CIF: Small: Graph Structure Discovery of Networked Dynamical Systems

CIF：小：网络动力系统的图结构发现

• 批准号: 2327905
• 负责人: Jose Moura
• 金额: $ 60万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-05-15 至 2027-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2327905&HistoricalAwards=false
• 关键词: CIF; Small; Graph; Structure; Discovery

Many systems arising in important application domains are complicated interconnections of many components. These systems are commonly referred to as networks of agents, and the observed behavior of one agent depends on the behavior of the many other agents, observed or not, in the network. Examples of such systems include not only biological or brain networks, gene regulatory networks, and pandemics spreading over populations, but also large critical physical infrastructures like the electric-power grid. For example, with brain networks, it is important to infer from electroencephalography (EEG) recordings which neural networks form in order to better understand the neural activity and thereby provide a means to better diagnose a number of brain injuries or diseases. The project will develop methods to determine the unknown and hidden connections among the parts (agents) of a system, often a necessary first step to understand the global behavior of the overall system. In complex systems, like EEG arrays, the number of measuring probes is small compared to the much larger number of unobserved but interconnected components. The methods to be developed will reliably infer the connections among the agents that are observed or measured, even in the presence of many latent, unobserved parts of the system. These methods will have broad applicability across many different practical domains. The project will support at least two PhD students and will engage a broad, diverse group of Master and undergraduate students at Carnegie Mellon University.The problem of uncovering the interconnections among parts of a network dynamical system (NDS), known as structure identification, has received significant attention in the research community. But the success of current approaches is limited by various factors. For example, some methods require total observability, i.e., observing the activity of all the interconnected agents in the NDS. However, this is often unrealistic due to the large scale of many NDS or because it is impractical or impossible to track the behavior of all the agents (e.g., neuron activity in a brain network). A second limitation relates to assuming that the samples of the observed behavior of different agents are independent and identically distributed. Again, such an assumption is very limiting since, in many scenarios, there are significant dependencies in the observed behaviors across time and across agents. The research pursued will consider the total- and partial-observability contexts with possibly temporal and spatial (across-agent) dependencies. For every pair of agents, the approach engineers a high-dimensional feature vector that is then input to a classifier that clusters the features, with a high-dimensional manifold separating the connected pairs from the unconnected pairs. The work will provide theoretical guarantees regarding the separability of the features as well as the stability of the separating manifold to various regimens of connectivity, observability, and disturbances affecting the behaviors of the agents. The generalizability of the approach will also be studied, e.g., training with a lower-dimensional NDS and then inferring the structure of much larger-scale systems. The project will test the methods with synthetic and real-word datasets drawn from a number of practically relevant applications.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.

在重要的应用领域中产生的许多系统都是许多组件的复杂互连。这些系统通常被称为代理网络，并且一种代理的观察到的行为取决于网络中许多其他代理的行为，无论是否观察到。此类系统的例子不仅包括生物或大脑网络，基因调节网络以及传播在种群上的大流行，还包括大型关键的物理基础设施（例如电力网格）。例如，通过脑网络，重要的是从脑电图（EEG）记录中推断出神经网络形成的记录，以便更好地了解神经活动，从而提供了一种更好地诊断许多脑损伤或疾病的方法。该项目将开发方法来确定系统的零件（代理）之间未知和隐藏的连接，通常是了解整体系统全球行为的必要第一步。在复杂的系统（例如脑电图阵列）中，与数量更大的未观察到相互联系的组件相比，测量探针的数量很少。即使在系统的许多潜在，未观察到的部分，要开发的方法将可靠地推断出观察或测量的代理之间的连接。这些方法将在许多不同的实践领域具有广泛的适用性。 该项目将至少支持两名博士学位学生，并将在卡内基·梅隆大学（Carnegie Mellon University）参与一群广泛的硕士和本科生。发现网络动力系统（NDS）部分（称为结构识别）之间的互连问题在研究界受到了极大的关注。但是当前方法的成功受到各种因素的限制。例如，某些方法需要总可观察性，即观察NDS中所有互连剂的活性。但是，由于许多ND的规模很大，或者是由于不切实际或不可能跟踪所有药物的行为（例如，在大脑网络中的神经元活动）是不切实际的，这通常是不现实的。第二个限制与假设不同试剂的观察到行为的样本是独立的且分布相同的。同样，这样的假设是非常有限的，因为在许多情况下，跨时间和跨代理的观察到的行为都有显着的依赖性。所进行的研究将考虑可能具有时间和空间（跨机构）依赖性的全部和部分观察性环境。对于每对代理，该方法工程师都有一个高维特征向量，然后将其输入到分类器的分类器中，该分类器将特征分类，具有高维的歧管将连接的对与未连接的对分开。这项工作将提供有关特征的可分离性以及分离歧管与各种连通性，可观察性和影响代理行为行为的干扰的稳定性的理论保证。该方法的普遍性还将进行研究，例如，使用较低维的NDS进行训练，然后推断出大量大规模系统的结构。该项目将通过从许多实际相关的应用程序中绘制的合成和现实词数据集测试方法。该奖项反映了NSF的法定任务，并使用基金会的知识分子优点和更广泛的影响审查标准，认为值得通过评估来获得支持。