用物理约束提升神经网络求解湍流，无需实验数据即可高效预测复杂工况。

Physics-informed neural networks (PINNs) demonstrate promising potential in parameterized engineering turbulence optimization problems but face challenges, such as high data requirements and low computational accuracy when applied to engineering turbulence problems. This study proposes a framework that enhances the ability of PINNs to solve parametric turbulence problems without training datasets from experiments or CFD-Parametric Turbulence PINNs (PT-PINNs)). Two key methods are introduced to improve the accuracy and robustness of this framework. The first is a soft constraint method for turbulent viscosity calculation. The second is a pre-training method based on the conservation of flow rate in the flow field. The effectiveness of PT-PINNs is validated using a three-dimensional backward-facing step (BFS) turbulence problem with two varying parameters (Re = 3000-200000, ER = 1.1-1.5). PT-PINNs produce predictions that closely match experimental data and computational fluid dynamics (CFD) results across various conditions. Moreover, PT-PINNs offer a computational efficiency advantage over traditional CFD methods. The total time required to construct the parametric BFS turbulence model is 39 hours, one-sixteenth of the time required by traditional numerical methods. The inference time for a single-condition prediction is just 40 seconds-only 0.5% of a single CFD computation. These findings highlight the potential of PT-PINNs for future applications in engineering turbulence optimization problems.