Interval Based Parameter Identification for System Biology
Mohsen Alami · KTH Publication Database DiVA (KTH Royal Institute of Technology) · 2012
This master thesis studies the problem of parameter identification for system biology. Two methods have been studied. The method of interval analysis uses subpaving as a class of objects to manipulate and store inner and outer approximations of compact sets. This method works well with the model given as a system of differential equations, but has its limitations, since the analytical expression for the solution to the ODE is not always obtainable, which is needed for constructing the inclusion function. The other method, studied, is SDP-relaxation of a nonlinear and non-convex feasibility problem. This method, implemented in the toolbox bio.SDP, works with system of difference equations, obtained using the Euler discretization method. The discretization method is not exact, raising the need of bounding this discretization error. Several methods for bounding this error has been studied. The method of ∞-norm optimization, also called worst-case-∞-norm is applied on the one-step error estimation method. The methods have been illustrated solving two system biological problems and the resulting SCP have been compared.