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

信息扩散领域旨在了解信息（如新闻、疾病和危机）如何使用大数据集在社会系统中传播。这类研究对于理解人类动态，发现传染病或安全风险等早期威胁，并提出监测和控制其传播的有效措施至关重要。该项目将建立一个理论框架，以表征空间异构多通道通信的信息传播。本研究对资讯传播的理解提供了新的见解，将有助于推动研究领域的发展，以及国家的健康、繁荣和福利。该项目将提供各种教育活动，吸引追求STEM学科的K-12、本科生和研究生，特别是那些来自代表性不足、获得教育资源有限的群体的学生。这些学生将有机会接受数学和编程技能的全面培训，使他们成为下一代STEM专业人员的一部分。本项目旨在开发一种新的范例，利用度量图上基于边缘的微分方程来模拟大型时空数据集的信息扩散。该范式将利用信息扩散的两步理论来形成社会群体的度量图，然后使用数据驱动模型来描述信息沿着不同但可能相关的渠道扩散的特征。通过将信息扩散的物理原理与数学上可证明的数据驱动策略相结合，这种方法实现了既可解释又具有计算效率的建模。该研究还将作为连续统微分方程和离散微分方程之间的桥梁，促进分析和图论之间的结果转化。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.