The recent surge of interest in physics-informed neural network (PINN) methods has led to a wave of studies that attest to their potential for solving partial differential equations (PDEs) and predicting the dynamics of physical systems. However, the predictive limitations of PINNs have not been thoroughly investigated. We look at the flow around a 2D cylinder and find that data-free PINNs are unable to predict vortex shedding. Data-driven PINN exhibits vortex shedding only while the training data (from a traditional CFD solver) is available, but reverts to the steady state solution when the data flow stops. We conducted dynamic mode decomposition and analyze the Koopman modes in the solutions obtained with PINNs versus a traditional fluid solver (PetIBM). The distribution of the Koopman eigenvalues on the complex plane suggests that PINN is numerically dispersive and diffusive. The PINN method reverts to the steady solution possibly as a consequence of spectral bias. This case study reaises concerns about the ability of PINNs to predict flows with instabilities, specifically vortex shedding. Our computational study supports the need for more theoretical work to analyze the numerical properties of PINN methods. The results in this paper are transparent and reproducible, with all data and code available in public repositories and persistent archives; links are provided in the paper repository at \url{https://github.com/barbagroup/jcs_paper_pinn}, and a Reproducibility Statement within the paper.

翻译：物理信息神经网络（PINN）方法近期的研究热潮引发了众多研究，这些研究证实了其在求解偏微分方程（PDE）及预测物理系统动力学方面的潜力。然而，PINN的预测局限性尚未得到充分探究。我们以二维圆柱绕流为例，发现无数据PINN无法预测涡流脱落。数据驱动PINN仅在训练数据（来自传统计算流体力学求解器）可用时展现出涡流脱落现象，但当数据流停止时，其解会退化为稳态解。我们采用动态模态分解分析了PINN与传统流体求解器（PetIBM）所得解中的库普曼模态。复平面上的库普曼特征值分布表明，PINN具有数值色散和耗散特性。PINN方法退化为稳态解可能源于谱偏置效应。本案例研究对PINN预测含失稳流动（特别是涡流脱落）的能力提出了质疑。我们的计算研究表明，需要更多理论工作来分析PINN方法的数值特性。本文结果透明且可复现，所有数据与代码均公开在持久性存档库中；相关链接见本文仓库\url{https://github.com/barbagroup/jcs_paper_pinn}，文中亦包含可复现性声明。