Infrastructure systems are critical for society's resilience, government operation, and overall defense. Thereby, it is imperative to develop informative and computationally efficient analysis methods for infrastructure systems, which reveal system vulnerabilities and recoverability. To capture practical constraints in systems analyses, various layers of complexity play a role, including limited element capacities, restoration resources, and the presence of interdependence among systems. High‐fidelity modeling such as mixed integer programming and physics‐based modeling can often be computationally expensive, making time‐sensitive analyses challenging. Furthermore, the complexity of recovery solutions can reduce analysis transparency. An alternative, presented in this work, is a reduced‐order representation, dubbed a recovery operator, of a high‐fidelity time‐dependent recovery model of a system of interdependent networks. The form of the operator is assumed to be a time‐invariant linear dynamic model apt for infrastructure restoration. The recovery operator is generated by applying system identification techniques to numerous disaster and recovery scenarios. The proposed compact representation provides simple yet powerful information regarding systemic recovery dynamics, and enables generating fast suboptimal recovery policies in time‐critical applications.