NEDMP: Neural Enhanced Dynamic Message Passing

TL;DR

This paper introduces NEDMP, a hybrid neural network and message passing approach that improves the accuracy of predicting stochastic spreading processes on complex networks, especially those with many loops.

Contribution

The paper presents a novel hybrid model combining Graph Neural Networks with Dynamic Message Passing to enhance inference accuracy in complex networks.

Findings

NEDMP outperforms traditional DMP in various network structures.

The hybrid model generalizes better to unseen network conditions.

Training improves the accuracy of stochastic spreading predictions.

Abstract

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.