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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 solvingpartial differential equations (PDEs) and predicting the dynamics of physicalsystems. However, the predictive limitations of PINNs have not been thoroughlyinvestigated. We look at the flow around a 2D cylinder and find that data-freePINNs are unable to predict vortex shedding. Data-driven PINN exhibits vortexshedding only while the training data (from a traditional CFD solver) isavailable, but reverts to the steady state solution when the data flow stops.We conducted dynamic mode decomposition and analyze the Koopman modes in thesolutions obtained with PINNs versus a traditional fluid solver (PetIBM). Thedistribution of the Koopman eigenvalues on the complex plane suggests that PINNis numerically dispersive and diffusive. The PINN method reverts to the steadysolution possibly as a consequence of spectral bias. This case study reaisesconcerns about the ability of PINNs to predict flows with instabilities,specifically vortex shedding. Our computational study supports the need formore theoretical work to analyze the numerical properties of PINN methods. Theresults in this paper are transparent and reproducible, with all data and codeavailable in public repositories and persistent archives; links are provided inthe paper repository at \url{https://github.com/barbagroup/jcs_paper_pinn}, anda Reproducibility Statement within the paper.

Predictive Limitations of Physics-Informed Neural Networks in Vortex Shedding