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This paper proposes a physics-guided recurrent neural network model (PGRNN)that combines RNNs and physics-based models to leverage their complementarystrengths and improve the modeling of physical processes. Specifically, we showthat a PGRNN can improve prediction accuracy over that of physical models,while generating outputs consistent with physical laws, and achieving goodgeneralizability. Standard RNNs, even when producing superior predictionaccuracy, often produce physically inconsistent results and lackgeneralizability. We further enhance this approach by using a pre-trainingmethod that leverages the simulated data from a physics-based model to addressthe scarcity of observed data. The PGRNN has the flexibility to incorporateadditional physical constraints and we incorporate a density-depthrelationship. Both enhancements further improve PGRNN performance. Although wepresent and evaluate this methodology in the context of modeling the dynamicsof temperature in lakes, it is applicable more widely to a range of scientificand engineering disciplines where mechanistic (also known as process-based)models are used, e.g., power engineering, climate science, materials science,computational chemistry, and biomedicine.

Physics Guided RNNs for Modeling Dynamical Systems: A Case Study in Simulating Lake Temperature Profiles