This NSF CAREER project aims to develop a new class of energy-efficient artificial intelligence (AI) models that can infer the internal behavior of complex energy systems from limited sensor measurements. Many critical infrastructures, including power grids and thermal energy systems, contain regions that cannot be directly instrumented, yet safe and reliable operation requires knowledge of internal conditions such as temperature, voltage, and power balance. Existing AI methods are often computationally intensive, tailored to a single system or component, and challenging to deploy in power-constrained environments such as substations, industrial facilities, and remote monitoring stations. The project will bring transformative change by creating compact foundation models that learn the governing structure of dynamic energy systems and reconstruct unmeasured states in real-time while operating within strict energy budgets on facility-grade or fog-level compute. This will be achieved by integrating physics-aware learning methods, adaptive modeling strategies, and energy-efficient architectures. The intellectual merit of the project includes advancing the theoretical foundations for compact foundation models that generalize across heterogeneous dynamic energy systems and establishing principles for energy-efficient AI. The broader impacts of the project include improving the reliability and resilience of national energy infrastructure, enabling real-time monitoring of critical systems with limited sensing coverage, developing open-access educational curricula on AI for energy systems, and training the next generation of students at the intersection of artificial intelligence, energy engineering, and infrastructure resilience. The project addresses a fundamental challenge in modern energy infrastructure: many systems are governed by differential–algebraic equations, which couple dynamic physical processes with network constraints, as seen in electric power grids where d