We develop a robust computational framework to infer the motion of a flexible cylinder undergoing vortex induced vibration. Given scattered data in space–time on displacement and hydrodynamic forces, we use physics-informed neural networks (PINNs) (Raissi et al., 2019) to infer the entire motion and characterize the induced vibration by accurately estimating the structural parameters. The developed framework has the flexibility to simultaneously analyze the data over different space–time sub-domains and hence to yield more accurate estimations. We examine the efficiency of the formulation by estimating the damping coefficient of the flexible cylinder, where the training data is obtained by forward simulation of the coupled fluid–solid equations.