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

arXiv: https://arxiv.org/abs/1710.11431 · HTML: https://mlsanity.com/paper/1710.11431/

## Key facts

- Cited by 131 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2017.

## Built on by (most cited first, 30 of 131)

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- [j-Wave: An open-source differentiable wave simulator](https://mlsanity.com/paper/2207.01499/) (2022)
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## Abstract (arXiv)

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 urlhttps://github.com/arkadaw9/PGNN.