BibTeX

@article{2011.02838v1,
Author        = {Ushnish Sengupta and Maximilian L. Croci and Matthew P. Juniper},
Title         = {Real-time parameter inference in reduced-order flame models with
  heteroscedastic Bayesian neural network ensembles},
Eprint        = {2011.02838v1},
ArchivePrefix = {arXiv},
PrimaryClass  = {cs.LG},
Abstract      = {The estimation of model parameters with uncertainties from observed data is a
ubiquitous inverse problem in science and engineering. In this paper, we
suggest an inexpensive and easy to implement parameter estimation technique
that uses a heteroscedastic Bayesian Neural Network trained using anchored
ensembling. The heteroscedastic aleatoric error of the network models the
irreducible uncertainty due to parameter degeneracies in our inverse problem,
while the epistemic uncertainty of the Bayesian model captures uncertainties
which may arise from an input observation's out-of-distribution nature. We use
this tool to perform real-time parameter inference in a 6 parameter G-equation
model of a ducted, premixed flame from observations of acoustically excited
flames. We train our networks on a library of 2.1 million simulated flame
videos. Results on the test dataset of simulated flames show that the network
recovers flame model parameters, with the correlation coefficient between
predicted and true parameters ranging from 0.97 to 0.99, and well-calibrated
uncertainty estimates. The trained neural networks are then used to infer model
parameters from real videos of a premixed Bunsen flame captured using a
high-speed camera in our lab. Re-simulation using inferred parameters shows
excellent agreement between the real and simulated flames. Compared to Ensemble
Kalman Filter-based tools that have been proposed for this problem in the
combustion literature, our neural network ensemble achieves better
data-efficiency and our sub-millisecond inference times represent a savings on
computational costs by several orders of magnitude. This allows us to calibrate
our reduced-order flame model in real-time and predict the thermoacoustic
instability behaviour of the flame more accurately.},
Year          = {2020},
Month         = {Oct},
Note          = {Machine Learning and the Physical Sciences Workshop at the 34th
  Conference on Neural Information Processing Systems (NeurIPS) 2020},
Url           = {http://arxiv.org/abs/2011.02838v1},
File          = {2011.02838v1.pdf}
}