Modelling the flame response of turbulent flames via data-driven approaches is challenging due, among others, to the presence of combustion noise. Neural network methods have shown good potential to infer laminar flames' linear and nonlinear flame response when externally forced with broadband signals. The present work extends those studies and analyses the ability of neural network models to evaluate the linear and nonlinear flame response of turbulent flames. In the first part of this work, the neural network is trained to evaluate and interpolate the linear flame response model when presented with data obtained at various thermal conditions. In the second part, the neural network is trained to infer the nonlinear flame response model when presented with time series exhibiting sufficient large amplitudes. In both cases, the data is obtained from a large eddy simulation of an academic combustor when acoustically forced by broadband signals.

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 for the reconstruction of quantities 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. Both approaches are also shown to be robust with respect to noise.

Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural network and data, often fail to accurately simulate the evolution of the system dynamics over a sufficiently long time and in a physically consistent manner. Therefore, we propose a hybrid approach that uses a neural network model in combination with an incomplete partial differential equations (PDEs) solver that provides known, but incomplete physical information. In this study, we demonstrate that the results obtained from the incomplete PDEs can be efficiently corrected at every time step by the proposed hybrid neural network—PDE solver model, so that the effect of the unknown physics present in the system is correctly accounted for. For validation purposes, the obtained simulations of the hybrid model are successfully compared against results coming from the complete set of PDEs describing the full physics of the considered system. We demonstrate the validity of the proposed approach on a reactive flow, an archetypal multi-physics system that combines fluid mechanics and chemistry, the latter being the physics considered unknown. Experiments are made on planar and Bunsen-type flames at various operating conditions. The hybrid neural network—PDE approach correctly models the flame evolution of the cases under study for significantly long time windows, yields improved generalization and allows for larger simulation time steps.

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 a 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.

Accurate demand forecasts can help on-line retail organizations better plan their supply-chain processes. The challenge, however, is the large number of associative factors that result in large, non-stationary shifts in demand, which traditional time series and regression approaches fail to model. In this paper, we propose a Neural Network architecture called AR-MDN, that simultaneously models associative factors, time-series trends and the variance in the demand. We first identify several causal features and use a combination of feature embeddings, MLP and LSTM to represent them. We then model the output density as a learned mixture of Gaussian distributions. The AR-MDN can be trained end-to-end without the need for additional supervision. We experiment on a dataset of an year's worth of data over tens-of-thousands of products from Flipkart. The proposed architecture yields a significant improvement in forecasting accuracy when compared with existing alternatives.