Computational Challenges in Sampling and Representation of Uncertain Reaction Kinetics in Large Dimensions

Abstract

This work focuses on constructing functional representations of quantities of interest (QoIs) of an uncertain system in high dimension. Attention is focused on the ignition delay time of an iso-octane air mixture, using a detailed chemical mechanism with 3,811 elementary reactions. Uncertainty in all reaction rates is directly accounted for using associated uncertainty factors, assuming independent log-uniform priors. A Latin hypercube sample (LHS) of the ignition delay times was first generated, and the resulting database was then exploited to assess the possibility of constructing polynomial chaos (PC) representations in terms of the canonical random variables parametrizing the uncertain rates. We explored two avenues, namely sparse regression (SR) using LASSO, and a coordinate transform (CT) approach. Preconditioned variants of both approaches were also considered, namely using the logarithm of the ignition delay time as QoI. Both approaches resulted in representations of the ignition delay with similar representation errors. However, the CT approach was able to reproduce better the empirical distribution of the underlying LHS ensemble, and also preserved the positivity of the ignition delay time. When preconditioned representations were considered, however, similar performances were obtained using CT and SR representations. The results also revealed that both the CT and SR representations yield consistent global sensitivity estimates. The results were finally used to test a reduced dimension representation, and to outline potential extensions of the work.