Parameter Set Selection for Dynamic Systems under Uncertainty via Dynamic Optimization and Hierarchical Clustering

Dynamic models often contain adjustable parameters that are not precisely known prior to estimation. It is common that only a subset of these parameters can be accurately estimated because of correlations between parameters, the structure of the model, and the limited availability of experimental data. One approach for identifying a subset of parameters for estimation is to perform clustering of the parameters into groups based upon their sensitivity vectors. However, this has the drawback that uncertainty cannot be directly incorporated into the procedure as the sensitivity vectors are based upon the nominal values of the parameters. This paper addresses this challenge by presenting a parameter set selection technique that can take uncertainty in the parameter space into account. This is achieved by defining sensitivity cones, where a sensitivity cone includes all sensitivity vectors of a parameter for different values, resulting from the uncertainty, in the parameter space. Parameter clustering can then be performed based upon the angles between the sensitivity cones, instead of the angle between sensitivity vectors. One of the challenges of this approach is related to computation of the sensitivity cones, which is performed via dynamic optimization in this work, in order to allow application of the technique to systems with a large number of parameters. The presented technique is applied to two case studies: a CSTR model and a signal transduction pathway model.