ATD: An Edge-Based PDE Paradigm and Inverse Analysis for Spatiotemporal Information Diffusion and Threat Detection

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The field of information diffusion aims to understand how information (such as news, diseases, and crises) spreads within social systems using large datasets. This type of research is crucial for comprehending human dynamics, detecting early-stage threats like infectious diseases or security risks, and proposing effective measures to monitor and control their spread. This project will establish a theoretical framework to characterize information propagation with spatially heterogeneous multiple-channel communications. By providing novel insights into the understanding of information propagation, this study will contribute to advancing the field of research, as well as the nation's health, prosperity, and welfare. The project will provide various educational activities to engage K-12, undergraduate, and graduate students pursuing STEM disciplines, particularly those from underrepresented groups with limited access to educational resources. These students will have the opportunity to receive comprehensive training in mathematical and programming skills, enabling them to become part of the next generation of STEM professionals. This project aims to develop a novel paradigm to model information diffusion for large spatiotemporal datasets using edge-based differential equations on metric graphs. The paradigm will take advantage of the two-step theory of information diffusion to form a metric graph of social groups, and then characterize information diffusion along distinct yet likely correlated channels using data-driven models. By combining the physics of information diffusion and mathematically-provable data-driven strategies, this approach achieves modeling that is both interpretable and computationally efficient. The research will also serve as a bridge between continuum differential equations and discrete differential equations, facilitating the translation of results between analysis and graph theory.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.