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

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.