The interconnected, interdependent nature of wide-area modern power systems necessitates effective integration of increasingly larger-scale, heterogeneous, and spatially distributed physical assets with a multitude of ubiquitous cyber devices. Conventional admittance-matrix-based power grid topological models have been shown to lack analytical capabilities to effectively model ubiquitous flexibility, capacity, and prosumer profiles and enable granular and accurate controls of the ultra-high-dimensional distributed energy resources. This project aims to transcend the state-of-the-art, and will develop a data adaptive graph generation module, topological data analytical techniques with multiple filtrations, higher-order network models, and input layers for deep neural networks that take topological signatures and higher-order interactions for (dynamic) networks. The project will integrate ubiquitous, high-dimensional information structures on transmission nodes by taking properties of power systems as special directions and designing new perspectives at the intersection of algebraic topology, commutative algebra, and deep learning. Fundamentally, this project will directly benefit local and national interests as well as guide the modeling, operation, and control of wide-area power transmission networks with ultra-high-dimensional penetration of distributed energy resources and energy storage systems. The project framework will serve as a tool to enhance the reliability and resi