  In reacting flow systems, thermoacoustic instability characterized by high
amplitude pressure fluctuations, is driven by a positive coupling between the
unsteady heat release rate and the acoustic field of the combustor. When the
underlying flow is turbulent, as a control parameter of the system is varied
and the system approach thermoacoustic instability, the acoustic pressure
oscillations synchronize with heat release rate oscillations. Consequently,
during the onset of thermoacoustic instability in turbulent combustors, the
system dynamics transition from chaotic oscillations to periodic oscillations
via a state of intermittency. Thermoacoustic systems are traditionally modeled
by coupling the model for the unsteady heat source and the acoustic subsystem,
each estimated independently. The response of the unsteady heat source, the
flame, to acoustic fluctuations are characterized by introducing external
unsteady forcing. This necessitates a powerful excitation module to obtain the
nonlinear response of the flame to acoustic perturbations. Instead of
characterizing individual subsystems, we introduce a neural ordinary
differential equation (neural ODE) framework to model the thermoacoustic system
as a whole. The neural ODE model for the thermoacoustic system uses time series
of the heat release rate and the pressure fluctuations, measured simultaneously
without introducing any external perturbations, to model their coupled
interaction. Further, we use the parameters of neural ODE to define an anomaly
measure that represents the proximity of system dynamics to limit cycle
oscillations and thus provide an early warning signal for the onset of
thermoacoustic instability.
