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

Jost Arndt, Utku Isil, Michael Detzel, Wojciech Samek, Jackie Ma

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 github.com/Jostarndt/Synthetic_Datasets_for_Temporal_Graphs.

Keywords: Graph, Spatio-Temporal, PDE, Epidemiology, SIR

Code: https://github.com/Jostarndt/Synthetic_Datasets_for_Temporal_Graphs

Assigned Action Editor: ~Yi_Liu12

Submission Number: 98