Fighting the Curse of Dimensionality: A Method for Model Validation and Uncertainty Propagation for Complex Simulation Models.

This dissertation develops a method for analyzing a parameterized simulation model in conjunction with experimental data obtained from the physical system the model is thought to describe. Two questions are considered: Is the model compatible with the data so as to indicate its validity? Given the experimental data, what does the model predict about a given system property of interest when the uncertainty in the data is propagated through the model? The each of these questions is formulated as a constrained optimization problem. Experimental data and their associated uncertainties are used to develop inequality constraints on the parameter vector of the model. Similarly, prior information on plausible values of the model parameters is incorporated as additional constraints. Using constraints to describe the data readily enables the integration of diverse, heterogeneous data which may have arisen from multiple sources by the combination of constraints that describe each piece of data. This aspect has led us to adopt the name Data Collaboration for the collection of ideas described in this dissertation. The optimization framework implicitly considers the ensemble of parameter values that are compatible with the given data. This enables the implications of the model to be explored without explicit consideration of parameter values. In particular, an intermediate step of parameter estimation is not required. The chief difficulty in the proposed approach is that constrained optimization problems are highly difficult to solve in the general case. Hence a technique is developed to over- and under-estimate the optimal value of an optimization. To develop these estimates, the objective and constraint functions are approximated. Consequently some rigor is sacrificed. The investigation of three real-world examples shows the approach is potentially applicable to complex simulation models featuring a high-dimensional parameter space. In the first example a methane combustion model with more than 100 uncertain parameters is invalidated. The procedure identifies two major data outliers, which were corrected upon reexamination of the raw experimental data. The model passes the validation test with these corrected data. Models for two cellular signaling phenomena are also studied. These respectively involve 9 and 27 uncertain parameters.