用物理约束神经网络，从稀疏数据重建复杂形状周围非定常流场。

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like computer vision and natural language processing, obtaining such datasets for engineering applications is prohibitively expensive. Physics-Informed Neural Networks (PINNs), a branch of Physics-Informed Machine Learning (PIML), tackle this challenge by embedding physical principles within neural network architectures. PINNs have been extensively explored for solving diverse forward and inverse problems in fluid mechanics. Nonetheless, there is limited research on employing PINNs for flow reconstruction from sparse data under constrained computational resources. Earlier studies were focused on forward problems with well-defined data. The present study attempts to develop models capable of reconstructing the flow field data from sparse datasets mirroring real-world scenarios. This study focuses on two cases: (a) two-dimensional (2D) unsteady laminar flow past a circular cylinder and (b) three-dimensional (3D) unsteady turbulent flow past an ultra-large container ship (ULCS). The first case compares the effectiveness of training methods like Standard PINN and Backward Compatible PINN (BC-PINN) and explores the performance enhancements through systematic relaxation of physics constraints and dynamic weighting of loss function components. The second case highlights the capability of PINN-based models to learn underlying physics from sparse data while accurately reconstructing the flow field for a highly turbulent flow.