The Evolution of Data-Driven Low-Dimensional Manifolds for Combustion: From Canonical Flames to Biofuels

Detailed chemical kinetics remains a major barrier to predictive computational fluid dynamics of chemically complex renewable fuels. This critical state-of-the-art review evaluates whether data-driven low-dimensional manifold methods have progressed from statistical compression to deployable reduced combustion models, with emphasis on biofuel applications. A reproducible evidence-identification and charting process classified 45 primary-evidence publications comprising 73 applications by fuel, reduction method, reconstruction and closure strategy, simulation framework, and validation tier. The evidence shows that global principal component analysis, its local, kernel, and higher-order variants, and autoencoder-based neural formulations can compactly reconstruct thermochemical states, while transported reduced coordinates have achieved a posteriori demonstrations in one-dimensional turbulence, Reynolds-averaged simulations, large-eddy simulations, direct numerical simulations, and engine-relevant ignition. The strongest solver-coupled evidence remains concentrated in methane, syngas, hydrogen-rich, hydrocarbon-surrogate, and ammonia–hydrogen systems. By contrast, biofuel-relevant ethanol and dimethyl ether studies remain predominantly a priori, despite promising compression of multistage and device-relevant thermochemical states. Across methods, the principal bottleneck has shifted from dimensionality reduction to closure accuracy, training-domain coverage, physical admissibility, differential diffusion, stiffness, and safe out-of-distribution response. Credible biofuel combustion simulation therefore requires closure-complete, physically constrained, uncertainty-aware models validated a posteriori in multidimensional and device-relevant configurations, with matched parent-chemistry accuracy, stability, memory, and end-to-end cost.