# Non-separable Spatio-temporal Graph Kernels via SPDEs

arXiv: https://arxiv.org/abs/2111.08524 · HTML: https://mlsanity.com/paper/2111.08524/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 57 references that are in the map.
- First posted on arXiv 16 Nov 2021.

## Builds on (most cited first, 14 of 14)

- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [Machine Learning on Graphs: A Model and Comprehensive Taxonomy](https://mlsanity.com/paper/2005.03675/) (2020)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Models](https://mlsanity.com/paper/2104.07788/) (2021)
- [Mat'ern Gaussian processes on Riemannian manifolds](https://mlsanity.com/paper/2006.10160/) (2020)
- [Mat'ern Gaussian Processes on Graphs](https://mlsanity.com/paper/2010.15538/) (2020)
- [Kernel-based Reconstruction of Graph Signals](https://mlsanity.com/paper/1605.07174/) (2016)
- [Chickenpox Cases in Hungary: a Benchmark Dataset for Spatiotemporal Signal Processing with Graph Neural Networks](https://mlsanity.com/paper/2102.08100/) (2021)
- [Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs](https://mlsanity.com/paper/1612.03615/) (2016)
- [The SPDE Approach to Mat'ern Fields: Graph Representations](https://mlsanity.com/paper/2004.08000/) (2020)

## Built on by (most cited first, 11 of 11)

- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [TSGM: A Flexible Framework for Generative Modeling of Synthetic Time Series](https://mlsanity.com/paper/2305.11567/) (2023)
- [Hodge-Compositional Edge Gaussian Processes](https://mlsanity.com/paper/2310.19450/) (2023)
- [Gaussian Processes on Cellular Complexes](https://mlsanity.com/paper/2311.01198/) (2023)
- [Topological Schr"odinger Bridge Matching](https://mlsanity.com/paper/2504.04799/) (2025)
- [Scalable Deep Gaussian Markov Random Fields for General Graphs](https://mlsanity.com/paper/2206.05032/) (2022)
- [GKNet: Graph Kalman Filtering and Model Inference via Model-based Deep Learning](https://mlsanity.com/paper/2506.22004/) (2025)
- [Stochastic PDE representation of random fields for large-scale Gaussian process regression and statistical finite element analysis](https://mlsanity.com/paper/2305.13879/) (2023)
- [Iterated INLA for State and Parameter Estimation in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2402.17036/) (2024)
- [Deep Gaussian Markov Random Fields for Graph-Structured Dynamical Systems](https://mlsanity.com/paper/2306.08445/) (2023)
- [Differentiable Lifting for Topological Neural Networks](https://mlsanity.com/paper/2608.01160/) (2026)

## Abstract (arXiv)

Gaussian processes (GPs) provide a principled and direct approach for inference and learning on graphs. However, the lack of justified graph kernels for spatio-temporal modelling has held back their use in graph problems. We leverage an explicit link between stochastic partial differential equations (SPDEs) and GPs on graphs, introduce a framework for deriving graph kernels via SPDEs, and derive non-separable spatio-temporal graph kernels that capture interaction across space and time. We formulate the graph kernels for the stochastic heat equation and wave equation. We show that by providing novel tools for spatio-temporal GP modelling on graphs, we outperform pre-existing graph kernels in real-world applications that feature diffusion, oscillation, and other complicated interactions.