FastGEMF: Scalable High-Speed Simulation of Stochastic Spreading Processes over Complex Multilayer Networks

TL;DR

This study introduces FastGEMF, a novel, scalable simulation framework for exact, high-speed modeling of Markov chain processes on complex multi-layer networks, and introduces an event-driven algorithm with cautious update strategies, supporting diverse multi-compartment spreading processes.

Abstract

Predicting the spread of processes across complex multi-layered networks has long challenged researchers due to the intricate interplay between network structure and propagation dynamics. Each layer of these networks possesses unique characteristics, further complicating analysis. To authors' knowledge, a comprehensive framework capable of simulating various spreading processes across different layers, particularly in networks with millions of nodes and connections, has been notably absent. This study introduces a novel framework that efficiently predicts Markov Chain processes over large-scale networks, while significantly reducing time and space complexity. This approach enables exact simulation of spreading processes across extensive real-world multi-layer networks, accounting for diverse influencers on each layer. FastGEMF provides a baseline framework for exact simulating stochastic spread processes, facilitating comparative analysis of models across diverse domains, from epidemiology to social media dynamics.

Figures (11)

• Figure 1: Overall Structure complex multiplayer networks along with multi-agent transition graph that each node undergoes to. In the contact graphs, the solid line, arrows and width of lines denotes undirected, directed and weighted properties of the graphs, respectively. For the transition graphs solid and dashed arrows show edge-based and node-based transitions, respectively. Dotted grey arrows specify the state which induces the transition. $\beta^c_{l_i,a\rightarrow b}$ denotes the rate for transition from state $a$ to $b$ under interaction with neighbors which are in state $c$ at layer $l_i$. $\delta_{b\rightarrow a}$ is for the rate of transtition from state $b$ to $a$, which is independent of its interaction with other individuals
• Figure 2: Diagram of conventional stochastic simulator algorithm modified for GEMF
• Figure 3: edge -based transition rate matrix
• Figure 4: proposed optimized stochastic simulator algorithm
• Figure 5: An example of cautious update approach, demonstrates a state transition from Infected (I) to Recovered (R) in SEIR model. The highlighted yellow color represents the only nodes undergoing update at this timestep. Below the graph, the transition effect matrix specifies the states affected by each transition