In this paper, we conducted a selective review on the recent progress in physics insight and modeling of flexible cylinder flow-induced vibrations (FIVs). FIVs of circular cylinders include vortex-induced vibrations (VIVs) and wake-induced vibrations (WIVs), and they have been the center of the fluid-structure interaction (FSI) research in the past several decades due to the rich physics and the engineering significance. First, we summarized the new understanding of the structural response, hydrodynamics, and the impact of key structural properties for both the isolated and multiple circular cylinders. The complex FSI phenomena observed in experiments and numerical simulations are explained carefully via the analysis of the vortical wake topology. Following up with several critical future questions to address, we discussed the advancement of the artificial intelligent and machine learning (AI/ML) techniques in improving both the understanding and modeling of flexible cylinder FIVs. Though in the early stages, several AL/ML techniques have shown success, including auto-identification of key VIV features, physics-informed neural network in solving inverse problems, Gaussian process regression for automatic and adaptive VIV experiments, and multi-fidelity modeling in improving the prediction accuracy and quantifying the prediction uncertainties. These preliminary yet promising results have demonstrated both the opportunities and challenges for understanding and modeling of flexible cylinder FIVs in today's big data era.

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