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

Physics Guided Recurrent Neural Networks For Modeling Dynamical Systems: Application to Monitoring Water Temperature And Quality In Lakes