The modeling and simulation of turbulent combustion must account for the contribution of many chemical species and the effect of turbulence on their transport and reactions. Such reactions must span a wide range of timescales and often present bottlenecks in accelerating simulations. Data from experiments or simulations enables tools to accelerate simulations and develop accurate predictions of important turbulence-chemistry interactions. Several methods designed to exploit this data are presented and discussed. They are motivated by and rooted in traditional paradigms in turbulent combustion that rely heavily on the existence of a low-dimensional manifold for the composition space and its coupling with turbulent transport. The methods also rely on machine learning techniques for model order reduction, the extraction of closure from observations and models, and learning predictions of reaction rates and chemical states from low-dimensional descriptions of these states. These methods include principal component transport for combustion direct numerical simulations, methods to develop closure models and construct closure terms from multiscalar measurements, and deep operator networks for chemistry integration and acceleration. They provide pathways for efficient simulations of turbulent combustion and overcome the inherent limitations of predicting these complex flows.

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• Combustion
• Reacting flows
• Turbulent reacting flows
• Machine learning models