Deterministic methods for sensitivity and uncertainty analysis in large-scale computer models

The fields of sensitivity and uncertainty analysis have traditionally been dominated by statistical techniques when large-scale modeling codes are being analyzed. These methods are able to estimate sensitivities, generate response surfaces, and estimate response probability distributions given the input parameter probability distributions. Because the statistical methods are computationally costly, they are usually applied only to problems with relatively small parameter sets. Deterministic methods, on the other hand, are very efficient and can handle large data sets, but generally require simpler models because of the considerable programming effort required for their implementation. The first part of this paper reports on the development and availability of two systems, GRESS and ADGEN, that make use of computer calculus compilers to automate the implementation of deterministic sensitivity analysis capability into existing computer models. This automation removes the traditional limitation of deterministic sensitivity methods. The second part of the paper describes a Deterministic sensitivity methods. The second part of the paper describes a Deterministic Uncertainty Analysis (DUA) method that uses derivative information as a basis to propagate parameter probability distributions to obtain result probability distributions. The last part of the paper demonstrates the deterministic approach to sensitivity and uncertainty analysis as applied to a sample problem that models the flow of water through a borehole