On the optimisation of reaction progress variables in reacting flows using machine learning

A novel approach is proposed for the automatic generation of reaction progress variables (PVs), which serve as key coordinates in low-dimensional manifold methods for combustion modelling. For multi-step kinetics, PVs are commonly defined as weighted linear combinations of species mass fractions using empirical formulations that are inherently fuel- and condition-specific. In the present work, the monotonicity requirement is reformulated as a binary classification problem and solved using a support vector machine (SVM). The soft-margin formulation accommodates mutually inconsistent constraints, while L1 regularisation promotes a sparse PV definition. Residual monotonicity violations are quantified using the metric Em. The method is first evaluated for six freely propagating premixed flames involving hydrocarbon, carbon-free, and compound fuels under different molecular-transport assumptions. No monotonicity violation (Em=0) is detected in any of the cases examined. The framework is then applied to an NH3/CH4/air counterflow flamelet library. The empirical PV exhibits Em=9.1643×10−3 and would require the removal of non-monotone flamelets, reducing the maximum representable temperature from 2177 to approximately 2091 K. In contrast, the SVM-optimised PV preserves all steady flamelets. Finally, both PV definitions are assessed in partially premixed NH3/CH4/air flames at mixture-fraction gradients of 7.2 and 8.0 m−1 using finite-rate chemistry calculations as references. The optimised PV more accurately predicts the triple-flame position, flame-branch curvature, and species distributions, reducing the relative L2 errors of temperature, CO, CO2, and OH by 4.145–12.048 percentage points. These results demonstrate the robustness and general applicability of the proposed method for automated PV construction and thermochemical-state retrieval.