Title: Fully Convolutional Approach for Simulating Wave Dynamics. Abstract: We investigate the performance of fully convolutional networks to predict the motion and interaction of surface waves in open and closed complex geometries. We focus on a U-Net type architecture and assess its ability to capture and extrapolate wave propagation in time as well as the reflection, interference and diffraction of waves.  We investigate how well the network generalises both to long-time predictions and to geometric configurations not seen during training. We demonstrate that this neural network is capable of accurately predicting the height distribution of waves on a liquid surface within curved and multi-faceted open and closed geometries, when only simple box and right-angled corner geometries were seen during training. We found that the RMSE of the predictions remained of order $1\times10^{-4}$ times the characteristic length of the domain for at least 20 time-steps.