The promise and peril of uncertainty quantification using response surface approximations

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Abstract
Conventional sampling-based uncertainty quantification (UQ) methods involve generating large numbers of random samples on input variables and calculating output statistics by evaluating the computational model for each set of samples. For real world applications, this method can be computationally prohibitive due to the cost of the model and the time required for each simulation run. Using response surface approximations may allow for the output statistics to be estimated more accurately when only a limited number of simulation runs are available. This paper describes an initial investigation into response surface based UQ using both kriging and multivariate adaptive regression spline surface approximation methods. In addition, the impact of two different data sampling methods, Latin hypercube sampling and orthogonal array sampling, is also examined. The data obtained from this study indicate that caution should be exercised when implementing response surface based methods for UQ using very low sample sizes. However, this study also shows that there are clear cases where response surface based UQ provides a gain in accuracy versus conventional sampling-based UQ methods.