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

信息传播领域旨在了解信息（如新闻，疾病和危机）如何使用大型数据集在社会系统中传播。这种类型的研究对于理解人类动态，检测传染病或安全风险等早期威胁，并提出有效措施来监测和控制其传播至关重要。本计画将建立一个理论架构来描述空间异质多频道通讯的资讯传播特性。通过对信息传播的理解提供新的见解，这项研究将有助于推进研究领域，以及国家的健康，繁荣和福利。该项目将提供各种教育活动，以吸引K-12，本科生和研究生追求STEM学科，特别是那些来自代表性不足的群体，获得教育资源有限。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专业人士的一部分。该项目旨在开发一种新的范式，使用度量图上基于边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表征信息沿着沿着不同但可能相关的渠道的扩散。通过结合信息扩散的物理学和可证明的数据驱动策略，这种方法实现了可解释和计算效率的建模。该研究还将作为连续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换。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.