"Many of the most urgent decisions in modern power systems are fundamentally combinatorial, with feasible spaces that dwarf the number of atoms in the known universe. Traditional approaches based on integer and nonlinear programming often lock us into brittle formulations that may struggle to scale with the granularity, complexity, and uncertainty we will face in tomorrow’s grid. In this talk, I present a new algorithmic framework that bridges combinatorial and continuous optimization through physics-aware approximation. By integrating the structure of power flow equations with tools from high-dimensional statistics, spectral graph theory, and differentiable optimization, I show how core problems like topology inference and network reconfiguration can be solved efficiently. This work lays the foundation for a new generation of grid-aware AI systems: adaptive, interpretable, and capable of acting in real time under uncertainty."