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Parameter Range Reduction in Ordinary Differential Equation Models

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Abstract

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.

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Acknowledgments

This work was supported by an Ontario Graduate Scholarship, a Natural Sciences and Engineering Council of Canada (NSERC) Postgraduate Scholarship and a NSERC Discovery Grant.

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  1. University of Guelph, Guelph, ON , N1G 2W1, Canada

    Andrew Skelton & Allan R. Willms

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  1. Andrew Skelton
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  2. Allan R. Willms
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Correspondence to Andrew Skelton.

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Skelton, A., Willms, A.R. Parameter Range Reduction in Ordinary Differential Equation Models. J Sci Comput 62, 517–531 (2015). https://doi.org/10.1007/s10915-014-9865-6

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  • DOI: https://doi.org/10.1007/s10915-014-9865-6

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