基于簇更新的网络系统随机动力学稀有事件采样方法
Rare-event sampling for stochastic dynamics in network systems using cluster updates
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中文总结 AI 辅助
该研究针对复杂网络稀有宏观事件采样难题，提出条件路径蒙特卡洛（CPMC）方法，在亲属关系网络SIS动力学中验证了其用于稀有大规模疫情暴发风险分析的潜力。
中文摘要 AI 辅助
理解复杂网络中的随机演化是物理、生物、工程、社会科学及金融等领域的核心挑战。通信网络的级联故障、大规模疫情暴发、社会观点快速转变等最具影响的宏观事件，往往由罕见的局域随机过程汇聚而成，且需突破特定瓶颈。Gillespie法等标准正向时间模拟算法因灾难性拒绝率，对这类现象的研究效率低下。分裂法、过渡路径采样等先进稀有事件技术应用于复杂异质网络时，常受动力学陷阱、路径退化、谱系关联或临界慢化问题困扰。我们借鉴平衡凝聚态物理中的圈算法，提出一种名为条件路径蒙特卡洛（CPMC）的新技术以克服该挑战。CPMC通过对时空簇执行非局域更新且无拒绝操作，生成严格满足目标宏观边界条件（如大规模网络故障发生）的轨迹马尔可夫链。我们通过对亲属关系网络上SIS动力学中罕见大规模疫情暴发开展简单风险因素分析，验证了该框架的潜力。
英文摘要
Understanding the stochastic evolution in complex networks is a central challenge across physics, biology, engineering, social science, and finance. The most consequential macroscopic events, like cascading failures in communication networks, widespread epidemic outbreaks, and rapid shifts in societal opinions, often emerge from a confluence of rare, localized stochastic processes and need to pass certain bottlenecks. Standard forward-time simulation algorithms like the Gillespie method are inefficient for the investigation of such phenomena due to catastrophic rejection rates. Advanced rare-event techniques like splitting methods and transition-path sampling often suffer from kinetic trapping, path degeneracy, genealogical correlations, or critical slowing down when applied to complex heterogeneous networks. We propose to overcome this challenge by establishing a novel technique called conditional-path Monte Carlo (CPMC), inspired by loop algorithms from equilibrium condensed-matter physics. By employing non-local updates on spacetime clusters without rejections, CPMC generates a Markov chain of trajectories that all strictly respect the targeted macroscopic boundary conditions like the occurrence of a massive network failure. We demonstrate the framework's potential by performing a simple risk factor analysis for rare large-scale epidemic outbreaks in SIS dynamics on kinship networks.
发表机构
- Duke University（杜克大学）
- University of Maryland, College Park（马里兰大学帕克分校）
- National Quantum Laboratory, University of Maryland, College Park（马里兰大学帕克分校国家量子实验室）
机构由 AI 辅助整理，请以论文原文为准。
