  In this paper, we introduce a novel framework for combining scientific
knowledge within physics-based models and recurrent neural networks to advance
scientific discovery in many dynamical systems. We will first describe the use
of outputs from physics-based models in learning a hybrid-physics-data model.
Then, we further incorporate physical knowledge in real-world dynamical systems
as additional constraints for training recurrent neural networks. We will apply
this approach on modeling lake temperature and quality where we take into
account the physical constraints along both the depth dimension and time
dimension. By using scientific knowledge to guide the construction and learning
the data-driven model, we demonstrate that this method can achieve better
prediction accuracy as well as scientific consistency of results.
