  This paper demonstrates the ability of neural networks to reliably learn the
nonlinear flame response of a laminar premixed flame, while carrying out only
one unsteady CFD simulation. The system is excited with a broadband, low-pass
filtered velocity signal that exhibits a uniform distribution of amplitudes
within a predetermined range. The obtained time series of flow velocity
upstream of the flame and heat release rate fluctuations are used to train the
nonlinear model using a multi-layer perceptron. Several models with varying
hyperparameters are trained and the dropout strategy is used as regularizer to
avoid overfitting. The best performing model is subsequently used to compute
the flame describing function (FDF) using mono-frequent excitations. In
addition to accurately predicting the FDF, the trained neural network model
also captures the presence of higher harmonics in the flame response. As a
result, when coupled with an acoustic solver, the obtained neural network model
is better suited than a classical FDF model to predict limit cycle oscillations
characterized by more than one frequency. The latter is demonstrated in the
final part of the present study. We show that the RMS value of the predicted
acoustic oscillations together with the associated dominant frequencies are in
excellent agreement with CFD reference data.
