# Kriging Convolutional Networks

arXiv: https://arxiv.org/abs/2306.09463 · HTML: https://mlsanity.com/paper/2306.09463/

## Key facts

- Cited by 31 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 15 Jun 2023.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Hyperparameters and Tuning Strategies for Random Forest](https://mlsanity.com/paper/1804.03515/) (2018)

## Built on by (most cited first, 30 of 31)

- [Towards Unifying Diffusion Models for Probabilistic Spatio-Temporal Graph Learning](https://mlsanity.com/paper/2310.17360/) (2023)
- [KITS: Inductive Spatio-Temporal Kriging with Increment Training Strategy](https://mlsanity.com/paper/2311.02565/) (2023)
- [Prompt-Based Spatio-Temporal Graph Transfer Learning](https://mlsanity.com/paper/2405.12452/) (2024)
- [Graph-based Virtual Sensing from Sparse and Partial Multivariate Observations](https://mlsanity.com/paper/2402.12598/) (2024)
- [Spatial-temporal Forecasting for Regions without Observations](https://mlsanity.com/paper/2401.10518/) (2024)
- [Joint Estimation and Prediction of City-wide Delivery Demand: A Large Language Model Empowered Graph-based Learning Approach](https://mlsanity.com/paper/2408.17258/) (2024)
- [Non-Neighbors Also Matter to Kriging: A New Contrastive-Prototypical Learning](https://mlsanity.com/paper/2401.12681/) (2024)
- [SSIN: Self-Supervised Learning for Rainfall Spatial Interpolation](https://mlsanity.com/paper/2311.15530/) (2023)
- [STA-GANN: A Valid and Generalizable Spatio-Temporal Kriging Approach](https://mlsanity.com/paper/2508.16161/) (2025)
- [MoGERNN: An Inductive Traffic Predictor for Unobserved Locations](https://mlsanity.com/paper/2501.12281/) (2025)
- [Spatio-Temporal Graph Neural Network for Urban Spaces: Interpolating Citywide Traffic Volume](https://mlsanity.com/paper/2505.06292/) (2025)
- [DeepTopoNet: A Framework for Subglacial Topography Estimation on the Greenland Ice Sheets](https://mlsanity.com/paper/2505.23980/) (2025)
- [Inductive Spatial Temporal Prediction Under Data Drift with Informative Graph Neural Network](https://mlsanity.com/paper/2409.13253/) (2024)
- [Positional Encoder Graph Quantile Neural Networks for Geographic Data](https://mlsanity.com/paper/2409.18865/) (2024)
- [Urban Incident Prediction with Graph Neural Networks: Integrating Government Ratings and Crowdsourced Reports](https://mlsanity.com/paper/2506.08740/) (2025)
- [Improving Greenland Bed Topography Mapping with Uncertainty-Aware Graph Learning on Sparse Radar Data](https://mlsanity.com/paper/2509.08571/) (2025)
- [AnchorGK: Anchor-based Incremental and Stratified Graph Learning Framework for Inductive Spatio-Temporal Kriging](https://mlsanity.com/paper/2512.21569/) (2025)
- [Spatio-Temporal Partial Sensing Forecast for Long-term Traffic](https://mlsanity.com/paper/2408.02689/) (2024)
- [A Survey and Benchmarking of Spatial-Temporal Traffic Data Imputation Models](https://mlsanity.com/paper/2412.04733/) (2024)
- [Inductive Spatio-Temporal Kriging with Physics-Guided Increment Training Strategy for Air Quality Inference](https://mlsanity.com/paper/2503.09646/) (2025)
- [RelMap: Reliable Spatiotemporal Sensor Data Visualization via Imputative Spatial Interpolation](https://mlsanity.com/paper/2508.01240/) (2025)
- [Leakage-Free Evaluation and Distribution-Robust Spatio-Temporal Graph Learning for Inductive Kriging](https://mlsanity.com/paper/2509.23631/) (2025)
- [Spatio-temporal Multivariate Time Series Forecast with Chosen Variables](https://mlsanity.com/paper/2510.24027/) (2025)
- [Learning Subglacial Bed Topography from Sparse Radar with Physics-Guided Residuals](https://mlsanity.com/paper/2511.14473/) (2025)
- [A Hybrid Inductive-Transductive Network for Traffic Flow Imputation on Unsampled Locations](https://mlsanity.com/paper/2512.17984/) (2025)
- [A Geolocation-Aware Multimodal Approach for Ecological Prediction](https://mlsanity.com/paper/2601.08750/) (2026)
- [PlugSI: Plug-and-Play Test-Time Graph Adaptation for Spatial Interpolation](https://mlsanity.com/paper/2602.09824/) (2026)
- [Uniform Inductive Spatio-Temporal Kriging](https://mlsanity.com/paper/2603.05301/) (2026)
- [AdaKernel: Learning Adaptive Kernel Parameters for Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2606.01283/) (2026)
- [Zhinv: Real-time hub-height wind field reconstruction using only local sparse observations](https://mlsanity.com/paper/2607.25298/) (2026)

## Abstract (arXiv)

Spatial interpolation is a class of estimation problems where locations with known values are used to estimate values at other locations, with an emphasis on harnessing spatial locality and trends. Traditional Kriging methods have strong Gaussian assumptions, and as a result, often fail to capture complexities within the data. Inspired by the recent progress of graph neural networks, we introduce Kriging Convolutional Networks (KCN), a method of combining the advantages of Graph Convolutional Networks (GCN) and Kriging. Compared to standard GCNs, KCNs make direct use of neighboring observations when generating predictions. KCNs also contain the Kriging method as a specific configuration. We further improve the model's performance by adding attention. Empirically, we show that this model outperforms GCNs and Kriging in several applications. The implementation of KCN using PyTorch is publicized at the GitHub repository: https://github.com/tufts-ml/kcn-torch.