Physics-Informed machine learning for turbulent combustion in aerospace propulsion: bridging physical rigour and data intelligence

Turbulent combustion dictates efficiency, stability, and emissions in gas turbines, scramjets, and rocket engines; however, its multiscale turbulence-chemistry interactions remain difficult to forecast with conventional Reynolds-averaged and large-eddy simulation (LES) frameworks under realistic operational conditions. Although data-driven models offer computational efficiency, their limited physical consistency and inadequate extrapolation capabilities limit their applicability in safety-critical propulsion applications. Physics-informed machine learning (PIML) has emerged as a promising paradigm by embedding governing equations, physical constraints, and conservation laws directly into learning architectures, thereby enabling greater accuracy with reduced data dependence. This review systematically scrutinizes recent advancements in PIML for turbulent reacting flows, encompassing physics-informed neural networks, neural operators, and hybrid physics-data models integrated with Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) solvers. Emphasis is placed on their proficiency to address stiffness, turbulence-chemistry coupling, and multi-fidelity data integration under propulsion-relevant conditions. Key challenges related to data scarcity, scalability, uncertainty quantification, and model interpretability are critically discussed. The review concludes with a forward-looking roadmap accentuating constraint-aware learning, adaptive modelling, and digital twin integration as indispensable for reliable, real-time combustion prediction. These advancements directly bolster sustainable propulsion technologies aligned with UN Sustainable Development Goals 7 and 9, advocating for cleaner energy conversion and innovation-driven aerospace systems.HighlightsPIML bridges physics-based modelling with data-driven intelligence in combustion.Hybrid neural operators improve prediction in turbulent reacting flows.Constraint-preserving learning enhances physical fidelity and scalability.Adaptive sampling accelerates convergence under sparse data conditions.Roadmap proposed for uncertainty-aware, digital-twin-ready PIML frameworks.PIML transforms real-time combustion simulation for next-gen propulsion.