# Probabilistic modeling of lake surface water temperature using a Bayesian spatio-temporal graph convolutional neural network

arXiv: https://arxiv.org/abs/2109.13235 · HTML: https://mlsanity.com/paper/2109.13235/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 15 references that are in the map.
- First posted on arXiv 27 Sep 2021.

## Builds on (most cited first, 11 of 11)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Bayesian graph convolutional neural networks for semi-supervised classification](https://mlsanity.com/paper/1811.11103/) (2018)
- [Bayesian Recurrent Neural Networks](https://mlsanity.com/paper/1704.02798/) (2017)
- [Bayesian Graph Convolutional Neural Networks using Node Copying](https://mlsanity.com/paper/1911.04965/) (2019)
- [Bayesian Spatio-Temporal Graph Convolutional Network for Traffic Forecasting](https://mlsanity.com/paper/2010.07498/) (2020)

## Built on by (most cited first, 2 of 2)

- [Time Series Predictions in Unmonitored Sites: A Survey of Machine Learning Techniques in Water Resources](https://mlsanity.com/paper/2308.09766/) (2023)
- [HydroGAT: Distributed Heterogeneous Graph Attention Transformer for Spatiotemporal Flood Prediction](https://mlsanity.com/paper/2509.02481/) (2025)

## Abstract (arXiv)

Accurate lake temperature estimation is essential for numerous problems tackled in both hydrological and ecological domains. Nowadays physical models are developed to estimate lake dynamics; however, computations needed for accurate estimation of lake surface temperature can get prohibitively expensive. We propose to aggregate simulations of lake temperature at a certain depth together with a range of meteorological features to probabilistically estimate lake surface temperature. Accordingly, we introduce a spatio-temporal neural network that combines Bayesian recurrent neural networks and Bayesian graph convolutional neural networks. This work demonstrates that the proposed graphical model can deliver homogeneously good performance covering the whole lake surface despite having sparse training data available. Quantitative results are compared with a state-of-the-art Bayesian deep learning method. Code for the developed architectural layers, as well as demo scripts, are available on https://renkulab.io/projects/das/bstnn.