Physics-based Dimensionality Reduction for Data-Based Models for Turbulent Premixed Combustion

Data-based models are an emerging approach for closure modeling in turbulent combustion simulations. Direct Numerical Simulations (DNS) provide a wealth of relevant data for training purposes, and these data-based approaches can provide pathways forward in the absence of adequate physics-based models. The vast amount of available data from a DNS leaves ambiguity with respect to the identification of the appropriate inputs for a data-based model. This identification is often ad hoc, and adopting too many inputs can lead to overfitting the model. The dimensionality of the input space is often reduced via linear Principal Component Analysis (PCA) to identify irrelevant input quantities. PCA can lose information, however, as only a finite number of principal components are retained. Rather than use PCA, the dimensionality of the input space could be reduced by enforcing dimensional homogeneity between all input variables and the output, which preserves all information and includes nonlinear combinations of inputs. This approach, termed physics-based dimensionality reduction (PBDR), is presented in this work in the context of premixed turbulent combustion modeling. DNS databases of turbulent premixed jet flames at varying Karlovitz number are used to train data-based models for two quantities of interest in Large Eddy Simulation (LES) that are challenging to model with physics-based approaches: filtered progress variable dissipation rate and progress variable scalar flux. Data-based models trained with the PBDR approach are assessed against PCA as well as physics-based models for these quantities of interest. PBDR demonstrates considerable improvement in model generalizability when compared to PCA in terms of accuracy and neural network characteristics.