Derivative neural operators with physics-guided diffusion refinement for predicting two-phase flow dynamics

Time-dependent partial differential equations play a central role in modeling two-phase flow systems, but high-resolution long-term simulations remain computationally demanding. Although data-driven surrogate models provide efficient alternatives, they often suffer from temporal error accumulation and the loss of fine-scale physical structures. In this work, we propose a framework based on derivative neural operators with physics-guided diffusion refinement for fast high-resolution prediction of two-phase flow dynamics. A derivative neural operator is trained on coarse grids to learn the instantaneous temporal dynamics of the physical fields, and the predicted derivatives are advanced using a fourth-order Runge–Kutta scheme for stable and efficient time integration. During the refinement process, the gradient of the governing-equation residual is incorporated as conditional physical guidance, encouraging the refined fields to satisfy the underlying two-phase flow dynamics. In this framework, the coarse-grid derivative operator captures the dominant temporal dynamics, whereas the diffusion refinement recovers interfacial morphology and vortical details that are lost during coarse-grid prediction. Numerical results on several representative systems demonstrate that the proposed framework improves predictive accuracy and spatial resolution.