  For turbulent reacting flows, identification of low-dimensional
representations of the thermo-chemical state space is vitally important,
primarily to significantly reduce the computational cost of device-scale
simulations. Principal component analysis (PCA), and its variants, is a widely
employed class of methods. Recently, an alternative technique that focuses on
higher-order statistical interactions, co-kurtosis PCA (CoK-PCA), has been
shown to effectively provide a low-dimensional representation by capturing the
stiff chemical dynamics associated with spatiotemporally localized reaction
zones. While its effectiveness has only been demonstrated based on a priori
analysis with linear reconstruction, in this work, we employ nonlinear
techniques to reconstruct the full thermo-chemical state and evaluate the
efficacy of CoK-PCA compared to PCA. Specifically, we combine a CoK-PCA/PCA
based dimensionality reduction (encoding) with an artificial neural network
(ANN) based reconstruction (decoding) and examine a priori the reconstruction
errors of the thermo-chemical state. In addition, we evaluate the errors in
species production rates and heat release rates that are nonlinear functions of
the reconstructed state as a measure of the overall accuracy of the
dimensionality reduction technique. We employ four datasets to assess
CoK-PCA/PCA coupled with ANN-based reconstruction: a homogeneous reactor for
autoignition of an ethylene/air mixture that has conventional single-stage
ignition kinetics, a dimethyl ether (DME)/air mixture which has two-stage
ignition kinetics, a one-dimensional freely propagating premixed ethylene/air
laminar flame, and a two-dimensional homogeneous charge compression ignition of
ethanol. The analyses demonstrate the robustness of the CoK-PCA based
low-dimensional manifold with ANN reconstruction in accurately capturing the
data, specifically from the reaction zones.
