "10.1007/978-3-540-68942-3_21",
       pages = "235--246",
       abstract = "This paper aims at sensitivity analysis of differential algebraic equation (DAE)
         systems, generated from mathematical models, specified in equation-based modeling languages. Modern
         simulation languages (e.g. Modelica) use an equation-based syntax enriched by facilities for
         object-oriented modeling, hierarchical system decomposition and code reuse in libraries.
         Sophisticated compiler tools exist for generating efficient run-time code from a given model
         specification. These tools rely on powerful algorithms for code optimization and equations
         rearrangement. Particularly, automatic differentiation (AD) is already used, though for the
         different task of DAE- index reduction. Clearly, the mentioned facilities should be exploited as far
         as possible in a new AD tool for sensitivity analysis. In this paper, three possible levels at which
         AD can be applied are discussed. These are given by AD on run time code, flat model and library
         level. Then the new source-to-source AD tool (ADModelica) is introduced which takes the second
         approach. Particularly, it is shown that there are several differences between AD methods for
         classical procedural languages and equation-based modeling languages.",
       crossref = "Bischof2008AiA",
       booktitle = "Advances in Automatic Differentiation",
       publisher = "Springer",
       editor = "Christian H. Bischof and H. Martin B{\"u}cker and Paul D. Hovland and Uwe
         Naumann and J. Utke",
       isbn = "978-3-540-68935-5",
       issn = "1439-7358",
       year = "2008",
       ad_area = "Differential-Algebraic Equation"
}


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