The large eddy simulation (LES) of turbulent combustion is pertinent to numerous applications of practical importance such as internal combustion engines, gas turbines, industrial furnaces, and propulsion systems. These simulations are inherently complex owing to the intricacies of turbulent flow, chemical kinetics, and the interaction between them. In LES, only the large scales of the flow field are resolved, while motions at the small scales, generally referred to as subgrid scales (SGS), are modeled. SGS models based on transported Filtered Density Function (FDF) approaches are attractive because they provide closed-form representations of the highly non-linear chemical source terms in transport equations. However, applying these models to realistic flame calculations is challenging due to the high costs associated with numerically integrating the stiff finite-rate chemical kinetics ordinary differential equations (ODEs). The first part of this talk focuses on a data-driven framework that employs neural ODEs (NODE) to speed up the integration of stiff chemistry. The performance of this approach is demonstrated for hydrogen-air combustion in a pairwise mixing stirred reactor (PMSR) with varying mixing timescales.

An alternative to the high-fidelity transported FDF approach is the low-fidelity moments method, which reduces the chemistry description to one or two characteristic variables and incorporates SGS statistics through presumed FDF. One example of this is non-premixed flames with infinitely fast chemistry, where the thermochemical state depends solely on mixture fraction. The second part of the talk focuses on deep neural network (DNN) models for predicting the FDF of
mixture fraction in variable density 3-D mixing layers. The performance of the DNN-FDF model is seen to be more accurate than the conventional beta FDF model based on the appraisal compared to high-fidelity simulation predictions from direct numerical simulation (DNS) and transported FDF.