High fidelity numerical simulations are crucial for high-speed engine design optimization and operation control; however, their prohibitive computational cost hinders practical applications. In this work, a hybrid generative diffusion modeling framework is proposed for auto-regressive prediction of supersonic combustion dynamics. The approach synergistically combines a physics-constrained U-Net with a generative diffusion model through a novel hybrid inference strategy. This hybrid method first introduces a physics-based U-Net to generate a fast initial prediction via a tailored loss function with warm-up scheduling and adaptive weighting of physical constraints. This prediction is then refined through a forward annealing step followed by a controllable number of diffusion-based denoising iterations. Performance of the hybrid method was evaluated against three benchmark cases, including the cylinder wake flow, forward-facing step compressible flow, and supersonic combustion flow. The results demonstrate superior performance in morphological accuracy, global statistics, and local error metrics, and notably, the hybrid model remains stable even in data-limited regimes where the U-Net alone diverges. Furthermore, this design dramatically reduces computational cost, which achieves 60%–80% lower inference time compared to full diffusion models while preserving high fidelity and long-term prediction accuracy. This work underscores the potential of hybrid generative modeling to enable efficient, robust, and physically consistent predictions for complex, high-speed reactive flows.
Li et al. (2026) studied this question.