CAREER: Network Resilience: Theories, Algorithms, and Applications

网络是相互依赖和动态组件的集合，这些组件构成了许多不同规模的关键系统，例如社会系统，食品供应链和我们大脑中的神经网络。然而，这些网络可能非常容易发生故障。一个小的扰动可能会使整个网络跨越一个临界点，并将其突然地、不可逆转地转移到一个不希望的状态，导致大规模的灾难性崩溃。例如，生态网络中的大规模破坏，电网中的级联故障，以及人类和动物网络中的社会习俗变化。弹性是网络系统在面对内部干扰和环境变化时调整其活动以保持基本功能并避免大的变化的能力。韧性损失的代价有时是无法承受的：截至2021年1月25日，COVID-19大流行病的爆发已导致全球超过200万人死亡，并继续导致越来越多的人死亡，越来越多的经济活动被关闭。该奖项旨在为复杂网络系统的弹性开发一个通用的理论和实践基础，用于不同领域的系统，如生物学，生态学，交通运输等。该奖项将设计快速准确的算法来预测系统的弹性，即使只有部分信息是已知的，提供方法来防止生态，生物或经济系统的崩溃，并指导技术系统的设计，以适应内部故障和环境变化。包括K-12在内的学生将通过多种方式学习网络和弹性，从研究机会到讲座和网络攻击游戏设计，防御者旨在创建一个具有有限资源的弹性网络，以抵御攻击者的战略破坏。该项目的技术目标分为三个方面。第一个推力创建了一个统一的理论，通过放松一些假设并认识到动态组件之间和相互作用系统之间的不同类型的相互作用，捕获了不同系统的普遍弹性行为。第二个推力设计快速和准确的算法，预测系统的弹性与不完整的信息的拓扑结构或动态。最后一个推力通过拓扑适应和基于状态的控制来描述其在操作轨迹和整个恢复过程中的准备情况，从而开发用于增强弹性的数学工具，从而实现可持续，可恢复和弹性的系统设计。这三个研究重点将通过对进展的全面评估来验证，包括计算机模拟和真实世界的实验。这项研究工作将为网络弹性奠定基础，使预测和控制具有足够的普遍性，将其应用于许多领域，其中对不利扰动的弹性是最重要的问题。这个CAREER项目实现了目前如何理解网络弹性的范式转变，产生变革性的想法，以提高网络系统的最佳构建和管理方式（人造系统）或自我组织和适应（自然系统）该奖项反映了NSF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。

Networks are collections of interdependent and dynamic components that make up many crucial systems of various scales, such as the social systems, food supply chains, and the neural networks in our brain. However, these networks can be highly vulnerable to failures. A small disturbance may bring the whole network across a tipping point and shift it abruptly and irreversibly to an undesired state, resulting in large catastrophic collapses. Examples are mass extinctions in ecological networks, cascading failures in power grids, and social convention changes in human and animal networks. Resilience is the ability of networked systems to adjust their activity to retain basic functionality and avoid large shifts in the face of internal disturbances and environmental changes. The cost of resilience loss sometimes is unaffordable: The outbreak of the COVID-19 pandemic has caused over two million deaths worldwide as of January 25, 2021, and continues to kill increasingly more people and shut down increasingly more economic activities. This award aims to develop a universal theoretical and practical foundation for the resilience of complex networked systems, for systems from different fields, such as biology, ecology, transportation, and many more. This award will design fast and accurate algorithms to predict a system's resilience even when only partial information is known, offering ways to prevent the collapse of ecological, biological, or economic systems and guide the design of technological systems resilient to both internal failures and environmental changes. Students, including K-12, will be engaged in learning about networks and resilience in multiple ways, ranging from research opportunities to lectures and a cyber-attack game design, where the defender aims to create a resilient network with limited recourses to withstand the attacker's strategic damages.The technical aims of the project are divided into three thrusts. The first thrust creates a unified theory that captures a universal resilience behavior of different systems by relaxing some assumptions and recognizing different types of interactions between the dynamical components and among interacting systems. The second thrust designs fast and accurate algorithms for predicting systems' resilience with incomplete information on the topology or dynamics. The last thrust develops mathematical tools for resilience enhancement through topology adaptation and state-based control to characterize their readiness during the operation trajectory and throughout the recovery process, enabling sustainable, recoverable, and resilient system design. These three research thrusts will be validated by a comprehensive evaluation of the progress, including computer simulations and real-world experiments. This research effort will produce the foundation for network resilience that allows prediction and controlling it with sufficient generality to apply it to many areas where resilience to adverse perturbations is of paramount concern. This CAREER project enables a paradigm shift in how network resilience is currently understood, yielding transformative ideas to enhance how networked systems can best be built and managed (human-made systems) or self-organized and adapted (natural systems) to enhance their resilience to internal failures and external environmental changes.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.