Soft robots have a unique potential to harness advanced functionalities through materials engineering, chemistry, and advanced fabrication. However, modeling and control of soft robot bodies is challenging due to non-linearities and time-dependencies of materials physico-chemical properties. With the rapid development of artificial intelligence technologies, deep neural networks (DNN) have become an essential tool for exploring the relationships between inputs and outputs of challenging systems under complex environmental conditions. In this work, rather than physically modeling a soft robotic system, we treat the entire system, including its environment, as a complex but deterministic input-output system, and we use DNNs to estimate these relationships. As an application example, our training results show that DNNs can accurately simulate the physical properties of an underwater bio-inspired soft robot. Validation experiments show that measured propulsive forces are in good agreement with target values predicted by DNNs. Our experiments show the potential of using DNNs to accomplish rapid modeling of bio-inspired propulsion and facilitate control.