468307 A Mixed-Integer Formulation for Online Design of Model Discrimination Experiments
The design of dynamic experiments aims to maximize the information gained about the structure (for model discrimination) and parameters (for parameter estimation) of the system under consideration. This goal is typically formulated in terms of optimizing a metric of the Fisher information matrix (equivalent to minimizing the parameter covariance matrix) by changing the experimental set-up and conditions   . Several metrics have been explored for parameter estimation purposes  : the determinant (D-optimal design) minimizing the volume of the joint confidence region, the smallest eigenvalue (E-optimal design) minimizing the size of the largest axis, the trace (A-optimal design), minimizing the average axis, etc.
The design of dynamic experiments for model discrimination has fewer options, with most designs requiring a set of model candidates as a starting point. The experiment is then designed to maximize the difference between model predictions at the sampled points  . Model discrimination and parameter estimation criteria have also been combined by summing the two weighted objective functions for an experimental design that includes both objectives . Previous results have generally been reported for discrimination between alternate models, where the true solution is one of the candidate models.
In this work, we propose a new dynamic DoE approach, whereby we represent the (unknown) model as a combination of submodels  using binary variables to determine whether the submodels contribute to the final model structure. We examine the formulation of the optimal DoE problem for this new class of models using Fisher information matrix criteria, focusing on both model discrimination and parameter estimation. Further, we extend this approach with an online adaptation strategy, with the goal of accelerating the convergence of parameter estimates  .
We illustrate our results with a set of case studies concerning, i) model discrimination for a bioreactor (where we compare our results with previous literature), and ii) the identification of the mechanism and parameters of a complex reaction system under constraints related to avoiding undesirable side reactions throughout the experimental plan.
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