  Reduced-order models of flame dynamics can be used to predict and mitigate
the emergence of thermoacoustic oscillations in the design of gas turbine and
rocket engines. This process is hindered by the fact that these models,
although often qualitatively correct, are not usually quantitatively accurate.
As automated experiments and numerical simulations produce ever-increasing
quantities of data, the question arises as to how this data can be assimilated
into physics-informed reduced-order models in order to render these models
quantitatively accurate. In this study, we develop and test a physics-based
reduced-order model of a ducted premixed flame in which the model parameters
are learned from high speed videos of the flame. The experimental data is
assimilated into a level-set solver using an ensemble Kalman filter. This leads
to an optimally calibrated reduced-order model with quantified uncertainties,
which accurately reproduces elaborate nonlinear features such as cusp formation
and pinch-off. The reduced-order model continues to match the experiments after
assimilation has been switched off. Further, the parameters of the model, which
are extracted automatically, are shown to match the first order behavior
expected on physical grounds. This study shows how reduced-order models can be
updated rapidly whenever new experimental or numerical data becomes available,
without the data itself having to be stored.
