Derivation of Physically Motivated Constraints for Efficient Interval Simulations Applied to the Analysis of Uncertain Models of Blood Cell Dynamics
M. Freihold (University of Ulm, Germany), A. Rauh (University of Ulm, Germany) and E.P. Hofer (University of Ulm, Germany)
Interval arithmetic techniques such as ValEncIA-IVP allow to calculate guaranteed enclosures of all reachable states of dynamical systems under consideration of bounded uncertainties of both initial conditions and system parameters. Considering the fact that in naive implementations of interval algorithms, overestimation might lead to unnecessarily conservative results, suitable consistency tests are essential for obtaining tightest possible enclosures. In this contribution, a general framework for the use of constraints based on physically motivated conservation properties is presented. The application of such constraints in consistency tests is presented for a high-dimensional model of granulocytopoiesis in human blood cell dynamics.