Optimizing the geometry and increasing the efficiency through PTO control of oscillating surge wave energy converters require the development of effective reduced-order models that can predict their hydrodynamic response. We implement a multi-step approach to identify the coefficients of the equation governing this response. Data from quasi-static, free decay and torque-forced experiments are used to respectively identify and represent the stiffness, the radiation damping, and the added mass and nonlinear damping terms. Particularly, we implement a data-driven system discovery, referred to as Physics-Informed Neural Network, to identify the added mass and nonlinear damping coefficients in the governing equations. Validation is performed via comparing time series predicted by the reduced order model to the measured time series.