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Modern autonomous vehicle systems use complex perception and control components. These components can rapidly change during development of such systems, requiring constant re-testing. Unfortunately, high-fidelity simulations of these complex systems for evaluating vehicle safety are costly. The complexity also hinders the creation of less computationally intensive surrogate models. We present GAS, the first approach for creating surrogate models of complete (perception, control, and dynamics) autonomous vehicle systems containing complex perception and/or control components. GAS's two-stage approach first replaces complex perception components with a perception model. Then, GAS constructs a polynomial surrogate model of the complete vehicle system using Generalized Polynomial Chaos (GPC). We demonstrate the use of these surrogate models in two applications. First, we estimate the probability that the vehicle will enter an unsafe state over time. Second, we perform global sensitivity analysis of the vehicle system with respect to its state in a previous time step. GAS's approach also allows for reuse of the perception model when vehicle control and dynamics characteristics are altered during vehicle development, saving significant time. We consider five scenarios concerning crop management vehicles that must not crash into adjacent crops, self driving cars that must stay within their lane, and unmanned aircraft that must avoid collision. Each of the systems in these scenarios contain a complex perception or control component. Using GAS, we generate surrogate models for these systems, and evaluate the generated models in the applications described above. GAS's surrogate models provide an average speedup of $3.7\times$ for safe state probability estimation (minimum $2.1\times$) and $1.4\times$ for sensitivity analysis (minimum $1.3\times$), while still maintaining high accuracy.