Process-oriented sampling strategy for enhancing flow field reconstruction accuracy in physics-informed neural networks
摘要
Physics-Informed Neural Networks (PINNs) are sensitive to how collocation and labeled points are distributed, especially in unsteady flows with localized high-gradient dynamics. Existing sampling strategies are mainly uniform or residual-driven and may underutilize physically critical regions while oversampling low-information areas. We propose a process-oriented sampling framework that jointly optimizes collocation and labeled-data placement by prioritizing feature-rich regions. The framework supports two region definitions: (i) empirical regions identified by domain knowledge, such as the Karman vortex street, and (ii) automatically detected feature-dominant regions obtained through KDTree-based neighborhood search and vorticity-divergence analysis. The framework is evaluated using a two-dimensional cylinder wake at Re = 3900 and a high-Reynolds-number wind-flow case at Re = 4.8 × 10⁷. In the cylinder-wake case, increasing collocation density in feature-rich regions reduces reconstruction errors by up to one order of magnitude. For labeled data, a “fewer but better” effect is observed: strategically placing fewer labels in feature-rich regions outperforms placing more labels in non-feature regions. In the high-Re case, feature-dominant sampling improves prediction accuracy for u, v, and p, reducing errors by 14.7%, 14.5%, and 15.2%, respectively, compared with uniform sampling at the same point budget. In fixed-budget decaying-flow and high-Re settings, the proposed physics-guided allocation also achieves lower reconstruction errors than residual-based adaptive refinement while avoiding online residual evaluation and dynamic resampling. These results show that process-oriented, physics-aware allocation provides a scalable and effective route for improving PINN accuracy and physical consistency in complex flows.