AI 中文总结
本文针对Navier-Stokes涡脱问题，研究物理信息神经网络（PINN）技术的交互效应，发现仅周期性激活函数（SIREN）与因果加权结合可实现4.1%的平均相对L2误差，额外添加技术会导致性能下降，说明PINN干预措施存在非线性交互。
AI 中文摘要
物理信息神经网络（PINNs）将控制偏微分方程直接嵌入训练损失，为非定常流提供了一种替代昂贵CFD求解器的有前景方案。然而，为改进PINN训练提出的技术通常每次仅验证一种，这些技术是否真正可组合仍不明确。本文针对DFG/Schafer-Turek非定常圆柱尾流基准深入研究该问题。单独来看，几乎每项技术的表现均不优于未处理的基线。但将周期性激活函数（SIREN）与因果加权结合，可解锁此前无法触及的性能区间，重构的速度场与压力场相对于OpenFOAM参考解的平均相对L2误差为4.1%。添加更多技术反而会导致性能灾难性下降，表明单独有效的PINN干预措施可产生非线性交互，更复杂的训练方案未必更好。
英文摘要
Physics-informed neural networks (PINNs) embed governing partial differential equations directly into the training loss, offering a promising alternative to costly CFD solvers for unsteady flows. Yet the growing list of techniques proposed to improve PINN training is typically validated one at a time, leaving open whether these techniques actually compose. We study this question in depth on the DFG/Schafer-Turek unsteady cylinder wake benchmark. In isolation, nearly every technique performs no better than an untreated baseline. However, combining periodic (SIREN) activations with causal weighting unlocks a previously inaccessible regime, reconstructing velocity and pressure fields to within 4.1% average relative L2 error against an OpenFOAM reference solution. Adding further techniques instead causes catastrophic performance degradation, demonstrating that individually effective PINN interventions can interact nonlinearly and that more elaborate training recipes are not necessarily better.
