Modelica based computational tools for sensitivity analysis via automatic differentiation

• Modelica-basierte rechenbetonte Werkzeuge für Sensitivitätsanalyse durch automatisches Differenzieren

Elsheikh, Atiyah Mohamed Gamal; Naumann, Uwe (Thesis advisor)

Aachen : Publikationsserver der RWTH Aachen University (2012, 2014)
Dissertation / PhD Thesis

Aachen, Techn. Hochsch., Diss., 2012

Abstract

This work is mainly concerned with sensitivity analysis of DAE-based models described by the modern object-oriented modeling language Modelica. In this context, an automatic differentiation tool named as ADModelica is presented. It fully employs Modelica-based compiler techniques forming a new automatic differentiation approach for non-causal equation-based languages. Already existing open-source compiler tools are utilized for reducing implementation efforts. A generated output model efficiently represents a sensitivity equation system by which parameter sensitivities can be simulated using any existing Modelica simulation environment. The resulting tool has been successfully applied on high-level Modelica models in the field of Systems Biology. In benchmark examples, the performance of the generated models are better than applying common finite difference methods in terms of accuracy and runtime performance. Moreover, the representation of these models permits the exploitation of structural characteristics of sensitivity equation systems for significantly improved runtime performance on supercomputer clusters.Using ADModelica, several sensitivity analysis application studies of computationally, algorithmically and technically challenging nature have been performed towards the realization of stable efficient parameter estimation process of large and badly-scaled dynamical models. These studies cover among others: • The examination of several global multistart optimization methods w.r.t. results quality and implementation efforts, in particular the design of new derivative-based hybrid heuristic strategies• The determination of confidence regions of model parameters via identifiability analysis techniques based on linearized statistics and Monte Carlo bootstrap methods.Within this work furtherModelica-based both domain-dependent and domain-independent computational tools have been implemented such as:• A compact Modelica library for simplified kinetics for modeling complex reaction systems through which model families can be easily specified• A tool for visualizing scaled parameter sensitivities within a supervised master thesis • A Modelica-based editor for modeling biochemical reaction networks within a collaborative work with collegesFinally, this thesis also covers theoretical studies concerning the differential and the structural index of a DAE system and the corresponding sensitivity equation system with an interesting mathematically proven conclusion about their relationship.