Efficient regularization and uncertainty analysis using a global optimization methodology

The concept of the Pareto front has received considerable attention in the model calibration literature, particularly in conjunction with global search optimizers that have been developed for use in contexts where objective function surfaces are pitted with local optima or characterized by multiple broad regions of attraction in parameter space. In this paper, use of the Pareto concept in such calibration contexts is extended to include regularization and model predictive uncertainty analysis. Both of these processes can be formulated as constrained optimization problems in which a trade-off is analyzed between a set of constraints on model parameters on the one hand and maximization/minimization of one or a number of model outputs of interest on the other hand. In both cases, the optimal trade-off point, though being calculable on a theoretical basis for synthetic cases, must be chosen subjectively when working with real-world models. Two cases are presented to illustrate the methodology: one a synthetic groundwater model and the other a real-world surface water model.