  Predicting stochastic spreading processes on complex networks is critical in
epidemic control, opinion propagation, and viral marketing. We focus on the
problem of inferring the time-dependent marginal probabilities of states for
each node which collectively quantifies the spreading results. Dynamic Message
Passing (DMP) has been developed as an efficient inference algorithm for
several spreading models, and it is asymptotically exact on locally tree-like
networks. However, DMP can struggle in diffusion networks with lots of local
loops. We address this limitation by using Graph Neural Networks (GNN) to learn
the dependency amongst messages implicitly. Specifically, we propose a hybrid
model in which the GNN module runs jointly with DMP equations. The GNN module
refines the aggregated messages in DMP iterations by learning from simulation
data. We demonstrate numerically that after training, our model's inference
accuracy substantially outperforms DMP in conditions of various network
structure and dynamics parameters. Moreover, compared to pure data-driven
models, the proposed hybrid model has a better generalization ability for
out-of-training cases, profiting from the explicitly utilized dynamics priors
in the hybrid model. A PyTorch implementation of our model is at
https://github.com/FeiGSSS/NEDMP.
