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Parameter Estimation and Optimal Experiment Design for Nonlinear Transport in Degradation Processes of Xenobiotics in Soil
Georg Bock
bock@iwr.uni-heidelberg.de
IWR University of Heidelberg, Germany
Joint work with A. E. Dieses, J. P. Schloeder, O. Richter.The environmental fate of xenobiotics in soil is influenced by a number of processes including degradation, sorption and volatilisation. Mathematical modelling of these transport reaction systems leads to instationary partial differential equations coupled with nonlinear ODE. Optimization problems occur in the estimation of hydraulic, transport and degradation parameters as well as in highly complex optimal control problems to determine best experiments in terms of costs and identifiability. We present algorithms and software for an effective solution of such problems, which are based on a spatial discretization of the PDE (method of lines) and a multiple shooting discretization in time. The resulting large structured optimization problems are solved by specially tailored reduced Gauss-Newton and SQP methods which minimize the number of necessary directional derivatives to be computed. Real life applications to pesticide experiments are given.
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