Abstract
Parameter estimation in ordinary differential equations, although applied and refined in various fields of the quantitative sciences, is still confronted with a variety of difficulties. One major challenge is finding the global optimum of a log-likelihood function that has several local optima, e.g. in oscillatory systems. In this publication, we introduce a formulation based on continuation of the log-likelihood function that allows to restate the parameter estimation problem as a boundary value problem. By construction, the ordinary differential equations are solved and the parameters are estimated both in one step. The formulation as a boundary value problem enables an optimal transfer of information given by the measurement time courses to the solution of the estimation problem, thus favoring convergence to the global optimum. This is demonstrated explicitly for the fully as well as the partially observed Lotka-Volterra system.
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Acknowledgements
This work was supported by the MIP-DILI project, Innovative Medicines Initiative Joint Undertaking under grant agreement No. 115336. We thank our colleague Marcus Rosenblatt for supporting the computational implementation.
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Kaschek, D., Timmer, J. (2015). A Unified Approach to Integration and Optimization of Parametric Ordinary Differential Equations. In: Carraro, T., Geiger, M., Körkel, S., Rannacher, R. (eds) Multiple Shooting and Time Domain Decomposition Methods. Contributions in Mathematical and Computational Sciences, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-23321-5_12
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DOI: https://doi.org/10.1007/978-3-319-23321-5_12
Publisher Name: Springer, Cham
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