  This paper proposes a Bayesian data-driven machine learning method for the
online inference of the parameters of a G-equation model of a ducted, premixed
flame. Heteroscedastic Bayesian neural network ensembles are trained on a
library of 1.7 million flame fronts simulated in LSGEN2D, a G-equation solver,
to learn the Bayesian posterior distribution of the model parameters given
observations. The ensembles are then used to infer the parameters of Bunsen
flame experiments so that the dynamics of these can be simulated in LSGEN2D.
This allows the surface area variation of the flame edge, a proxy for the heat
release rate, to be calculated. The proposed method provides cheap and online
parameter and uncertainty estimates matching results obtained with the ensemble
Kalman filter, at less computational cost. This enables fast and reliable
simulation of the combustion process.
