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 general tank, is first tested to identify a neural network model able to provide the sloshing force that the fluid provide to the tank boundary when the tank is set on vertical motion. Under specific hypotheses the obtained reduced order model can be scaled to account for tanks with different size. This model is a computational cost-effective tool that can be exploited to simulate complex fluid structure interaction phenomena without involving computational fluid dynamics. As a proof of concept of the methodology another experiment involving a different tank with different size attached to a single degree of freedom mechanical model is considered to assess the effectiveness of the scaled neural network in predicting the sloshing forces when coupled with the structure. The free response of the second experimental setup is compared with that obtained by the related simulation in which the slosh dynamics is replaced by the neural-network based reduced order model. The neural-network based reduced order model for vertical sloshing is able to consistently reproduce the overall increase in damping performance of the system as a function of the oscillation amplitude