Physics-guided architecture (PGA) of LSTM models for uncertainty quantification in lake temperature modeling

This chapter focuses on meeting the need to produce neural network outputs that are physically consistent and also express uncertainties, a rare combination to date. It explains the effectiveness of physics-guided architecture - long-short-term-memory (PGA-LSTM) in achieving better generalizability and physical consistency over data collected from Lake Mendota in Wisconsin and Falling Creek Reservoir in Virginia, even with limited training data. Even though PGL formulations result in improvements in the generalization performance and lead to machine learning (ML) predictions that are more physically consistent, simply adding the physics-based loss function in the learning objective does not overcome the black-box nature of neural network architectures, which often involve arbitrary design choices. The temperature of water in a lake is a fundamental driver of lake biogeochemical processes, and it controls the growth, survival, and reproduction of fishes in the lake.