Liu, YujiaYujiaLiuYang, LuchunLuchunYangYe, MaokunMaokunYeWan, DechengDechengWanAbdel-Maksoud, MoustafaMoustafaAbdel-Maksoud2026-04-162026-04-162026-02-03Ocean engineering 351: 124460 (2026)https://hdl.handle.net/11420/62745The Moving Particle Semi-implicit (MPS) method is a widely used Lagrangian Particle method for simulating free-surface flows. In conventional MPS simulations, the solution of the pressure Poisson equation (PPE) in the pressure-projection step typically constitutes a major portion of the overall computational cost, particularly for large-scale particle systems. To address this issue, we propose a data-driven hybrid approach that integrates the MPS method with the Graph Attention Network (GAT), denoted as MPS-GAT. In this approach, GAT serves as a surrogate model to replace the traditional PPE solver for pressure estimation in MPS. The effectiveness of the proposed method is evaluated using a benchmark case of tank sloshing. The accuracy is verified by comparing the pressure predictions from MPS-GAT with numerical results obtained from solving the PPE. Spatial errors are quantified by differences in mesh-interpolated mean fields between MPS-GAT and traditional MPS method, and temporal errors by the discrepancy in the mean particle velocity and pressure over time. To evaluate generalization, the model is tested on sloshing scenarios with filling ratios, excitation frequencies, and amplitudes not included in the training data. Remarkably, the model exhibited exceptional generalization performance under internal-obstacle configurations despite their complete absence from the training distribution. Furthermore, the proposed hybrid method significantly improves computational efficiency. In our tests with particle counts from 1000 to 130000, MPS-GAT reduces the pressure estimation time by more than 30 times compared with the traditional MPS method when the particle number exceeds 120000. The speedup ratio increases further with larger particle counts, demonstrating clear advantages for large scale free surface flow simulations.en0029-80182026ElsevierGraph attention networkMPSPressure Poisson equationTank sloshingTechnology::600: TechnologyTechnology::620: Engineering::620.1: Engineering Mechanics and Materials ScienceJournal Article10.1016/j.oceaneng.2026.124460