Physics-Guided Architecture (PGA) of Neural Networks for Quantifying Uncertainty in Lake Temperature Modeling

TL;DR

This paper introduces a physics-guided neural network architecture for lake temperature modeling that ensures physical consistency and improves uncertainty quantification, especially with limited data.

Contribution

The novel PGA architecture integrates physical constraints directly into neural networks, enhancing uncertainty estimation without compromising physical realism.

Findings

Improved generalizability and physical consistency in temperature predictions.

Effective uncertainty quantification matching ground-truth distributions.

Applicable to datasets with limited training data.

Abstract

To simultaneously address the rising need of expressing uncertainties in deep learning models along with producing model outputs which are consistent with the known scientific knowledge, we propose a novel physics-guided architecture (PGA) of neural networks in the context of lake temperature modeling where the physical constraints are hard coded in the neural network architecture. This allows us to integrate such models with state of the art uncertainty estimation approaches such as Monte Carlo (MC) Dropout without sacrificing the physical consistency of our results. We demonstrate the effectiveness of our approach in ensuring better generalizability as well as physical consistency in MC estimates over data collected from Lake Mendota in Wisconsin and Falling Creek Reservoir in Virginia, even with limited training data. We further show that our MC estimates correctly match the distribution of ground-truth observations, thus making the PGA paradigm amenable to physically grounded uncertainty quantification.