CAREER: Network Geometry for Analyzing Complex Dynamical Systems

职业：用于分析复杂动力系统的网络几何

• 批准号: 1749937
• 负责人: Romeil Sandhu
• 金额: $ 50万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-02-15 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1749937&HistoricalAwards=false
• 关键词: CAREER; Network; Geometry; Analyzing; Complex

In modern technological world, we increasingly depend upon the reliability, robustness, quality of service and timeliness of exceedingly large interconnected dynamical systems including those of power distribution, transportation, and communication. Over the past twenty years, we have witness a dramatic rise of information in which the analysis of such systems invariably present challenging big data complexity issues. For example, in transferring resources and information, a key requirement is the ability to adapt and reconfigure in response to structural and dynamic changes while avoiding disruption of service. To this end, we propose to develop fundamental relationships between network functionality and certain topological and geometric properties of the corresponding graph. The thematic vision for this program is based on the recently discovered fact that the geometric notion of curvature (or how objects deviate from being flat) is positively correlated with a systems functional robustness or its ability to adapt to dynamic changes. While the developed theory and tools will be applicable to a broad set of dynamical systems, we will focus on cancer biology and man-made distributed malware. The accomplishments of this research will be disseminated through raising engineering awareness of the proposed research through K-12 outreach, publications, tutorials in the form of open-source software, and developed workshops. Specifically, given the rise of data (network) science, there is an increasing demand for engineers especially in national security areas where U.S. Veterans may serve an integral role. As such, we will work to directly engage veterans to engage in aspects of the proposed research while also providing vet dependent mentoring for better university preparation.This said, to accomplish these goals, the proposed research program aims to study the intimate connections between discrete geometry, optimal mass transport, entropy, and control to formulate new approaches to quantify and predict dynamical properties of complex networks at varying scales. System properties include, but not limited to, robustness, heterogeneity, and congestion. As such, this research fills a need by investigating network functionality through the confluent study of geometry and control that relies upon several observations with far reaching physical (statistical mechanics) and information theoretic significance. Specifically, by placing a probability structure on a graph, the advantage over existing methods is that the space of probabilities on graphs has much nicer properties than the underlying discrete space alone. The associated probability measures can then be endowed with a Riemannian structure whereby geodesic (shortest distance) paths ensue and convexity properties of the entropy along paths reflect on geometric qualities of the graph. Given this foundation, we can then begin to develop powerful geometric network tools rooted in optimal and stochastic control. Altogether, as geometry and control of networks is still in its infancy, this program addresses the increasing need to develop such areas as a further tool to understanding complex systems.

在现代技术世界中，我们越来越依赖于包括配电、运输和通信在内的超大型互连动态系统的可靠性、鲁棒性、服务质量和及时性。在过去的二十年里，我们见证了信息的急剧增长，其中对此类系统的分析总是提出具有挑战性的大数据复杂性问题。 例如，在转移资源和信息方面，一个关键要求是有能力根据结构和动态变化进行调整和重新配置，同时避免服务中断。为此，我们建议开发网络功能和相应图形的某些拓扑和几何性质之间的基本关系。该计划的主题愿景是基于最近发现的事实，即曲率的几何概念（或物体如何偏离平面）与系统功能鲁棒性或适应动态变化的能力呈正相关。 虽然开发的理论和工具将适用于广泛的动态系统，但我们将专注于癌症生物学和人为分布式恶意软件。这项研究的成果将通过K-12外展，出版物，开源软件形式的教程和开发的研讨会来提高对拟议研究的工程意识。具体来说，随着数据（网络）科学的兴起，对工程师的需求越来越大，特别是在国家安全领域，美国退伍军人可能会发挥不可或缺的作用。 因此，我们将努力直接让退伍军人参与拟议研究的各个方面，同时也提供兽医依赖的指导，以更好地为大学做准备。也就是说，为了实现这些目标，拟议的研究计划旨在研究离散几何，最佳质量输运，熵，和控制制定新的方法来量化和预测复杂网络在不同尺度上的动力学特性。 系统属性包括但不限于鲁棒性、异构性和拥塞。因此，本研究通过对几何和控制的融合研究来调查网络功能，从而满足了一种需求，这种融合研究依赖于具有深远物理（统计力学）和信息理论意义的几种观察。具体来说，通过在图上放置概率结构，与现有方法相比，图上的概率空间具有比单独的底层离散空间更好的属性。相关的概率测量，然后可以赋予黎曼结构，从而测地线（最短距离）的路径和凸性性质的熵沿着路径反映的几何质量的图形。 有了这个基础，我们就可以开始开发基于最优和随机控制的强大几何网络工具。 总之，由于网络的几何和控制仍处于起步阶段，该计划解决了日益增长的需求，以发展这些领域作为进一步的工具来理解复杂系统。

项目成果

An Asynchronous Multi-Agent Actor-Critic Algorithm for Distributed Reinforcement Learning

• 发表时间: 2019
• 作者: Yixuan Lin;Yu-Juan Luo;K. Zhang;Zhuoran Yang;Zhaoran Wang;T. Başar;Romeil Sandhu;Ji Liu

Characterizing Distances of Networks on the Tensor Manifold

在张量流形上表征网络距离

• DOI: 10.1007/978-3-030-36687-2_79
• 发表时间: 2019
• 期刊: International Conference on Complex Networks and Their Applications
• 作者: Islam, Bipul;Liu, Ji;Sandhu, Romeil
• 通讯作者: Sandhu, Romeil

An Interactive Control Approach to 3D Shape Reconstruction

3D 形状重建的交互式控制方法

• DOI: 10.23919/acc45564.2020.9147728
• 发表时间: 2020
• 期刊: American Control Conference
• 作者: Islam, Bipul;Liu, Ji;Yezzi, Anthony;Sandhu, Romeil
• 通讯作者: Sandhu, Romeil

A feasibility study of radar-based shape and reflectivity reconstruction using variational methods

使用变分法基于雷达的形状和反射率重建的可行性研究

• DOI: 10.1088/1361-6420/abd299
• 发表时间: 2021
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: Bignardi, Samuel;Joseph Yezzi, Anthony;Yildirim, Alper;Barnes, Christopher F;Sandhu, Romeil
• 通讯作者: Sandhu, Romeil

Maxwells Demon: Controlling Entropy via Discrete Ricci Flow Over Networks

麦克斯韦妖：通过网络上的离散里奇流控制熵

• DOI: 10.1007/978-3-030-38965-9_9
• 发表时间: 2019
• 期刊: ArXiv
• 作者: Romeil Sandhu;Ji Liu
• 通讯作者: Ji Liu