Data-Driven Learning and Geometric Embedding for Reduction and Control of Complex Heterogeneous Networks

用于减少和控制复杂异构网络的数据驱动学习和几何嵌入

基本信息

批准号：
1763070
负责人：
Jr-Shin Li
金额：
$ 32.5万
依托单位：
Washington University
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：
2018-08-15 至 2022-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1763070&HistoricalAwards=false
关键词：
Data Driven Learning Geometric Embedding

项目摘要

Complex systems in which multiple agents (components) affect each other dynamically are prevalent in nature and human society in different scales, such as neurons in the brain, bees in a hive, and human beings in a social network. Undesirable behavior of such systems, in the form of disease, economic collapse, rumor spreading, and social unrest, has generated considerable interest in understanding the dynamic structures of such complex networks and devising ways to control them. Despite the abundance of data, ease of access, and advances in data science, obtaining reliable models of such networks remains a very challenging problem. The scale of these emerging complex systems also poses a great difficulty. These obstacles also form a bottleneck for analyzing and engineering the dynamic structures (e.g., synchrony and clustering) and for controlling the collective behavior in such complex networks. This project will develop a unified data-driven framework to investigate fundamental questions regarding how to extract dynamics of a large-scale complex system or network from its simulation or measurement data, and how to control this system if the dynamics reconstruction is successful and reliable. The project will also support new initiatives to promote interdisciplinary education for students from traditionally underserved populations in local high schools in the city of St. Louis, MO, through the creation of summer research opportunities.By bridging systems and control theory with concepts and methods from algebraic geometry, time-series analysis, and machine learning, a unified data-driven framework will be established. Specifically, a novel approach based on spectral decomposition will be developed to extract the dynamics of a complex system and decode the topology of a complex network using its time-series data. The properties of the reconstructed network, e.g., connectivity and the coupling strength of nodes, will then be utilized to synthesize a dynamically-proximate reduced network that is tractable for control-theoretic analysis and design. Furthermore, novel topological and geometrical approaches will be derived to construct local and global embedding of high-dimensional data to low-dimensional manifolds, which will reveal hidden topological structures in large data sets and characterize transitions of flow of the underlying dynamical system. In collaboration with researchers in biology and chemistry, the network inference, dimensionality reduction, and control techniques will be applied to a diverse set of complex systems from cells to societies, for example, for decoding functional connectivity in cellular networks and analyzing social synchronization in groups of animals.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.

多个主体（组件）动态地相互影响的复杂系统在不同尺度的自然和人类社会中普遍存在，例如大脑中的神经元、蜂巢中的蜜蜂以及社交网络中的人类。此类系统以疾病、经济崩溃、谣言传播和社会动荡等形式出现的不良行为，引起了人们对理解此类复杂网络的动态结构并设计控制它们的方法的极大兴趣。尽管数据丰富、易于访问且数据科学不断进步，但获得此类网络的可靠模型仍然是一个非常具有挑战性的问题。这些新兴复杂系统的规模也带来了很大的困难。这些障碍也形成了分析和设计动态结构（例如同步和集群）以及控制此类复杂网络中集体行为的瓶颈。该项目将开发一个统一的数据驱动框架，以研究如何从仿真或测量数据中提取大规模复杂系统或网络的动力学，以及如何控制该系统（如果动力学重建成功且可靠）的基本问题。该项目还将通过创造暑期研究机会，支持新举措，以促进密苏里州圣路易斯市当地高中传统上服务不足群体学生的跨学科教育。代数几何、时间序列分析和机器学习，将建立统一的数据驱动框架。具体来说，将开发一种基于谱分解的新方法来提取复杂系统的动态并使用其时间序列数据解码复杂网络的拓扑。然后，重建网络的属性（例如节点的连接性和耦合强度）将用于合成易于控制理论分析和设计的动态近似简化网络。此外，将推导出新的拓扑和几何方法来构建高维数据到低维流形的局部和全局嵌入，这将揭示大数据集中隐藏的拓扑结构并表征底层动力系统的流动转变。与生物学和化学研究人员合作，网络推理、降维和控制技术将应用于从细胞到社会的各种复杂系统，例如，解码细胞网络中的功能连接和分析群体中的社会同步该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。