Parameter estimation with (almost) deterministic global optimization

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Computer-aided process systems engineering supports the industrial and medical sector by predicting real-world processes based on mathematical models. These models require parameter estimation and only deterministic global optimization allows to conclude on the suitability of the model. However, comparatively small problems are already challenging for existing general-purpose deterministic solvers. Thus, we want to develop a(n) (almost) deterministic global optimization approach with large data sets. We exploit the similarities between a simpler estimation problem based on a subset of the data and the complete estimation problem to decrease the overall computational burden. In detail, we propose to use the simple problem for the lower bounding within the branch-and-bound method for solving the complete problem. Whenever required, we adapt the size of the simple problem by a data augmentation step. Since single data points may affect the global solution, our proposed approach can be deterministic only with respect to a certain confidence level. We envision the parameter estimation for more complex applications ranging from reaction kinetics of industry-relevant processes to the spread of an infectious disease. Besides, our methodology can be applied by software tools of other groups, too.