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Parameter Estimation for High-Dimensional PDE Models Using a Reduced Approach

  • Robert Kircheis
  • Stefan Körkel
Conference paper
Part of the Contributions in Mathematical and Computational Sciences book series (CMCS, volume 9)

Abstract

Partial differential equations (PDE) are indispensable to describe complex processes. PDE constrained parameter estimation is still a prevailing topic of research. The increase in computation time with increasing complexity of the problem is one of the main problems. With the application of multiple shooting, the number of required derivatives for the generalized Gauss–Newton method rises rapidly. We introduce a method to overcome this challenge. By using directional derivatives the computational effort can be reduced to the minimal number. We demonstrate our methods with help of the heat equation.

Keywords

Newton Method Multiple Shooting Partial Differential Equation Differential Algebraic Equation Parameter Estimation Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Financial support by BASF SE and HGS MathComp is gratefully acknowledged.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.IWR HeidelbergHeidelberg UniversityHeidelbergGermany

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