The use of neural networks (NN) to accelerate fluid simulations have seen an increase in interest in the past years. One such way is the use of NN based multi-fidelity models, where NNs are trained on data produced by higher-order and low-order numerical methods to produce residual models of the errors that allow for correcting the model based on lower-order numerical methods. In advanced numerical simulations the increased accuracy enabled by the use of higher-order numerical methods generally come at an increased computational cost compared to their lower-order counterparts, usually due to an increase in degrees of freedom (DoF) as well as more restrictive time-stepping conditions. We propose a neural network accelerated finite-difference (NN-FD) method for wave simulation using potential flow, through a multi-fidelity modeling approach to improve computational efficiency and accuracy. High-order finite-difference (FD) methods can be used to generate training data for a neural network, which learns to correct the errors of a lower-order FD scheme. The goal of this correction is to effectively allow the low-order FD scheme to achieve higher accuracy without incurring the associated computational cost. In earlier work on time-dependent purely hyperbolic equations, multi-fidelity modeling has been shown to achieve a reduction in computational cost in comparison to the high-order FD methods and that the NN-FD approach maintains higher-order convergence rates and achieves lower errors compared to standalone low-order FD methods. In the current work, this method is extended to the free surface potential flow equations and in this talk, we will present the method, along with our numerical results to illuminate the potential of utilizing multi-fidelity methods in the context of advanced free surface wave models.