Scientific machine learning in combustion for discovery, simulation, and control

Combustion science is undergoing a transformation, driven by the need to model increasingly complex, multi-scale systems and accelerate progress toward cleaner, more efficient energy technologies. While traditional modeling approaches remain foundational, they face growing limitations under modern demands such as alternative fuels, stringent emission standards, and extreme operating environments. This review explores how scientific machine learning (SciML), which integrates data-driven models with physical constraints, is reshaping combustion research across three central fronts: model discovery, simulation acceleration, and system state reconstruction. We highlight recent advances in parameter estimation, reaction mechanism generation, and interpretable model discovery using tools such as physics-informed neural networks, chemical reaction neural networks, symbolic regression, and governing equation-constrained parameter optimization. For simulation, we examine neural surrogates, operator learning, and physics-inspired architectures that enable fast and accurate predictions while preserving physical fidelity. Finally, we review emerging methods for reconstructing full-field combustion states from sparse data, enabling mutual inference across physical quantities and advancing digital twin development through multi-modal data fusion. Together, these developments demonstrate how SciML is enabling new capabilities for combustion modeling, diagnostics, and control. As the field evolves, continued progress will depend on integrating domain knowledge with scalable algorithms, rigorous uncertainty quantification, and cross-disciplinary collaboration, paving the way for next-generation combustion systems that are intelligent, adaptive, and physically grounded.