Performing measurements in reacting flows is a challenging task due to the complexity of measuring all quantities of interest simultaneously or limitations in the optical access. To compensate for this, recent advances in deep learning have shown a strong potential in augmenting the information content in datasets composed of partial measurements by reconstructing the quantities that could not be measured. The present work analyses the use of such deep learning tools in two different cases. First, Convolutional Neural Networks (CNNs) are used to reconstruct the heat release rate (HRR) from velocity measurements in a methane/air premixed flame under harmonic excitation. The CNNs are trained from complete datasets at some specific frequencies and amplitudes of excitation and their ablility to reconstruct the HRR for different operating conditions with good accuracy is demonstrated. Secondly, an alternate approach based on Physics-Informed Neural Networks that do not require the training data to have all the quantities is explored. It is applied to a puffing pool fire where the velocity field is reconstructed from observations of pressure, temperature and density with good accuracy.

Multi-layer perceptrons with different numbers of hidden layers and variable neurons were investigated to model the nonlinear flame response of a Bunsen-type flame. The neural network models demonstrate the ability to learn the flame describing function (FDF) for a laminar premixed flame, while using only one computational fluid dynamics (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 a regularizer to avoid overfitting. The best performing model is subsequently used to compute the 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 RMS value of the predicted acoustic oscillations, together with the associated dominant frequencies are in excellent agreement with CFD reference data.