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We focus on an efficient approach for quantification of uncertainty in complex chemical reaction networks with a large number of uncertain parameters and input conditions. Parameter dimension reduction is accomplished by computing an active subspace that predominantly captures the variability in the quantity of interest (QoI). In the present work, we compute the active subspace for a H2/O2 mechanism that involves 19 chemical reactions, using an efficient iterative strategy. The active subspace is first computed for a 19-parameter problem wherein only the uncertainty in the pre-exponents of the individual reaction rates us considered. This is followed by the analysis of a 36-dimensional case wherein the activation energies and initial conditions are also considered uncertain. In both cases, a 1-dimensional active subspace is observed to capture the uncertainty in the QoI, which indicates enormous potential for efficient statistical analysis of complex chemical systems. In addition, we explore links between active subspaces and global sensitivity analysis, and exploit these links for identification of key contributors to the variability in the model response. 

Surrogate modeling has become a critical component of scientific computing in situationsinvolving expensive model evaluations. However, training a surrogate model can be remark-ably challenging and even computationally prohibitive in the case of intensive simulationsand large-dimensional systems. We develop a systematic approach for surrogate model con-struction in reduced input parameter spaces. A sparse set of model evaluations in the originalinput space is used to approximate derivative based global sensitivity measures (DGSMs)for individual uncertain inputs of the model. An iterative screening procedure is developedthat exploits DGSM estimates in order to identify theunimportantinputs. The screeningprocedure forms an integral part of an overall framework for adaptive construction of a sur-rogate in the reduced space. The framework is tested for computational efficiency throughan initial implementation in simple test cases such as the classic Borehole function, and asemilinear elliptic PDE with a random source function. The framework is then deployed fora realistic application from chemical kinetics, where we study the ignition delay in an H2/O2reaction mechanism with 19 and 33 uncertain rate-controlling parameters. It is observed thatsignificant computational gains can be attained by constructing accurate low-dimensionalsurrogates using the proposed framework.