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

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.