This project advances physics-informed machine learning techniques for modeling turbulent reacting flows by developing and applying neural operator frameworks trained on high-fidelity direct numerical simulation (DNS) data. Building upon our recent progress in neural operator methods, particularly the development of Koopman-inspired operators (kFNO, kCNN), we aim to further enhance the accuracy, computational efficiency, and physical interpretability of sub-grid-scale (SGS) combustion models used in Large Eddy Simulation (LES). Our approach addresses key limitations of traditional LES combustion modeling, notably the dependence on numerous tunable parameters that restrict predictive accuracy and generalizability across diverse combustion scenarios. We propose to expand the recently developed parametric neural operator models to incorporate hybrid instability mechanisms—such as the Darrieus-Landau (DL) and diffusive-thermal (DT) instabilities—enabling rapid and robust predictions of unsteady, nonlinear flame evolution under various flow and chemical conditions. The performance and generalization capabilities of these advanced models will be rigorously validated against newly generated DNS databases, as well as in practical LES applications. This continuation project will significantly extend our previous achievements, offering a powerful and efficient computational framework that combines deep learning with rigorous physical constraints. The resulting physics-informed neural operator methods promise substantial improvements in the modeling accuracy and computational speed for turbulent combustion simulations, directly addressing critical needs in industrial and scientific applications.