Data Assimilation Using Heteroscedastic Bayesian Neural Network Ensembles for Reduced-Order Flame Models

The parameters of a level-set flame model are inferred using an ensemble of heteroscedastic Bayesian neural networks (BayNNEs). The neural networks are trained on a library of 1.7 million observations of 8500 simulations of the flame edge, obtained using the model with known parameters. The ensemble produces samples from the posterior probability distribution of the parameters, conditioned on the observations, as well as estimates of the uncertainties in the parameters. The predicted parameters and uncertainties are compared to those inferred using an ensemble Kalman filter. The expected parameter values inferred with the BayNNE method, once trained, match those inferred with the Kalman filter but require less than one millionth of the time and computational cost of the Kalman filter. This method enables a physics-based model to be tuned from experimental images in real time.