Adaptive residual-gradient sampling PINNs for unsteady wake reconstruction around offshore cylinder arrays

Accurate reconstruction of unsteady wakes around offshore cylindrical structures is important for assessing wake interference, flow-induced loads, and the hydrodynamic environment of pile groups, marine risers, and related systems. Physics-informed neural networks (PINNs) provide a mesh-free surrogate modelling approach for such unsteady flows, but their accuracy depends strongly on collocation-point placement in evolving wake and boundary-layer regions. Here, we propose Adaptive Residual-Gradient Unified Sampling (ARGUS) to improve spatial collocation-point selection for cylinder-array wake reconstruction. RAD, RAR-D, and ARGUS are evaluated under a shared local temporal-window protocol. Within each window, ARGUS selects spatial collocation points using a scale-normalized probability density that combines current PDE residuals with a reference-field-derived gradient prior. In this benchmark, the gradient prior is precomputed from a COMSOL high-fidelity solution and is used only to guide sampling, not as an additional supervised loss term. The method is evaluated for two-dimensional incompressible flow past an equilateral triangular cylinder array at Re = 100. Compared with Grid, LHS, RAD and RAR-D sampling, ARGUS reduces average velocity-field RMSE and MAE by 46.5% and 35.2%, respectively. It also improves far-wake prediction, where residual-driven methods tend to over-concentrate collocation points near the cylinders. These results indicate that residual-gradient adaptive sampling can improve PINN-based surrogate prediction for cylinder-array wakes.