This research is on the quantitative study of information propagation formed by stochastic processes on large complex networks and its applications in threat detection. It includes both theoretical analysis and algorithmic developments of inference, optimization and control of these processes based on rigorous mathematical concepts and advanced deep learning techniques. This research is motivated and has extensive applications in many important real-world problems that involve vast amounts of random events on large complex networks, such as user interactions and news spreads on social networks (e.g., Twitter and Facebook), cyberattacks on the Internet, and epidemical spreads in a population consisting of diverse communities.

In the above problems, the fundamental element is a viral signal (e.g., a commercial advertisement, a piece of news, a tweet, or an infectious disease) originated from one or multiple source nodes propagates to their neighbors, then to the neighbors of these neighbors, and so on, over the network. This is a highly random process since it is unknown whether and when each individual node would be affected by its neighbor, and all the randomness at these individual nodes is further complicated with the heterogeneous structure of the large network. Therefore, it is important to answer these questions: (a) If there is an outbreak of a viral signal, how to accurately predict the number of nodes that will be affected in the future? (b) how to quickly identify the source of the outbreak? and (c) How to optimally deploy detectors at a limited amount of node (due to budget constraint) on the network such that random outbreaks in the future can be detected in shortest time?

In this project, the PI and his students made several major contributions to answer the above questions by developing rigorous mathematical analysis and efficient numerical algorithms. They developed a novel learning framework using neural mean-field (NMF) dynamics for inference and estimation to answer the question (a). This new framework leverages the Mori-Zwanzig formalism to obtain an exact evolution equation of the individual node infection probabilities (infection here refers to the adoption of the viral signal under consideration, such as a piece of news or an infectious virus). They also show that such phenomenon can be described by a delay differential equation where the memory integral can be approximated by time-convolution operators learned from data. Using only historical information propagation data, this new framework can simultaneously learn the structure of the network and predict the evolution of node infection probabilities for new outbreaks. To answer questions (b) and (c), they developed an optimal control approach to solve the source identification and outbreak detection problems, respectively. For source identification, the source nodes identities are considered as the control variable and the true source can be found as the optimal control which yields an information propagation closest to the observed one. For outbreak detection, the source outbreak probabilities are the control, and the optimal control is found by minimizing the expected first detection time. The results generated by this project provide deep understanding of the mathematical properties of information propagation in networks. These led to adaptive optimization and control strategies to harness the propagations processes and control the risks of new threat.

The research completed in this project also motivated a few works related to the proposed topic. In particular, the work on inverse optimal transport and mean-field dynamics explores new ways to understand and learn the mechanism of diffusion networks and its direct applications in threat detection. The work on solving Wasserstein Hamiltonian flows and approximating solution operators of evolution PDEs provide new approaches to generate samples and optimally control points in high-dimensional spaces.

This project supported two graduate students, including one female, to work on the research problems under the supervision of the PI. The female student has graduated with a PhD degree in mathematics in 2021 and became an R&D scientist to work on information propagations on networks at CareerBuilder Inc., an employment website company based in Chicago. The other student is conducting research in the same line and expected to earn his PhD degree in 2025.

Last Modified: 10/09/2023
Modified by: Xiaojing Ye