A robust optimization approach to experimental design for model discrimination of dynamical systems

摘要

A high-ranking goal of interdisciplinary modeling approaches in the naturalsciences are quantitative prediction of system dynamics and model basedoptimization. For this purpose, mathematical modeling, numerical simulation andscientific computing techniques are indispensable. Quantitative modelingclosely combined with experimental investigations is required if the model issupposed to be used for sound mechanistic analysis and model predictions.Typically, before an appropriate model of a experimental system is founddifferent hypothetical models might be reasonable and consistent with previousknowledge and available data. The parameters of the model up to an estimatedconfidence region are generally not known a priori. Therefore one has toincorporate possible parameter configurations of different models into a modeldiscrimination algorithm. In this article we present a numerical algorithmwhich calculates a design of experiments which allows an optimal discriminationof different hypothetic candidate models of a given dynamic system for the mostinappropriate parameter configurations within a parameter range via a worstcase estimate. The design criterion comprises optimal measurement time points.The used criterion is derived from the Kullback-Leibler divergence. Theunderlying optimization problem can be classified as a semi infiniteoptimization problem which we solve in an outer approximation approachstabilized by a homotopy strategy. We present the theoretical framework as wellas the numerical algorithmic realization.