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

该论文提出了一种物理引导的循环神经网络模型，结合了循环神经网络与基于物理的模型，利用它们的互补优势来改善物理过程建模的精度，从而在各种科学和工程领域得到应用。

物理导向循环神经网络模拟动力系统：以模拟湖泊温度剖面为案例研究