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Rapidly and accurately estimating the impact of design decisions on performance metrics is critical to both the manual and automated design of wireless sensor networks. Estimating system-level performance metrics such as lifetime, data loss rate, and network connectivity is particularly challenging because they depend on many factors, including network design and structure, hardware characteristics, communication protocols, and node reliability. This paper describes a new method for automatically building efficient and accurate predictive models for a wide range of system-level performance metrics. These models can be used to eliminate or reduce the need for simulation during design space exploration. We evaluate our method by building a model for the lifetime of networks containing up to 120 nodes, considering both fault processes and battery energy depletion. With our adaptive sampling technique, only 0.27% of the potential solutions are evaluated via simulation. Notably, one such automatically produced model outperforms the most advanced manually designed analytical model, reducing error by 13% while maintaining very low model evaluation overhead. We also propose a new, more general definition of system lifetime that accurately captures application requirements and decouples the specification of requirements from implementation decisions.