Fast marine craft dynamics in waves differ significantly from those of displacement vessels. While linear seakeeping theories are generally adequate for bodies predominantly supported by buoyancy, they fail when the dominant supporting force is hydrodynamic lift, as in planing hulls. In such cases, strongly nonlinear hydrodynamic phenomena govern the lift generated by the planing surface. Moreover, modern high-performance hulls often feature complex geometries, such as hard chines, multiple steps, and deadrise bottoms, to enhance efficiency and operability. Although several reduced-order modeling approaches have been shown to be effective, they typically require extensive experimental campaigns or high-fidelity numerical simulations to provide the data needed for model calibration. Recent advances in system identification and machine learning offer promising alternatives to reduce the number of required runs while retaining predictive capability. This paper presents a comparison between two different modeling approaches. The first is the Sparse Identification of Nonlinear Dynamics (SINDy) framework, developed in the last decade as an effective tool for discovering governing equations of nonlinear dynamical systems. This approach yields compact, interpretable models in which the identified terms admit a clear physical meaning. The second model is learning based neural ordinary differential equation (neural ODE) forecaster. It compresses the past 0.5 seconds of history of measured kinematics with a GRU into a compact state. That state is then propagated forward with the learned ODE and converts into predictions of the next 0.25 seconds of vertical force and moment. Experimental data are used to train and validate the proposed models. The experiments were conducted at the U.S. Naval Academy and consist of forced vertical motions of a double-stepped planing hull in calm water and in regular head waves. The resulting models are shown to accurately predict the hydrodynamic loads, including forces and moments, acting on the hull from prescribed motions.