# Synthetic Datasets for Machine Learning on Spatio-Temporal Graphs using PDEs

arXiv: https://arxiv.org/abs/2502.04140 · HTML: https://mlsanity.com/paper/2502.04140/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 6 Feb 2025.

## Builds on (most cited first, 13 of 13)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Datasheets for Datasets](https://mlsanity.com/paper/1803.09010/) (2018)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [PDEBENCH: An Extensive Benchmark for Scientific Machine Learning](https://mlsanity.com/paper/2210.07182/) (2022)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Spatial-Temporal Graph ODE Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2106.12931/) (2021)
- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [PyTorch Geometric Temporal: Spatiotemporal Signal Processing with Neural Machine Learning Models](https://mlsanity.com/paper/2104.07788/) (2021)
- [ClimODE: Climate and Weather Forecasting with Physics-informed Neural ODEs](https://mlsanity.com/paper/2404.10024/) (2024)
- [Scalable Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2209.06520/) (2022)
- [TGB 2.0: A Benchmark for Learning on Temporal Knowledge Graphs and Heterogeneous Graphs](https://mlsanity.com/paper/2406.09639/) (2024)
- [Predicting COVID-19 pandemic by spatio-temporal graph neural networks: A New Zealand's study](https://mlsanity.com/paper/2305.07731/) (2023)

## Built on by (most cited first, 3 of 3)

- [INDEQS: Informed Neural controlled Differential EQuationS](https://mlsanity.com/paper/2606.19138/) (2026)
- [Learning Spatio-Temporal Foundation Models from Pure Synthetic Data](https://mlsanity.com/paper/2607.16251/) (2026)
- [TWIG: A Time-Causal Wavelet Operator for Autoregressive Forecasting on Irregular Graphs](https://mlsanity.com/paper/2609.22585/) (2026)

## Abstract (arXiv)

Many physical processes can be expressed through partial differential equations (PDEs). Real-world measurements of such processes are often collected at irregularly distributed points in space, which can be effectively represented as graphs; however, there are currently only a few existing datasets. Our work aims to make advancements in the field of PDE-modeling accessible to the temporal graph machine learning community, while addressing the data scarcity problem, by creating and utilizing datasets based on PDEs. In this work, we create and use synthetic datasets based on PDEs to support spatio-temporal graph modeling in machine learning for different applications. More precisely, we showcase three equations to model different types of disasters and hazards in the fields of epidemiology, atmospheric particles, and tsunami waves. Further, we show how such created datasets can be used by benchmarking several machine learning models on the epidemiological dataset. Additionally, we show how pre-training on this dataset can improve model performance on real-world epidemiological data. The presented methods enable others to create datasets and benchmarks customized to individual requirements. The source code for our methodology and the three created datasets can be found on https://github.com/github-usr-ano/Temporal_Graph_Data_PDEs.