Parameter Range Reduction in Ordinary Differential Equation Models

This paper presents an algorithm for parameter range reduction in systems of ordinary differential equations. Parameter values are assumed only to be known to lie in potentially large regions of parameter space. Interval arithmetic and a family of monotonic discretizations are used to prune regions of parameter space that are inconsistent with given time series data. The algorithm is tested on two ordinary differential equation models and the reduced ranges are shown to significantly improve the performance of traditional parameter estimation methods.