Partial Differential Equation Models for Large Networks

大型网络的偏微分方程模型

• 批准号: 0700559
• 负责人: Edwin Chong
• 金额: $ 27.68万
• 依托单位: Colorado State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-05-01 至 2012-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0700559&HistoricalAwards=false
• 关键词: Partial; Differential; Equation; Models; Large

This project involves continuum models of large networks using partial differential equations (PDEs). The premise is that some global characteristics of very large networks can be captured by continuum models that consider the behavior of the components on the scale of the aggregate rather than of the individual. The project involves an interdisciplinary team of an electrical engineer with notable expertise in networks, a statistician experienced in asymptotic analysis of stochastic processes and statistical modeling, and an applied mathematician with expertise in modeling and numerical simulation involving nonlinear PDEs. Successful completion of this project will result in the ability to analyze the performance of large networks with a computational effort that is not possible using conventional Monte Carlo simulation.Intellectual Merit: This project contains significant intellectual merit for engineering as well as mathematics. From the mathematical point of view, both creating mathematical descriptions of the continuum behavior of large networks and analyzing the resulting differential equations pose real challenges. From the engineering point of view, continuum modeling will require a detailed understanding of network behavior on the smallest scale of a few nodes and identification of global characteristics that can be modeled.Broader Impacts:This project will also have both an immediate positive impact on the current students of the principal investigators and on training future students. The students working on problems originating in the modeling of networks will have an invaluable practical component to their theses. This will significantly widen their career opportunities in industry and interdisciplinary settings. This in turn will provide a powerful recruiting tool for Colorado State University in the future.

该项目涉及使用偏微分方程（PDE）的大型网络的连续模型。其前提是，大型网络的某些全局特征可以通过连续体模型来捕捉，该模型考虑的是集合规模而不是个体规模上的组件行为。 该项目涉及一个跨学科的团队，其中包括一名在网络方面具有显着专业知识的电气工程师，一名在随机过程和统计建模的渐近分析方面经验丰富的统计学家，以及一名在涉及非线性偏微分方程的建模和数值模拟方面具有专业知识的应用数学家。 该项目的成功完成将使您能够分析大型网络的性能，而传统的Monte Carlo模拟无法实现这一点。智力优势：该项目在工程和数学方面都具有重要的智力优势。 从数学的角度来看，创建大型网络连续行为的数学描述和分析由此产生的微分方程都构成了真实的挑战。从工程学的角度来看，连续体建模需要在最小的几个节点上详细了解网络行为，并识别可以建模的全局特征。更广泛的影响：该项目也将对主要研究者的当前学生和未来学生的培训产生直接的积极影响。研究网络建模问题的学生将对他们的论文有非常宝贵的实用价值。这将大大拓宽他们在行业和跨学科环境中的职业机会。这反过来又将为科罗拉多州立大学在未来提供一个强大的招聘工具。