Hybrid Unsupervised Cluster-wise Regression Approach for Representing the Flamelet Tables

A novel hybrid unsupervised cluster-wise regression approach is developed to represent the flamelet tables and speed up the computations in turbulent combustion simulations. The proposed machine learning method utilizes a cluster-wise regression technique where specialized deep neural networks are trained on different parts of the input space. A new recursive unsupervised clustering (RUC) approach is proposed that leads to a lower root-mean-square error by over 30% and improves the individual cluster's mean absolute error by over 20%. The RUC approach enables identifying different combustion manifolds within the input space. The regression models unique to these identified manifolds accurately capture the thermo-chemical scalars for the given input data set. To balance the tradeoffs between the accuracy of flamelet table predictions and the complexities of the RUC algorithm, a hybrid model is introduced that switches between a single neural network (SNN) which is a single regression model, and the SUC RUC approaches. The hybrid unsupervised cluster-wise-regression model benefits from the lower computational costs of SNN for parts of the input space where the SNN prediction error is low and switches to the unsupervised clustering models, that is, standard (SUC) and recursive (RUC) in areas where the SNN performs poorly. The hybrid model is trained on four-dimensional steady flamelet tables and used to model methane combustion by adopting the Sandia Flame D configuration. The hybrid clustering method more accurately captures the experimental measurements of temperature, carbon monoxide (CO), and hydroxyl radical (OH) mass fraction compared to the SNN model. A new hybrid model offers significant improvements in accuracy as compared to the SNN model along with reduction of computational storage by 2 orders of magnitude compared to the original flamelet approach and reduces the total computational time in 3D reacting flow simulations.