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Parameter Estimation and Optimum Experimental Design for Differential Equation Models

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Book cover Model Based Parameter Estimation

Part of the book series: Contributions in Mathematical and Computational Sciences ((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.

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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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Authors and Affiliations

  1. Interdisciplinary Center for Scientific Computing, Heidelberg University, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Hans Georg Bock, Stefan Körkel & Johannes P. Schlöder

Authors
  1. Hans Georg Bock
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  2. Stefan Körkel
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  3. Johannes P. Schlöder
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Corresponding author

Correspondence to Stefan Körkel .

Editor information

Editors and Affiliations

  1. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Hans Georg Bock

  2. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 294, Heidelberg, 69120, Germany

    Thomas Carraro

  3. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Willi Jäger

  4. Interdisciplinary Center for, Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Stefan Körkel

  5. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Johannes P. Schlöder

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Bock, H.G., Körkel, S., Schlöder, J.P. (2013). Parameter Estimation and Optimum Experimental Design for Differential Equation Models. In: Bock, H., Carraro, T., Jäger, W., Körkel, S., Rannacher, R., Schlöder, J. (eds) Model Based Parameter Estimation. Contributions in Mathematical and Computational Sciences, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30367-8_1

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