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

By Anuj Karpatne, William Watkins, Jordan S. Read, Vipin Kumar. arXiv.org, 2017

661 citations recorded by the source corpus.

This paper introduces a novel framework for learning data science models by using the scientific knowledge encoded in physics-based models. This framework, termed as physics-guided neural network (PGNN), leverages the output of physics-based model simulations along with observational features to generate predictions using a neural network architecture. Further, we present a novel class of learning objective for training neural networks, which ensures that the model predictions not only show lower errors on the training data but are also \emph{consistent} with the known physics. 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 in the learning of neural network model parameters. 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 physical consistency of results.

Subfields: Environmental Engineering, Statistical and Nonlinear Physics, Water Science and Technology

View Paper: https://www.semanticscholar.org/paper/9ec33f323bab1d39a674b0400c8ed3331a12beed

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Citations in the corpus

Physics-informed machine learning: case studies for weather and climate modelling (2021, methodology): “[13] for modelling lake temperatures; Beucler et al.”
Integrating Physics-Based Modeling with Machine Learning: A Survey (2020, methodology): “Karpatne et al [128] showed that using the output of a physics-based model as one feature in an ML model along with inputs used to drive the physics-based model for lake temperature modeling can improve predictions.”
Potential, challenges and future directions for deep learning in prognostics and health management applications (2020, background): “…for integrating domain knowledge in the learning process, including physics-informed neural networks (Raissi et al., 2019; Raissi, 2018), physics-guided neural networks (Karpatne et al., 2017), semantic-based regularization (Diligenti et al., 2017) and integration of logic rules (Hu et al., 2016a).”
Deep convolutional neural networks for eigenvalue problems in mechanics (2018, methodology): “As is standard practice in modern NN implementations, all input material property data is normalized through mean normalization xnorm = x − x̄ xmax − xmin , (16)”
Deep learning in environmental remote sensing: Achievements and challenges (2020, background): “For example, Karpatne et al. (2017) established a physics-constrained NN model for the problem of lake temperature modeling.”
Informed Machine Learning – A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems (2019, methodology): “It can then be used as an additional performance metric for model comparison [12].”
Towards Physics-informed Deep Learning for Turbulent Flow Prediction (2019, background): “[1, 12] proposed physics guided neural networks to model temperature of lakes by explicitly regularising the loss function with physical constraints.”
Machine Learning for the Geosciences: Challenges and Opportunities (2017, background): “such as air temperature, wind speed, and solar radiation, in conjunction with the outputs of physics-based models of lake temperature [91].”
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, methodology): “In the context of lake temperature modeling, Karpatne et al. [140] includes a physics-based penalty that ensures that predictions of denser water are at lower depths than predictions of less dense water, a known monotonic relationship.”
Can deep learning beat numerical weather prediction? (2021, background): “One of the ﬁrst studies to demonstrate that physical constraints can efﬁciently reduce systematic biases in lake temperature predictions, while at the same time enhancing generalization capability, was Karpatne et al. [129].”
Deep Learning of Subsurface Flow via Theory-guided Neural Network (2019, background): “Karpatne et al. (2017) also proposed a physics-guided neural network (PGNN) model, which adds physics-based loss into the learning objective function of neural network to obtain scientifically consistent results.”
Process‐Guided Deep Learning Predictions of Lake Water Temperature (2019, background): “…Learning models have shown great promise to improve prediction accuracy of water column lake temperatures; however, implementations are currently limited to one or two well ‐ observed lakes where models were trained and evaluated under similar conditions (Jia et al., 2019; Karpatne et al., 2018).”