Summary: We present a new approach to simulating wave-structure interaction dynamics using proper orthogonal decomposition by directly employing eigenmodes extracted from particle image velocimetry experimental data. A low-dimensional Galerkin model is constructed incorporating up to 12 modes and time-dependent boundary conditions. A penalty method is introduced to deal effectively with such boundary conditions. Our results suggest that this model represents accurately the flow dynamics, and it is asymptotically stable without the use of any ad hoc dissipation or other stabilization schemes. Our findings are documented by applying this approach to studying the vorticity dynamics of wave-cylinder interactions at Keulegan-Carpenter numbers of 9.3 and 13.9.