Simultaneous optimization and uncertainty quantification

• Authors: Genetha A. Gray;Herbert K. H. Lee;John Guenther
• Venue: Journal of Computational Methods in Sciences and Engineering - Special issue on Advances in Simulation-Driven Optimization and Modeling
• Year: 2012

Optimization is often used to perform model calibration, the process of inferring the values of model parameters so that the results of the simulations best match observed behavior. It can both improve the predictive capability of the model and curtail the loss of information caused by using a numerical model instead of the actual system. At its heart is the comparison of experimental data and simulation results. Complicating this comparison is the fact that both data sets contain uncertainties which must be quantified in order to make reasonable comparisons. Therefore, uncertainty quantification (UQ) techniques can be applied to identify, characterize, reduce, and, if possible, eliminate uncertainties. Incorporation of UQ into the calibration process can drastically improve the usefulness of computational models. Current approaches are serial approaches in that first, the calibration parameters are identified and then, a series of runs dedicated to UQ analysis is completed. Although this approach can be effective, it can be computationally expensive or produce incomplete results. Model analysis that takes advantage of intermediate optimization iterates can reduce the expense, but the sampling done by the optimization algorithms is not ideal. In this paper, we will review serial approaches and propose a joint calibration and UQ approach that combines Bayesian statistical models and derivative-free optimization in order to monitor sensitivity information throughout the calibration process.