Online parameter inference for the simulation of a Bunsen flame using heteroscedastic Bayesian neural network ensembles

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.