Physics field super-resolution reconstruction via enhanced diffusion model and fourier neural operator

• A novel FNO-diffusion framework is proposed for high-fidelity super-resolution of flow fields. • Adaptive weighted FNO and residual-guided diffusion effectively capture global dependencies and fine details. • Stability and efficiency are ensured via a Markov chain formulation and adaptive ODE solver for reverse diffusion. With the growing demand for high-precision flow field simulations in computational science and engineering, the super-resolution reconstruction of physical fields has attracted considerable research interest. However, traditional numerical methods often entail high computational costs, involve complex data processing, and struggle to capture fine-scale high-frequency details. To address these challenges, we propose an innovative super-resolution reconstruction framework that integrates a Fourier neural operator (FNO) with an enhanced diffusion model. The framework employs an adaptively weighted FNO to process low-resolution flow field inputs, effectively capturing global dependencies and high-frequency features. Furthermore, a residual-guided diffusion model is introduced to further improve reconstruction performance. This model uses a Markov chain to map high-resolution fields to low-resolution counterparts and incorporates a reverse diffusion process solved by an adaptive time-step ordinary differential equation (ODE) solver, ensuring both stability and computational efficiency. Experimental results demonstrate that the proposed framework significantly outperforms existing methods in terms of accuracy and efficiency, offering a promising solution for fine-grained data reconstruction in scientific simulations.