In this work, physics-based recurrent neural network (RNN) modeling approaches are proposed for a general class of nonlinear dynamic process systems to improve prediction accuracy by incorporating a priori process knowledge. Specifically, a hybrid modeling method is first introduced to integrate first-principles models and RNN models. Subsequently, a partially-connected RNN modeling method that designs the RNN structure based on a priori structural process knowledge, and a weight-constrained RNN modeling method that employs weight constraints in the optimization problem of the RNN training process are developed. The proposed physics-based RNN models are utilized in model predictive controllers and applied to a chemical process network example to demonstrate their improved approximation performance compared to the fully-connected RNN model that is developed as a black box model. (C) 2020 Elsevier Ltd. All rights reserved.