CAREER: From Fragmentation to Integration: Advancing Cross-Graph Dynamics in Interdependent Networks

About This Grant

Complex systems—like transportation networks, power grids, and social platforms—often behave in surprisingly similar ways, even though they arise from very different fields. For example, the flow of traffic and the distribution of electricity both follow fundamental rules, such as conservation laws and flow dynamics. Despite these shared principles, research into these systems tends to remain siloed within specific disciplines, missing opportunities to leverage common insights. This project seeks to bridge these gaps by creating graph-based computational tools that uncover shared patterns in diverse system behaviors, enabling scientists to reuse knowledge across fields and reduce redundant efforts. Beyond studying individual systems, the research explores the dynamics of interconnected systems, where interactions between networks can produce unexpected and complex outcomes. For instance, controlling a disease outbreak might fail unless social awareness and behavioral changes are also addressed. Similarly, adding a new road to ease traffic could unintentionally make congestion worse. Another example involves electric vehicles (EVs): their simultaneous charging near busy highways can overload local power grids. By examining these interactions holistically, the project aims to develop tools that predict and prevent cascading failures, optimize resources, and strengthen system resilience. A strong emphasis is also placed on interdisciplinary education and outreach to prepare the next generation of researchers to tackle challenges in managing interconnected systems, benefiting society at large. This research develops a unified framework to analyze general graph dynamics and interconnected networks through three primary objectives. First, to develop a theoretical framework by deriving a generalized, interpretable framework for graph dynamics using advanced methods such as sparse symbolic dynamics to extract governing equations, probabilistic methods to model uncertainties in dynamic behaviors and uncover hidden patterns, and optimization techniques leveraging shared physical principles like conservation laws and flow dynamics. Second, to model interconnected systems by investigating how dynamics in one network, such as disease-spreading networks, affect others, like social awareness networks. To address the non-linear and often counterintuitive behaviors of interconnected systems, the project will create high-fidelity digital twin simulations that integrate domain-specific knowledge with probabilistic models. Established techniques like Lyapunov exponents will also be adapted for networked systems to enable early prediction and precise intervention. Third, to conduct community engagement and outreach by promoting awareness of the societal benefits of this research by introducing new interdisciplinary topics, connecting a variety of application domains, and ensuring the research outcomes have a broad and lasting impact across fields. Together, these efforts lay the groundwork for advancing our understanding and management of complex behaviors in interconnected systems, offering solutions to real-world challenges while fostering interdisciplinary collaboration. 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.