Uncovering flame physics with machine learning: application to the reaction rate in hydrogen flames

Convolutional Neural Networks (CNNs) are used as analytical tools to investigate the relationship between the progress variable field and the local chemical source term in lean premixed hydrogen flames. Rather than employing machine learning for modelling, CNNs are leveraged to analyse the physical information contained in spatially resolved fields from direct numerical simulations. CNNs are particularly well suited for this task because they exploit spatial correlations and multi-scale structures, allowing an assessment of how spatial organisation influences the source term. The analysis demonstrates that the progress variable based on water, $C_{\rm H_2O}$, contains all the information required to accurately parametrise the chemical source term whereas $C_{\rm H_2}$ alone does not. The inclusion of the mixture fraction $Z$ improves the accuracy of the latter but provides no significant additional information to the CNN when the spatial field of $C_{\rm H2O}$ is used as input. The same behaviour is observed in both a laminar thermodiffusively unstable flame and a turbulent slot-jet hydrogen flame, indicating that $C_{\rm H_2O}$ is a robust single variable for parametrisation. A complementary scale analysis in the laminar case shows that spatial features extending over at least two laminar flame thicknesses are required to reconstruct the source term accurately, thereby identifying the characteristic scale in the progress variable field that carries this information. These results demonstrate how machine learning can uncover physical dependencies that remain hidden to classical statistical analyses.