Abstract：[Significance] With the development of combustion science, large amounts of data containing various kinds of effective physical information are generated by numerical simulation and experimental measurement. Traditional research methods mainly apply model-based physical rules to illustrate such information. However, as the amount of data increases, data-driven methods have gradually gained research attention. Due to the remarkable success of machine learning (ML) techniques in data analysis and processing, they also offer a new way of processing large amounts of data in the field of combustion. [Progress] This study reviews the applications of ML in turbulent combustion, including chemical reactions, combustion modeling, engine performance prediction and optimization, and combustion instability prediction and control. The challenges and future prospects are also discussed. In the area of chemical reactions, the use of ML has been successfully demonstrated for the simplification and optimization of chemical mechanisms as well as for the efficient representation of chemical systems. Similarly, ML applications have produced encouraging results for modeling subgrid-scale processes and for parameterizing PDFs, often outperforming physics-based closure models in a priori studies. However, caution should be exercised in extrapolating these findings to a posteriori applications. Moreover, further studies are necessary to examine the performance of these data-driven models that are typically generated for specific operating conditions in practical applications. To address the limitations of regression models, physics-informed neural networks provide avenues for incorporating physical principles and other fundamental consistencies that are necessary for enabling robust combustion simulations. As for applications in engines, robust intelligent control via ML has only become feasible for combustion experiments in recent years, mainly due to the developments of deep learning. As such, these methods are still not feasible for commercial applications. This is largely caused by the lack of confidence in ML models under unseen conditions, especially in safety-critical applications, and by the large amounts of online training required for the convergence of current ML methods. [Conclusions and Prospects] Given such a background, robustness study is still a top priority. Although many successful studies on the combination between ML and combustion research have been accomplished, the conceptualization of combustion problems in ML frameworks remains a laborious task. Formulating the problem into an ML framework is a prerequisite for the issue to be successfully solved using ML. Clarifying the combustion problem and carefully selecting and preprocessing the obtained data are important. In addition, the careful selection of the ML model, the loss function, and the training and tuning of the model are necessary components for building a predictive model. Moreover, the ML models exhibit various degrees of predictive uncertainties, which are exacerbated by the lack of interpretability in complex models. Therefore, there is an urgent need to establish ML methods with physical insights. More attempts, such as sample construction method, modeling method, and uncertainty quantification or sensitivity analysis, should be conducted to effectively verify the performance of the model. This ensures that the model abides by the laws of physics and that it can accurately represent the simulated system. The holistic combination of data-driven methods with physical insights could have profound impacts on all areas of combustion science and technology, such as data-assisted modeling and simulation techniques, in situ control and optimization strategies, and data-driven screening of alternative fuels.
安健, 陈宇轩, 苏星宇, 周华, 任祝寅. 机器学习在湍流燃烧及发动机中的应用与展望[J]. 清华大学学报（自然科学版）, 2023, 63(4): 462-472.
AN Jian, CHEN Yuxuan, SU Xingyu, ZHOU Hua, REN Zhuyin. Applications and prospects of machine learning in turbulent combustion and engines. Journal of Tsinghua University(Science and Technology), 2023, 63(4): 462-472.
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