Physics-informed neural-network analysis of free-surface wake and vortex-band interference past dual cylinders

Cylindrical members of offshore platforms and sea-crossing bridges are continuously exposed to traveling-wave-induced hydrodynamic loads, where rapid prediction and mechanistic interpretation of free-surface gas–liquid flow are both desirable. Conventional finite-volume simulations for complex two-phase configurations remain expensive and are difficult to reuse across boundary or geometric changes. To address these issues, we develop a physics-informed neural network framework that combines a residual-connected convolutional neural network geometric encoder with a Transformer attention mechanism in a transfer-learning architecture, termed the physics-informed residual-connected convolutional transformer network (PRCT-Net). High-fidelity reference solutions are generated using the Reynolds-averaged Navier–Stokes equations coupled with the volume of fluid method and the shear stress transport turbulence model and are used to validate traveling-wave-driven two-phase flow past two cylinders under multiple operating conditions. PRCT-Net achieves high-fidelity reconstruction of the free surface and the associated velocity and pressure fields while substantially accelerating inference; under the baseline condition, the maximum relative error of wave height is about 3.2%, velocity errors remain below 4% at all sampled instants, and the overall error is within 3.5%. A hierarchical freeze–unfreeze fine-tuning strategy further enables efficient cross-condition adaptation, reaching the target accuracy within 119 epochs while preserving a stable geometric–temporal latent space. From a mechanistic perspective, an overlapping V-shaped free-surface wake forms downstream at the steady stage and gradually decouples as cylinder spacing increases. The Ω field reveals V-shaped downstream vortex bands whose trajectory angles closely match those extracted from the free-surface wake. Leveraging PRCT-Net for rapid sampling over operating conditions, an empirical correlation for the wake–vortex trajectory angles is fitted, providing a quantitative and efficient tool for characterizing wake interference and vortex-band dynamics in free-surface flow past two cylinders.