Uncertainty Evaluation Through Mapping Identification in Intensive Dynamic Simulations

We study how the dependence of a simulation output on an uncertain parameter can be determined when simulations are computationally expensive and so can only be run for very few parameter values. Specifically, the methodology that is developed-known as the probabilistic collocation method (PCM)-permits selection of these few parameter values, so that the mapping between the parameter and the output can be approximated well over the likely parameter values, using a low-order polynomial. Several new analyses are developed concerning the ability of PCM to predict the mapping structure, as well as output statistics. A holistic methodology is also developed for the typical case where the uncertain parameter's probability distribution is unknown, and instead, only depictive moments or sample data (which possibly depend on known regressors) are available. Finally, the application of PCM to weather-uncertainty evaluation in air traffic flow management is discussed.