Applications of machine learning methods to combustion science and technology were reviewed especially on the papers introduced in seminars of Tsue-Nakaya laboratory in the University of Tokyo. A lot of machine learning methods as with deep neural network and convolution neural network introduced concepts based on numerical methods, the linear algebra and Bayesian statistics. Then, characteristics of the flame emission, which could be applicable to inputs of machine leaning methods, were explained. Time-resolved CH* chemiluminescence and near-infrared emissions from H₂O were observed to extracted features of the dynamics of high temperature combustion. Fundamentals of non-supervised dimensionality reduction methods were explained briefly: primary component analysis, proper orthogonal decomposition, dynamic mode decompositions, self-organizing map and gaussian process latent variable method. Applications of these methods were introduced focusing on combustion instabilities in a model rocket engine combustor with a pintle injector, a supersonic combustor, and a rich-hydrogen ram combustor. The results indicated that the machine learning methods were powerful tools to extracted the features of the unsteady combustion dynamics.

A technique using deep neural network (DNN) is introduced for the analysis of combustion dynamics recently. The functionality of the conventional machine learning, proper orthogonal decomposition (POD), technique, is summarized; and how it can be implemented by DNN is explained from mathematical viewpoint. Deep auto-encoder (DAE) consist of an encoder and a decoder networks is validated to be the superposition of POD and its variant, variational auto-encoder (VAE), is found to be suited for projecting the dynamics onto a low-order phase space. The superiority of the DAEs is explained through the flexibility in projection of the dynamic motion on a manifold in high-order space onto a low-dimensional phase space. The results of analysis using VAE is presented for the intrinsic combustion oscillation in a rocket combustor and for the cool flame oscillation of a droplet array. For both cases, VAE could determine the phase appropriately from the spatial distributions of various physical parameters; and it could derive the locus on 2D phase plane from time variation of the distributions. The distinctive attractor of nonlinear limit-cycle oscillations is written on the phase plane and the possibility of near-term prediction is demonstrated.

Machine learning technology is increasingly yielding major changes to scientific and engineering disciplines. The support vector machine and self-organizing map are the well-known classes of machine learning in the framework of statistical learning theory. Recent process in nonlinear time series analysis inspired by the theories of symbolic dynamics and complex networks, has opened up a new pathway for (i) an in-depth physical understanding and interpretation of nonlinear dynamics and (ii) the development of substitute detectors to capture a precursor of thermoacoustic combustion oscillations. This paper presents the applicability of the combined methodologies of nonlinear time series analysis, the support vector machine, and the self-organizing map, for an early detection of combustion oscillations in a swirl-stabilized combustor. We mainly consider two important analyses: complexity-entropy causality plane and the ordinal partition transition networks to capture a precursor of combustion oscillations.

Turbulent combustion modelling is one of most difficult topics in turbulent combustion community. There are many models are proposed so far, and recent development in machine learning (ML) technique shed light onto the application of ML on turbulent combustion modelling. This paper introduces several examples of turbulent combustion modelling utilizing machine learning with varied approaches, in conjunction with the conventional modelling approaches. Several important issues arising when applying developed machine learning model are also mentioned.

An application of neural network to look-up tables of tabulated chemistry is a promising technique for a detailed numerical simulation of turbulent reacting flows. In this article, an overview of ideas about new formulation and configuration of look-up tables for applying neural networks to compressible large-eddy simulation (LES) with laminar flamelet model is provided. The advantages of applying neural networks to look-up tables are outlined first, and two new formulations and input/output parameters of look-up tables required to apply this framework to compressible LES with laminar flamelet model are discussed. Then, configuration and training procedure of neural networks are described, and accuracy evaluations of these neural networks created based on a collection of one-dimensional laminar counterflow diffusion flames are conducted. Finally, numerical simulations of DLR scramjet test-engine combustor are conducted and calculation accuracy, calculation time and memory usage of proposed method using these neural networks are evaluated.

Pulsation control is one of the promising methods to drastically reduce friction drag of turbulent flows. In the present report, two approaches of machine learning of pulsating turbulent pipe flows are introduced. One is a prediction of temporal change of turbulent pipe flow using the flow fields calculated by direct numerical simulation (DNS) using Long Short-Term Memory (LSTM) coupled with Convolutional Auto Encoder (CAE). The periodic changes of flow velocities and friction drag coefficient were qualitatively reproduced by the model. The other is a prediction of pulsating flow by using thousands of experimental data. Two models are constructed using different units; Multi-Layer Perceptron (MLP) and LSTM. Both models well reproduced drag reduction rates for various pulsation patterns. Especially, the model based on LSTM showed good reproducibility of temporal changes in flow characteristics. Thus, it was shown that machine learning can be a reliable tool to predict characteristics of pulsating flows, which could be also utilized to optimize pulsation patterns in the future.

We computationally designed ultra-narrowband wavelength-selective thermal emitter by a materials-informatics method alternating between Bayesian optimization and electromagnetic wave calculation. For a given target infrared wavelength, the optimal structure was efficiently identified from over 8 billion candidates of multilayers consisting of multiple components (Si, Ge, and SiO₂). The resulting optimized structure was an aperiodic multi-layered metamaterial exhibiting high and sharp emissivity with the Q-factor of 273. The designed metamaterials were then fabricated, and reasonable experimental realization of the optimal performance was achieved with the Q-factor of 188, which was significantly higher than those of structures empirically designed and fabricated in the past. This is the demonstration where metamaterials designed by Bayesian optimization was realized in experiments. The results facilitate the machine-learning-based design of metamaterials and advance our understanding in the narrow-band thermal emission mechanism of aperiodic multi-layered metamaterials.

Non-intrusive particle size measurement method based on scattered light intensities of polarized lights is introduced. A linearly polarized laser passes through the test particles having a certain size distribution. Scattered light intensities observed in the perpendicular and parallel directions to the polarization plane are different. The ratio of the scattered light intensities is called the polarization ratio and is given as a function of the size distribution, the refractive index, the scattering angle and the incident beam wavelength. The two of four parameters, the scattering angle and the wavelength are known values. By comparing the polarization ratio calculated by Mie's scattering theory and that observed experimentally, the size distribution and refractive index are determined. But in this case, the number of equations is insufficient to determine the rest unknown parameters even if a simple log-normal distribution is assumed. By introducing another wavelength, this problem is solved. The multi-wavelength polarization ratio method extends the measurement range of the original single wavelength method, and is applied to soot particle measurement in flames and microplastics suspended in water.

Soot formation characteristics in the multi-phase combustion (spray flame and pulverized coal jet flame) in a simplified flow field were evaluated using two-dimensional laser induced incandescence (LII) and time resolved LII (TiRe-LII). For the spray flame, the effects of fuel droplet size distribution on soot formation in a laminar counterflow field are investigated. Sauter mean diameter (SMD) and droplet size distribution (DSD) of fuel spray (n-decane) are carefully controlled independently from the other conditions using a frequency-tunable vibratory orifice atomizer (VOA). Results show that the soot formation area and location are strongly affected by the SMD and by the DSD of the fuel spray. As the SMD of the fuel spray increases, the average soot formation area expands, and that the local suppression of soot formation is observed instantaneously in the spray flames because of the appearance of groups of unburned droplets. The size of soot particles in the spray flame tends to increase in the outer part of the soot formation area compared to soot in the inner part. For the pulverized coal jet flame, soot formation characteristics of a lab-scale pulverized coal flame were measured by performing carefully controlled LII and TiRe-LII for the first time. Results indicated that it is necessary to adjust the laser pulse fluence so that it is sufficiently high to heat all the soot particles to the sublimation temperature but sufficiently low to avoid making a significant change in the morphology of the soot particles and the superposition of the LII signal from the pulverized coal particles on that from the soot particles as well. Additionally, the soot volume fraction and the primary soot particle diameter increases with increasing the height above the burner in any radial distance. However, the variation of the soot particle diameter distribution along the radial direction becomes small in the downstream region. Transient soot formation processes are evaluated through simultaneous measurements of coal particles, polycyclic aromatic hydrocarbons (PAHs) and soot. Pairs of simultaneous measurements of “Mie scattering measurement for coal particles with laser induced fluorescence (LIF) for PAHs” and “LIF for PAHs with LII for soot” were performed to understand the transitive formation processes of soot particles in a pulverized coal flame, whose signals were successfully separated. Results show that existing regions of coal particles, PAHs and soot are overlapped from the time averaged viewpoint while there are almost no overlapped areas of coal particles, PAHs and soot from the instantaneous viewpoint.