Coastal development and urban planning are facing different issues including natural disasters and extreme storm events. The ability to track and forecast the evolution of the physical characteristics of coastal areas over time is an important factor in coastal development, risk mitigation and overall coastal zone management. Traditional bathymetry measurements are obtained using echo-sounding techniques which are considered expensive and not always possible due to various complexities. Remote sensing tools such as satellite imagery can be used to estimate bathymetry using incident wave signatures and inversion models such as physical models of waves. In this work, we present two novel approaches to bathymetry estimation using deep learning and we compare the two proposed methods in terms of accuracy, computational costs, and applicability to real data. We show that deep learning is capable of accurately estimating ocean depth in a variety of simulated cases which offers a new approach for bathymetry estimation and a novel application for deep learning.