Soft robots are made of compliant materials, which increase their flexibility but also presents modeling challenges. The difficulty mainly comes from material nonlinearity, infinite degrees of freedom, uncertain parameters, and complex calculations. This project uses physics-inspired neural networks to solve the last two problems. Based on the piece-wise constant curvature approximation, this work modifies Lagrangian and Hamiltonian neural networks for dynamic modeling of soft robots. In particular, local linear damping and actuator models are added to deep Lagrangian and Hamiltonian neural networks, and a one-step integration algorithm is used in the loss calculation. This project justifies the modified network structure and uses these new neural networks to learn the dynamic model of soft manipulators.