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

Abstract

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