In this paper, a nonlinear reduced order model based on neural networks is introduced in order to model vertical sloshing for use in fluid-structure interaction simulations. A box partially filled with water, representative of a wing tank, is first tested to identify a neural network model and then attached to a cantilever beam to test the effectiveness of the neural network in predicting the sloshing forces when coupled with the structure. The experimental set-up is equipped with accelerometers and load cells at the interface between the tank and an electrodynamic shaker, which provides vertical acceleration to the tank. Accelerations and interface forces measured during the experimental tests are employed to identify a recurrent network able to return the vertical sloshing forces when the tank is set on vertical motion. The identified model is then experimentally tested and assessed by its integration on the tip of a cantilever beam. The free response of the experimental setup are compared with those obtained by simulating an equivalent virtual model in which the identified reduced-order model is integrated to account for the effects of vertical sloshing.