A Variational Approach to Parameter Estimation in Ordinary Differential Equations

Details A Variational Approach to Parameter Estimation in Ordinary Differential Equations A Variational Approach to Parameter Estimation in Ordinary Differential Equations

2011-10-07

arxiv.org/abs/1110.1516v1

Biology

Quantitative Biology

Molecular Networks

Scientific paper

Ordinary differential equations are widely-used in the field of systems biology and chemical engineering to model chemical reaction networks. Numerous techniques have been developed to estimate parameters like rate constants, initial conditions or steady state concentrations from time-resolved data. In contrast to this countable set of parameters, the estimation of entire courses of network components corresponds to an innumerable set of parameters. The approach presented in this work is able to deal with course estimation for extrinsic system inputs or intrinsic reactants, both not being constrained by the reaction network itself. Our method is based on variational calculus which is carried out analytically to derive an augmented system of differential equations including the unconstrained components as ordinary state variables. Finally, conventional parameter estimation is applied to the augmented system resulting in a combined estimation of courses and parameters.

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