  We introduce a physics-informed neural network (PINN) method to study
thermoacoustic interactions leading to combustion instability in combustors.
Specifically, we employ a PINN to investigate thermoacoustic interactions in a
bluff body anchored flame combustor, representative of ramjet and industrial
combustors. Vortex shedding and acoustic oscillations appear in such
combustors, and their interactions lead to the phenomenon of vortex-acoustic
lock-in. Acoustic pressure fluctuations at three locations and the total flame
heat release rate serve as the measured data. The coupled parameterized model
is based on the acoustic equations and the van der Pol oscillator for vortex
shedding. The PINN was applied in the combustor, where the measurements
suitable for a future machine learning application were not anticipated at the
time of the experiments, as is the case in the vast majority of available data
in the literature. We demonstrate a good performance of PINN in generating the
acoustic field (pressure and velocity fluctuations) in the entire
spatiotemporal domain, along with estimating all the parameters of the model.
Therefore, this PINN-based model can potentially serve as an effective tool in
improving existing combustors or designing new thermoacoustically stable and
structurally efficient combustors.
