PRCT-Net: A Transfer-Learning Physics-Informed Convolutional Transformer for Fast Surrogate Prediction of Confined Dual-Cylinder 3D Free-Surface Two-Phase Flow

Abstract The supporting foundations of offshore engineering structures, such as offshore platforms and sea-crossing bridges, are continuously exposed to wave-induced loads. A thorough understanding of their hydrodynamic characteristics is essential for ensuring operational stability and extending service life. Traveling wave phenomena in such scenarios are representative gas-liquid two-phase flow problems. Conventional finite volume methods for simulating gas-liquid two-phase flows generally impose strict requirements on mesh resolution and time-step size. Accurate solutions become particularly difficult to obtain when the computational domain exhibits complex topological features. Furthermore, changes in boundary conditions or computational domains necessitate repeated simulations, which prevents the efficient reuse and long-term deployment of numerical models. To address these limitations, this study developed a physics-informed neural network framework that incorporated a Res-CNN-based (residual-connected convolutional neural network) geometric encoder and a transformer attention mechanism into a transfer learning architecture, referred to as PRCT-Net (physics-informed residual-connected convolutional transformer network). This study proposes a computational approach for three-dimensional gas-liquid two-phase flow problems. The effectiveness of the proposed method were validated by simulating traveling-wave flow fields around dual cylinders under multiple operating conditions. The results demonstrate that, compared with conventional finite volume methods, the proposed PRCT-Net substantially enhances computational efficiency while maintaining high prediction accuracy for two-phase flow problems. In addition, the model supports single-stage training and sustained deployment, enabling robust inference across a wide range of unseen operating conditions.