A novel approach for numerically propagating acoustic waves in two-dimensional quiescent media has been developed through a fully convolutional multi-scale neural network. This data-driven method managed to produce accurate results for long simulation times with a database of Lattice Boltzmann temporal simulations of propagating Gaussian Pulses, even in the case of initial conditions unseen during training time, such as the plane wave configuration or the two initial Gaussian pulses of opposed amplitudes. Two different choices of optimization objectives are compared, resulting in an improved prediction accuracy when adding the spatial gradient difference error to the traditional mean squared error loss function. Further accuracy gains are observed when performing an a posteriori correction on the neural network prediction based on the conservation of acoustic energy, indicating the benefit of including physical information in data-driven methods.