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Parameter Estimation and Optimum Experimental Design for Differential Equation Models

  • Hans Georg Bock
  • Stefan Körkel
  • Johannes P. Schlöder
Chapter
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 4)

Abstract

This article reviews state-of-the-art methods for parameter estimation and optimum experimental design in optimization based modeling. For the calibration of differential equation models for nonlinear processes, constrained parameter estimation problems are considered. For their solution, numerical methods based on the boundary value problem method optimization approach consisting of multiple shooting and a generalized Gauß–Newton method are discussed. To suggest experiments that deliver data to minimize the statistical uncertainty of parameter estimates, optimum experimental design problems are formulated, an intricate class of non-standard optimal control problems, and derivative-based methods for their solution are presented.

Keywords

Gauß–Newton method Multiple shooting Nonlinear differential-algebraic equations Optimum experimental design Parameter estimation Variance–covariance matrix 

Notes

Acknowledgements

The authors want to thank DFG for providing excellent research conditions within the Heidelberg Graduate School of Mathematical and Computational Methods for the Sciences. S. Körkel wants to thank BASF SE for funding his position and parts of his research group. Additional funding is granted by the German Federal Ministry for Education and Research within the initiative Mathematik für Innovationen in Industrie und Dienstleistungen.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Hans Georg Bock
    • 1
  • Stefan Körkel
    • 1
  • Johannes P. Schlöder
    • 1
  1. 1.Interdisciplinary Center for Scientific ComputingHeidelberg UniversityHeidelbergGermany

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