Combination of polynomial chaos and Kriging for reduced-order model of reacting flow applications

The combination of Proper Orthogonal Decomposition (POD) with Kriging has been shown to be a reliable choice for the development of Reduced-Order Models (ROMs) for the prediction of combustion data at unexplored operating conditions. In this study, POD is combined with Polynomial Chaos Expansion (PCE), with a combination of PCE and Kriging (PC-Kriging) and with Artificial Neural Networks (ANN) for the development of a ROM that can predict 2D combustion data for unexplored operating conditions. The choice of Non-negative Matrix Factorization (NMF) instead of POD as compression method is also investigated. This method is chosen because it can intrinsically guarantee the non-violation of physical constraints such as positivity of chemical species mass fractions, although POD's data reconstruction errors are lower. The performances of the POD and NMF in combination with the proposed supervised methods are compared, with prediction normalized root mean squared errors (NRMSE) being less than 10% for spatial fields of temperature, CH4 and O2 for all approaches. •POD and NMF are combined with a combination of Polynomial Chaos Expan-sion (PCE) and Kriging for a Reduced-Order Model (ROM) of combustion data.•POD and NMF are also combined with PCE only and Kriging only.•POD reconstructed the training data with a lower error than NMF, but NMF guaranteed that physical quantities are not reconstructed with negative values.•PC-Kriging performed with lower prediction errors than Kriging for smaller training sizes and for low approximation orders.•POD combined with PC-Kriging had lower prediction errors with respect to the combination of POD and ANN.