This paper presents a method to generate and utilize synthetic datasets based on partial differential equations (PDEs) to support spatiotemporal graph machine learning modeling research. We generate datasets using three PDEs to model various disaster and hazard phenomena such as epidemics, atmospheric particles, and tsunamis, and benchmark the performance of several machine learning models using the epidemic datasets. We also show that pre-training with synthetic datasets improves model performance on real epidemic data. The source codes of the proposed methodology and the three generated datasets are available on GitHub.