# Positional Encoder Graph Neural Networks for Geographic Data

arXiv: https://arxiv.org/abs/2111.10144 · HTML: https://mlsanity.com/paper/2111.10144/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 41 references that are in the map.
- First posted on arXiv 19 Nov 2021.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Reinforcement Learning with Unsupervised Auxiliary Tasks](https://mlsanity.com/paper/1611.05397/) (2016)
- [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020)
- [Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets](https://mlsanity.com/paper/1406.7343/) (2014)
- [SE-KGE: A Location-Aware Knowledge Graph Embedding Model for Geographic Question Answering and Spatial Semantic Lifting](https://mlsanity.com/paper/2004.14171/) (2020)
- [Learning to Steer by Mimicking Features from Heterogeneous Auxiliary Networks](https://mlsanity.com/paper/1811.02759/) (2018)
- [SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Loss](https://mlsanity.com/paper/2109.15044/) (2021)
- [Residual Correlation in Graph Neural Network Regression](https://mlsanity.com/paper/2002.08274/) (2020)
- [Structured Variational Inference in Continuous Cox Process Models](https://mlsanity.com/paper/1906.03161/) (2019)
- [Auxiliary-task learning for geographic data with autoregressive embeddings](https://mlsanity.com/paper/2006.10461/) (2020)
- [MERL: Multi-Head Reinforcement Learning](https://mlsanity.com/paper/1909.11939/) (2019)
- [Augmenting correlation structures in spatial data using deep generative models](https://mlsanity.com/paper/1905.09796/) (2019)

## Built on by (most cited first, 20 of 20)

- [Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks](https://mlsanity.com/paper/2310.06743/) (2023)
- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [Neural Bayes Estimators for Irregular Spatial Data using Graph Neural Networks](https://mlsanity.com/paper/2310.02600/) (2023)
- [GeoMultiTaskNet: remote sensing unsupervised domain adaptation using geographical coordinates](https://mlsanity.com/paper/2304.07750/) (2023)
- [Non-Neighbors Also Matter to Kriging: A New Contrastive-Prototypical Learning](https://mlsanity.com/paper/2401.12681/) (2024)
- [Forecasting West Nile Virus with Graph Neural Networks: Harnessing Spatial Dependence in Irregularly Sampled Geospatial Data](https://mlsanity.com/paper/2212.11367/) (2022)
- [Spatioformer: A Geo-encoded Transformer for Large-Scale Plant Species Richness Prediction](https://mlsanity.com/paper/2410.19256/) (2024)
- [Graph Neural Networks with Precomputed Node Features](https://mlsanity.com/paper/2206.00637/) (2022)
- [Inductive biases in deep learning models for weather prediction](https://mlsanity.com/paper/2304.04664/) (2023)
- [Beyond Grid Data: Exploring Graph Neural Networks for Earth Observation](https://mlsanity.com/paper/2411.03223/) (2024)
- [Mobility-Embedded POIs: Learning What A Place Is and How It Is Used from Human Movement](https://mlsanity.com/paper/2601.21149/) (2026)
- [Positional Encoder Graph Quantile Neural Networks for Geographic Data](https://mlsanity.com/paper/2409.18865/) (2024)
- [Disentangled and Self-Explainable Node Representation Learning](https://mlsanity.com/paper/2410.21043/) (2024)
- [Urban Incident Prediction with Graph Neural Networks: Integrating Government Ratings and Crowdsourced Reports](https://mlsanity.com/paper/2506.08740/) (2025)
- [Spatial Transfer Learning with Simple MLP](https://mlsanity.com/paper/2405.03720/) (2024)
- [Introduction to Graph Neural Networks for Machine Learning Engineers](https://mlsanity.com/paper/2412.19419/) (2024)
- [On the use of Graphs for Satellite Image Time Series](https://mlsanity.com/paper/2505.16685/) (2025)
- [RelMap: Reliable Spatiotemporal Sensor Data Visualization via Imputative Spatial Interpolation](https://mlsanity.com/paper/2508.01240/) (2025)
- [Multi-Modal Spatio-Temporal Graph Neural Network with Mixture of Experts for Soil Organic Carbon Prediction](https://mlsanity.com/paper/2606.16580/) (2026)
- [SalAngaBhava: A Sinhala Market Dataset for Aspect-based Sentiment Analysis](https://mlsanity.com/paper/2607.05259/) (2026)

## Abstract (arXiv)

Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world settings, where the spatial structure is more complex and explicitly non-Euclidean (e.g., road networks). Here, we propose PE-GNN, a new framework that incorporates spatial context and correlation explicitly into the models. Building on recent advances in geospatial auxiliary task learning and semantic spatial embeddings, our proposed method (1) learns a context-aware vector encoding of the geographic coordinates and (2) predicts spatial autocorrelation in the data in parallel with the main task. On spatial interpolation and regression tasks, we show the effectiveness of our approach, improving performance over different state-of-the-art GNN approaches. We observe that our approach not only vastly improves over the GNN baselines, but can match Gaussian processes, the most commonly utilized method for spatial interpolation problems.