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

Abstract: A high-ranking goal of interdisciplinary modeling approaches in the natural sciences are quantitative prediction of system dynamics and model based optimization. For this purpose, mathematical modeling, numerical simulation and scientific computing techniques are indispensable. Quantitative modeling closely combined with experimental investigations is required if the model is supposed to be used for sound mechanistic analysis and model predictions. Typically, before an appropriate model of a experimental system is found different hypothetical models might be reasonable and consistent with previous knowledge and available data. The parameters of the model up to an estimated confidence region are generally not known a priori. Therefore one has to incorporate possible parameter configurations of different models into a model discrimination algorithm. In this article we present a numerical algorithm which calculates a design of experiments which allows an optimal discrimination of different hypothetic candidate models of a given dynamic system for the most inappropriate parameter configurations within a parameter range via a worst case estimate. The design criterion comprises optimal measurement time points. The used criterion is derived from the Kullback-Leibler divergence. The underlying optimization problem can be classified as a semi infinite optimization problem which we solve in an outer approximation approach stabilized by a homotopy strategy. We present the theoretical framework as well as the numerical algorithmic realization.