  Complete computation of turbulent combustion flow involves two separate
steps: mapping reaction kinetics to low-dimensional manifolds and looking-up
this approximate manifold during CFD run-time to estimate the thermo-chemical
state variables. In our previous work, we showed that using a deep architecture
to learn the two steps jointly, instead of separately, is 73% more accurate at
estimating the source energy, a key state variable, compared to benchmarks and
can be integrated within a DNS turbulent combustion framework. In their natural
form, such deep architectures do not allow for uncertainty quantification of
the quantities of interest: the source energy and key species source terms. In
this paper, we expand on such architectures, specifically ChemTab, by
introducing deep ensembles to approximate the posterior distribution of the
quantities of interest. We investigate two strategies of creating these
ensemble models: one that keeps the flamelet origin information (Flamelets
strategy) and one that ignores the origin and considers all the data
independently (Points strategy). To train these models we used flamelet data
generated by the GRI--Mech 3.0 methane mechanism, which consists of 53 chemical
species and 325 reactions. Our results demonstrate that the Flamelets strategy
is superior in terms of the absolute prediction error for the quantities of
interest, but is reliant on the types of flamelets used to train the ensemble.
The Points strategy is best at capturing the variability of the quantities of
interest, independent of the flamelet types. We conclude that, overall, ChemTab
Deep Ensembles allows for a more accurate representation of the source energy
and key species source terms, compared to the model without these
modifications.
