Transfer learning with gradient-structural regularization for turbulent combustion under data scarcity

Hydrogen-fueled turbulent flames involve strong temperature and species gradients, making the preservation of small-scale flow and reaction structures challenging for combustion-field prediction under limited training data. To address data scarcity and the degradation of high-gradient structures in steady turbulent combustion multiphysics prediction, this study proposes a structurally regularized transfer-learning framework that integrates interpolation-augmented source-domain data with gradient-based structural regularization. In this framework, a gradient structure similarity (GSSIM) constraint is embedded as an explicit structural regularizer into the transfer-learning process, helping preserve the morphological consistency and sharpness of key flow structures, including shear layers, reaction fronts, and recirculation zones. The results show that incorporating GSSIM-based structural regularization improves prediction accuracy and error stability under small-sample conditions compared with transfer-learning models without this constraint. The proposed framework achieves simultaneous prediction of three-dimensional turbulent combustion fields, including velocity magnitude, temperature, OH mass fraction, and NO mass fraction, while better preserving essential flow and reaction structures in both interpolation and true extrapolation tests. These results suggest that embedding gradient-based structural priors into interpolation-augmented transfer learning provides an effective approach for data-efficient turbulent combustion-field prediction.