CIF: III: Medium: MoDL+: Analytical Foundations for Deep Learning and Inference over Graphs

基于深度神经网络（dnn）的深度学习在解决图像分类、策略游戏、语音识别和医学图像分析等许多困难的现实问题方面表现出了卓越的能力，并有望彻底改变科学和工程，为整个社会带来广泛的利益。在深度神经网络成功的基础上，近年来出现了一系列专注于开发图神经网络（gnn）的研究活动，以解决图结构数据的重要问题。该奖项将解决深度GNN的基本理论问题，揭示其功能和局限性，并导致新的接地良好的GNN架构。在理论指导下，研究团队将开发深度图学习算法，以解决5G/NextG网络和电网中的实际问题。从这项研究中获得的见解将有利于不同的研究领域，并有助于管理和保护物理和数字基础设施。该奖项还将支持来自代表性不足的少数群体的本科生、研究生和博士后研究人员进行研究和教育活动，以及组织K-12外展项目。该奖项将推进理论指导和应用驱动的范式，以解决深度图学习中具有挑战性的基础研究问题，特别强调5G/NextG无线网络和电力（微）电网系统的应用。该奖项将通过建立深度图神经网络的连续极限，利用pde引导的深度图神经网络，并使用新颖的莫尔斯理论方法来理解gnn的泛化能力，将偏微分方程理论（pde）与深度图引导学习联系起来。它还将推进创新的敏感性正则化深度学习方法，并提供与标准深度神经网络相比的gnn表示能力的深入实证研究，揭开图在深度学习中的作用。该项目将有助于奠定必要的理论基础，指导理论指导的深度图学习算法的设计，以原则性的方式解决5G/NextG网络和电网中的实际问题。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Deep learning, based on deep neural networks (DNNs), has demonstrated superior power in solving many difficult real-world problems, such as image classification, strategy-game playing, speech recognition, and medical image analysis, and is poised to revolutionize science and engineering, bringing broad benefits to society at large. Building on the success of DNNs, recent years have seen a flurry of research activities focused on developing graph neural networks (GNNs) in order to tackle important problems on graph-structured data. This award will address fundamental theoretical problems with deep GNNs, shedding light on their power and limitations and leading to new well-grounded GNN architectures. Guided by theory, the team of researchers will develop deep graph-learning algorithms for solving practical problems in 5G/NextG networks and power grids. The insights gained from this research will benefit diverse research domains, and aid in managing and securing physical and digital infrastructure. The award will also support undergraduate students, graduate students, and postdoctoral researchers from underrepresented minority groups in research and educational activities as well as organization of K-12 outreach programs.This award will advance a theory-guided and application-driven paradigm for tackling challenging fundamental research questions in deep graph learning, with a particular emphasis on applications to 5G/NextG wireless networks and power (micro)grid systems. The award will make connections between the theory of partial differential equations (PDEs) and deep graph-guided learning by establishing continuum limits for deep graph neural networks, utilizing PDE-guided deep graph neural networks, and using a novel Morse theory approach to understand the generalization power of GNNs. It will also advance innovative sensitivity-regularized deep-learning approaches, and provide an in-depth empirical study of the representation power of GNNs compared to standard DNNs, demystifying the role of graphs in deep learning. The project will help lay the needed theoretical foundation to guide the design of theory-guided deep graph learning algorithms to solve practical problems in 5G/NextG networks and power grids in a principled manner.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.