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

2025-02-06

AI Summary

To address the scarcity of real-world physical-process data and the lack of PDE-driven synthetic datasets in spatiotemporal graph machine learning, this work introduces the first systematic PDE-based synthetic spatiotemporal graph dataset tailored for disaster modeling—covering epidemic spread, PM₂.₅ dispersion, and tsunami wave propagation. Methodologically, it integrates high-fidelity PDE numerical solvers, irregular spatial sampling for graph construction, standardized STGNN benchmarking, and a pretraining framework designed for cross-domain transfer. Key contributions include: (1) releasing three open-source datasets with full implementation code; (2) empirically validating generalization on real-world pandemic forecasting, where pretraining reduces downstream prediction error by 18.7%; and (3) establishing a scalable, modular coupling paradigm bridging physics-informed PDE modeling and data-driven spatiotemporal graph learning.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Creation of synthetic datasets for spatio-temporal graphs
• Addressing data scarcity in PDE-based machine learning
• Benchmarking models on synthetic epidemiological datasets

Innovation

• Synthetic datasets via PDEs
• Benchmarking on epidemiological data
• Pre-training enhances real-world performance