A co-kurtosis PCA based dimensionality reduction with neural network reconstruction for chemical kinetics in reacting flows*

Identifying low-dimensional manifolds (LDMs) to represent the thermo-chemical state in reacting flows is crucial for significantly reducing the computational cost. The widely used principal component analysis (PCA) achieves this by obtaining an eigenvector basis for the LDM through an eigenvalue decomposition of the data covariance matrix. However, recent studies have revealed that PCA is not very sensitive to extreme-valued samples representing stiff chemical dynamics in spatiotemporally localized reaction zones. An alternative technique that focuses on higher-order joint statistical moments, co-kurtosis PCA (CoK-PCA), has demonstrated remarkable accuracy in capturing stiff chemical dynamics. However, the effectiveness of the CoK-PCA method has been comparatively assessed with PCA only in an a priori setting with a linear reconstruction method. In this work, we employ a nonlinear artificial neural network (ANN) based technique for reconstructing the original thermo-chemical state and evaluate the quality of the CoK-PCA LDM compared to PCA. Results from the a priori analyses of different datasets, which include a two-stage auto-ignition of dimethyl ether-air mixture, demonstrate the robustness of the CoK-PCA-ANN approach in accurately capturing the overall thermo-chemistry.