  We develop a systematic approach for surrogate model construction in reduced
input parameter spaces. A sparse set of model evaluations in the original input
space is used to approximate derivative based global sensitivity measures
(DGSMs) for individual uncertain inputs of the model. An iterative screening
procedure is developed that exploits DGSM estimates in order to identify the
unimportant inputs. The screening procedure forms an integral part of an
overall framework for adaptive construction of a surrogate in the reduced
space. The framework is tested for computational efficiency through an initial
implementation in simple test cases such as the classic Borehole function, and
a semilinear elliptic PDE with a random source term. The framework is then
deployed for a realistic application from chemical kinetics, where we study the
ignition delay in an H2/O2 reaction mechanism with 19 uncertain rate constants.
It is observed that significant computational gains can be attained by
constructing accurate low-dimensional surrogates using the proposed framework.
