Description

In systems with oscillatory behavior, the well-known least-squares objective function of a parameter estimation problem may have local minima, at least along certain directions in the parameter space. In this software practical, the Lotka Volterra equations shall be used as a simple model for predator-prey population dynamics. The Lotka Volterra model is known to show oscillatory behaviour and is thus well-suited for the study of local minima of parameter estimation problems.

The goal of the practical is to find local minima of the objective function of the parameter estimation problem for the Lotka Volterra system and to check whether or not the Gauss-Newton method is attracted by these minima.

Tasks

Preparation (preferably to be done in MATLAB)

• Generation of simulated measurement data for a reference parameter set and visualization of the objective function of the parameter estimation problem
• Investigation of the influence of measurement error and the number of measurement quantities

Main Part

• Implementation of the parameter estimation problem in PARFIT
• Check whether the local minima are attractive to the Gauss-Newton method in the single shooting mode of PARFIT
• Application of PARFIT in multiple shooting mode to the same test problem

Completion

• Written report and talk in the seminar of the SimOpt working group

Focus

Parameter estimation, usage of PARFIT

Size of the project

The project is suited as an advanced practical for one or two students or as a combined beginners and advanced practical for one student.

Requirements

• Knowledge on parameter estimation problems in dynamic systems (Num2 lecture)
• Programming skills in Fortran or C (on the level of Num1 or Num2 lecture)

Remarks

• Lacking knowledge concerning theory, programming skills and LaTeX (for the written report) may cause the workload to exceed 80h.
• The practical must be finished six month after the beginning.

Contact

Dipl.-Phys. Simon Lenz
Interdisciplinary Center for Scientific Computing (IWR)
Im Neuenheimer Feld 368
Universität Heidelberg

e-mail: simon.lenz@iwr.uni-heidelberg.de
Room : INF 368 (IWR), R 412