Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling

TLDR

The study proposes a physics‑guided neural network framework that fuses physics‑based model outputs with neural networks to enhance scientific discovery. PGNN combines physics‑based simulation outputs and observational data in a hybrid neural network, employs physics‑based loss functions to enforce consistency, and applies this approach to lake temperature modeling using a loss derived from temperature, density, and depth relationships, with all code and data publicly available. The framework improves generalizability and scientific consistency of predictions compared to conventional neural networks.

Abstract

This paper introduces a framework for combining scientific knowledge of physics-based models with neural networks to advance scientific discovery. This framework, termed physics-guided neural networks (PGNN), leverages the output of physics-based model simulations along with observational features in a hybrid modeling setup to generate predictions using a neural network architecture. Further, this framework uses physics-based loss functions in the learning objective of neural networks to ensure that the model predictions not only show lower errors on the training set but are also scientifically consistent with the known physics on the unlabeled set. We illustrate the effectiveness of PGNN for the problem of lake temperature modeling, where physical relationships between the temperature, density, and depth of water are used to design a physics-based loss function. By using scientific knowledge to guide the construction and learning of neural networks, we are able to show that the proposed framework ensures better generalizability as well as scientific consistency of results. All the code and datasets used in this study have been made available on this link \url{https://github.com/arkadaw9/PGNN}.