Two-stage physics-informed Fourier neural operator for super-resolution reconstruction and prediction of flow fields

High-fidelity reconstruction and prediction of flow fields from sparse observations present a persistent challenge in computational fluid dynamics and ocean engineering. This study introduces a two-stage physics-informed Fourier neural operator (FNO) framework designed for super-resolution reconstruction and prediction of flow fields under low-resolution conditions. To mitigate the spectral bias of FNOs and the optimization instability inherent in standard physics-informed learning, we employ a decoupled ‘Global Capture + Local Correction’ strategy. Stage 1 utilizes low-resolution data to efficiently capture dominant global dynamics, ensuring rapid convergence to a stable solution manifold. Stage 2 enforces high-resolution physical constraints via spectral differentiation, enabling the unsupervised recovery of fine-scale structures and ensuring physical consistency without reliance on high-resolution labels. The method is validated across three benchmarks of increasing complexity: the 1D viscous Burgers equation (16)× super-resolution, 1.19% relative L2 error), 2D Kolmogorov flow (4× super-resolution, 5.44%), and 2D tandem cylinder wake flow at Re=2.2×104 (4× super-resolution, 5.39%). Results demonstrate that the framework consistently outperforms standard FNO, physics-informed neural operator, and convolutional neural network-based super-resolution models, accurately recovering multiscale features with physical fidelity confirmed by proper orthogonal decomposition analysis and turbulence statistics. Furthermore, the framework demonstrates cross-geometry generalization to unseen cylinder spacing ( L/D=2) and maintains high predictive accuracy under measurement noise up to 5%. By harmonizing inference efficiency with physical rigor, this framework offers a robust, physics-consistent surrogate model for super-resolution reconstruction and prediction, enabling real-time hydrodynamic analysis in future digital twins.