Investigation of local scour predictions beneath a submerged cylinder using Fourier neural operator variants

Scour beneath submerged cylinders impacts the stability and lifetime of submarine pipelines, motivating fast surrogate models that can forecast scour evolution in real time. This study develops a Fourier neural operator (FNO)-based surrogate for predicting local scour beneath a submerged cylinder under steady inflow conditions. This problem is strongly nonlinear and contains a sharp interface between the deforming sediment bed and the water column, as well as multiscale interactions between the solid and fluid phases. These characteristics create formidable challenges for the accuracy and stability of conventional FNOs that aim to encode the flow using a limited number of Fourier modes. This study addresses these challenges with a novel U-Net enhanced FNO (U-FNO) architecture that augments global spectral convolutions with a U-Net path for local feature extraction. By using the data generated by a high-fidelity Eulerian–Eulerian two-phase flow model, the proposed U-FNO framework yields stable autoregressive rollouts with low relative errors across all predicted fields and achieves orders-of-magnitude faster inference than the baseline two-phase flow model. The results demonstrate that hybrid operator-learning architectures can extend FNOs' applicability to problems containing local sharp gradients, such as multiphase scour dynamics, while preserving computational efficiency.