# Spatial Aggregation and Temporal Convolution Networks for Real-time Kriging

arXiv: https://arxiv.org/abs/2109.12144 · HTML: https://mlsanity.com/paper/2109.12144/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 37 references that are in the map.
- First posted on arXiv 24 Sep 2021.

## Builds on (most cited first, 25 of 25)

- [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)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Convolutional Sequence to Sequence Learning](https://mlsanity.com/paper/1705.03122/) (2017)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [What graph neural networks cannot learn: depth vs width](https://mlsanity.com/paper/1907.03199/) (2019)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Neural Execution of Graph Algorithms](https://mlsanity.com/paper/1910.10593/) (2019)
- [Inductive Graph Neural Networks for Spatiotemporal Kriging](https://mlsanity.com/paper/2006.07527/) (2020)
- [Inductive Matrix Completion Based on Graph Neural Networks](https://mlsanity.com/paper/1904.12058/) (2019)
- [Missing Data Imputation with Adversarially-trained Graph Convolutional Networks](https://mlsanity.com/paper/1905.01907/) (2019)
- [Understanding the Representation Power of Graph Neural Networks in Learning Graph Topology](https://mlsanity.com/paper/1907.05008/) (2019)
- [Processing of missing data by neural networks](https://mlsanity.com/paper/1805.07405/) (2018)
- [Stacked Bidirectional and Unidirectional LSTM Recurrent Neural Network for Forecasting Network-wide Traffic State with Missing Values](https://mlsanity.com/paper/2005.11627/) (2020)
- [Hybrid Spatio-Temporal Graph Convolutional Network: Improving Traffic Prediction with Navigation Data](https://mlsanity.com/paper/2006.12715/) (2020)
- [Graph Markov Network for Traffic Forecasting with Missing Data](https://mlsanity.com/paper/1912.05457/) (2019)

## Built on by (most cited first, 27 of 27)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Uncertainty Quantification of Sparse Travel Demand Prediction with Spatial-Temporal Graph Neural Networks](https://mlsanity.com/paper/2208.05908/) (2022)
- [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)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Prompt-Based Spatio-Temporal Graph Transfer Learning](https://mlsanity.com/paper/2405.12452/) (2024)
- [Towards better traffic volume estimation: Jointly addressing the underdetermination and nonequilibrium problems with correlation-adaptive GNNs](https://mlsanity.com/paper/2303.05660/) (2023)
- [Deep hybrid model with satellite imagery: how to combine demand modeling and computer vision for behavior analysis?](https://mlsanity.com/paper/2303.04204/) (2023)
- [ST-GIN: An Uncertainty Quantification Approach in Traffic Data Imputation with Spatio-temporal Graph Attention and Bidirectional Recurrent United Neural Networks](https://mlsanity.com/paper/2305.06480/) (2023)
- [Graph-based Virtual Sensing from Sparse and Partial Multivariate Observations](https://mlsanity.com/paper/2402.12598/) (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)
- [Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approach](https://mlsanity.com/paper/2503.15845/) (2025)
- [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)
- [Time Series Supplier Allocation via Deep Black-Litterman Model](https://mlsanity.com/paper/2401.17350/) (2024)
- [AnchorGK: Anchor-based Incremental and Stratified Graph Learning Framework for Inductive Spatio-Temporal Kriging](https://mlsanity.com/paper/2512.21569/) (2025)
- [Advancing Transportation Mode Share Analysis with Built Environment: Deep Hybrid Models with Urban Road Network](https://mlsanity.com/paper/2405.14079/) (2024)
- [From Incomplete Coarse-Grained to Complete Fine-Grained: A Two-Stage Framework for Spatiotemporal Data Reconstruction](https://mlsanity.com/paper/2410.05323/) (2024)
- [A Survey and Benchmarking of Spatial-Temporal Traffic Data Imputation Models](https://mlsanity.com/paper/2412.04733/) (2024)
- [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)
- [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)
- [Bridge: Retrieval-Augmented Spatiotemporal Modeling for Urban Delivery Demand](https://mlsanity.com/paper/2605.19172/) (2026)
- [AdaKernel: Learning Adaptive Kernel Parameters for Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2606.01283/) (2026)

## Abstract (arXiv)

Spatiotemporal kriging is an important application in spatiotemporal data analysis, aiming to recover/interpolate signals for unsampled/unobserved locations based on observed signals. The principle challenge for spatiotemporal kriging is how to effectively model and leverage the spatiotemporal dependencies within the data. Recently, graph neural networks (GNNs) have shown great promise for spatiotemporal kriging tasks. However, standard GNNs often require a carefully designed adjacency matrix and specific aggregation functions, which are inflexible for general applications/problems. To address this issue, we present SATCN -- Spatial Aggregation and Temporal Convolution Networks -- a universal and flexible framework to perform spatiotemporal kriging for various spatiotemporal datasets without the need for model specification. Specifically, we propose a novel spatial aggregation network (SAN) inspired by Principal Neighborhood Aggregation, which uses multiple aggregation functions to help one node gather diverse information from its neighbors. To exclude information from unsampled nodes, a masking strategy that prevents the unsampled sensors from sending messages to their neighborhood is introduced to SAN. We capture temporal dependencies by the temporal convolutional networks, which allows our model to cope with data of diverse sizes. To make SATCN generalizable to unseen nodes and even unseen graph structures, we employ an inductive strategy to train SATCN. We conduct extensive experiments on three real-world spatiotemporal datasets, including traffic speed and climate recordings. Our results demonstrate the superiority of SATCN over traditional and GNN-based kriging models.