In the past few years, China's space science and application has entered the stage of the space station with large-scale space science experiments. The number of flight missions related to space science grows rapidly, meanwhile, the corresponding payloads from various fields of science become more complicated. This paper breaks through the traditional management mode in which the payloads of space science are usually monitored by space-ground telemetry links and proposes an approach to utilize workflow net models to monitor the experimental processes of on-orbit payloads in real time. This approach can effectively offload the pressure of space-ground communication as well as the pressure of ground monitor stations. In this approach, spectral graph clustering is used in decomposing a workflow net model when the model is too huge to be processed in parallel on one single GPU (graphic processing units) device, and hybrid parallel computing algorithms are designed to carry out conformance checking operations based on observed events from on-orbit payloads in real time. The algorithms are implemented with a gatherapply-scatter model in CUDA 9.0 (compute unified device architecture) on Jetson TX2i module and are benchmarked. The performance of the algorithms is acceptable for practical use on orbit. INDEX TERMS Petri nets, parallel processing, parallel algorithms, partitioning algorithms, network theory (graphs).