AI 中文总结
该研究提出两阶段物理信息神经网络SnapPINN，从稀疏含噪速度快照重建流场的压力、速度等，在湍流管流数据上实现高精度，还建立了可靠性图以指导实验条件选择。
AI 中文摘要
从实验速度测量数据重建压力和湍流量具有挑战性，尤其是在没有时间分辨数据的情况下。此外，低粒子浓度、有限分辨率和测量噪声等限制严重阻碍了准确流场的重建。我们提出SnapPINN，一种两阶段物理信息神经网络（PINN），可从单个稀疏含噪速度数据快照成功重建三维速度、其空间梯度、压力场，并估算湍动能耗散。在三维DNS湍流管流数据上评估时，SnapPINN采用正弦激活架构，包含顺序训练、解耦的速度和压力子网络。第一阶段，速度网络拟合粒子数据，同时强制满足不可压缩条件，作为物理一致的平滑算子，正则化速度梯度以抵抗噪声。第二阶段，速度网络被冻结，压力网络利用压力泊松方程和预训练的速度梯度进行训练。我们在100个测试用例上系统映射SnapPINN的重建性能，以模拟具有挑战性的实验条件，例如添加显著位置噪声、速度场线性化，以及低至完全解析DNS网格0.07%的粒子浓度。定量来看，即使在极其稀疏和含噪条件下，主体速度的重建误差在0.5%以内，对梯度敏感的能量耗散率误差低于50%，后验推断的Reτ误差在4%至24%之间。最后，我们建立了实用的可靠性图，显示在没有真值的情况下，哪些实验条件可能产生可靠的SnapPINN重建结果。
英文摘要
Reconstructing pressure and turbulence quantities from experimental velocity measurements is challenging, especially without time-resolved data. Furthermore, limitations such as low seeding density, finite resolution, and measurement noise severely hinder the reconstruction of accurate flow fields. We introduce SnapPINN, a two-stage physics-informed neural network (PINN) that successfully reconstructs 3D velocity, their spatial gradients, pressure fields and estimates turbulent kinetic energy dissipation from a single snapshot of sparse, noisy velocity data. Evaluated here on 3D DNS turbulent pipe flow data, SnapPINN uses a sine-activated architecture with sequentially trained, decoupled velocity and pressure sub-networks. In stage 1, the velocity network fits particle data while enforcing incompressibility, serving as a physically consistent smoothing operator that regularises velocity gradients against noise. In stage 2, the velocity network is frozen, and the pressure network is trained using the pressure Poisson equation and the pretrained velocity gradients. We systematically map reconstruction performance of SnapPINN across 100 test cases to mimic challenging experimental, such as adding significant position noise, linearization of velocity field and seeding sparsity as low as $0.07\%$ of the fully resolved DNS grid. Quantitatively, bulk velocity was reconstructed within $0.5\%$, while errors remained below $50\%$ for the gradient-sensitive energy dissipation rate and within $4$--$24\%$ for the a~posteriori inferred $\mathrm{Re}_τ$, even under extremely sparse and noisy conditions. Finally, we establish a practical reliability map that shows which experimental conditions are likely to yield reliable SnapPINN reconstructions in the absence of ground truth.
